from __future__ import print_function, division
from itertools import starmap, product
import numpy as np
import pandas as pd
import pickle
def obtainable(coins):
combos = set(coins)
combos.update(map(sum, product(coins, coins)))
return combos
coins = [1, 2, 4]
obtainable(coins)
{1, 2, 3, 4, 5, 6, 8}
values = set(range(1, 11))
def unobtainable(coins):
return values - obtainable(coins)
unobtainable(coins)
{7, 9, 10}
def possible_new_coin(coins, value):
if value % 2 == 0:
yield value // 2
for coin in coins:
if value > coin:
yield value - coin
set(possible_new_coin(coins, 7))
{3, 5, 6}
set(possible_new_coin(coins, 9))
{5, 7, 8}
set(possible_new_coin(coins, 10))
{5, 6, 8, 9}
class Combinator:
def __init__(self, n):
self.values = set(range(1, n+1))
self.combos = set()
self.considered = set()
self.smallest = 9999
def unobtainable(self, coins):
return self.values - obtainable(coins)
def add_combo(self, coins):
n = len(coins)
if n < self.smallest:
self.combos = set()
self.smallest = n
print('new smallest = ', n)
self.combos.add(coins)
def consider(self, coins):
if len(coins) > self.smallest:
return
if coins in self.considered:
return
if len(coins) < 10:
self.considered.add(coins)
bad_values = self.unobtainable(coins)
if len(bad_values) == 0:
self.add_combo(coins)
return
for value in sorted(bad_values):
for new_coin in sorted(possible_new_coin(coins, value)):
self.consider(coins | {new_coin})
def winners(self):
for combo in self.combos:
if len(combo) == self.smallest:
yield combo
cmap = {}
cmap[10] = Combinator(10)
cmap[10].values
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
cmap[10].consider(frozenset())
new smallest = 5 new smallest = 4
cmap[10].smallest
4
for winner in cmap[10].winners():
print(sorted(winner))
[1, 3, 5, 6] [1, 2, 3, 7] [1, 2, 5, 8] [1, 3, 4, 9] [1, 3, 4, 5] [1, 2, 5, 7] [1, 2, 4, 5] [1, 3, 4, 6]
cmap[15] = Combinator(15)
cmap[15].values
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
for winner in cmap[10].winners():
cmap[15].consider(winner)
new smallest = 6 new smallest = 5
cmap[15].consider(frozenset())
for winner in cmap[15].winners():
print(sorted(winner))
[1, 3, 5, 7, 8] [1, 3, 4, 9, 11]
def upgrade(cmap, source, dest):
cmap[dest] = Combinator(dest)
for winner in cmap[source].winners():
cmap[dest].consider(winner)
if cmap[dest].smallest > cmap[source].smallest:
print('considering 1')
cmap[dest].consider(frozenset((1, 2, 5)))
print('considering 2')
cmap[dest].consider(frozenset((1, 2, 4)))
print('considering 3')
cmap[dest].consider(frozenset((1, 3, 4)))
print('considering 4')
cmap[dest].consider(frozenset((1, 3, 5)))
cmap[dest].considered = set()
for winner in cmap[dest].winners():
print(sorted(winner))
cmap = {}
cmap[10] = Combinator(10)
cmap[10].consider(frozenset())
new smallest = 5 new smallest = 4
for n in range(10, 20):
print(n+1)
%time upgrade(cmap, n, n+1)
11 new smallest = 4 [1, 3, 5, 6] CPU times: user 0 ns, sys: 0 ns, total: 0 ns Wall time: 301 µs 12 new smallest = 4 [1, 3, 5, 6] CPU times: user 0 ns, sys: 0 ns, total: 0 ns Wall time: 96.3 µs 13 new smallest = 5 considering 1 considering 2 considering 3 considering 4 [1, 3, 5, 7, 8] [1, 3, 5, 6, 8] [1, 2, 5, 6, 8] [1, 2, 5, 8, 11] [1, 3, 5, 6, 10] [1, 2, 4, 6, 7] [1, 2, 4, 6, 9] [1, 2, 3, 4, 9] [1, 3, 4, 5, 8] [1, 3, 5, 6, 7] [1, 2, 5, 8, 10] [1, 3, 4, 9, 10] [1, 3, 4, 8, 9] [1, 3, 4, 9, 11] [1, 2, 4, 5, 11] [1, 3, 4, 6, 7] [1, 3, 4, 8, 10] [1, 3, 4, 6, 10] [1, 2, 5, 6, 7] [1, 3, 4, 7, 9] [1, 3, 5, 6, 12] [1, 2, 5, 7, 11] CPU times: user 8 ms, sys: 0 ns, total: 8 ms Wall time: 5.88 ms 14 new smallest = 5 [1, 2, 5, 7, 11] [1, 3, 5, 7, 8] [1, 3, 4, 9, 11] [1, 3, 5, 6, 8] [1, 3, 4, 6, 7] [1, 2, 5, 6, 8] [1, 3, 4, 8, 10] [1, 3, 4, 6, 10] [1, 3, 4, 7, 9] [1, 3, 5, 6, 7] [1, 2, 4, 6, 7] [1, 3, 4, 9, 10] [1, 2, 5, 6, 7] CPU times: user 0 ns, sys: 0 ns, total: 0 ns Wall time: 783 µs 15 new smallest = 6 new smallest = 5 [1, 3, 5, 7, 8] [1, 3, 4, 9, 11] CPU times: user 0 ns, sys: 0 ns, total: 0 ns Wall time: 642 µs 16 new smallest = 5 [1, 3, 5, 7, 8] CPU times: user 0 ns, sys: 0 ns, total: 0 ns Wall time: 125 µs 17 new smallest = 6 considering 1 considering 2 considering 3 considering 4 [1, 3, 5, 7, 8, 10] [1, 3, 4, 5, 7, 12] [1, 2, 5, 6, 8, 9] [1, 2, 5, 6, 9, 11] [1, 3, 4, 7, 9, 14] [1, 3, 5, 7, 9, 10] [1, 2, 4, 5, 11, 12] [1, 3, 5, 6, 8, 9] [1, 2, 5, 7, 8, 10] [1, 3, 4, 6, 11, 12] [1, 3, 5, 7, 8, 14] [1, 2, 4, 6, 8, 11] [1, 3, 4, 7, 8, 10] [1, 3, 4, 8, 9, 14] [1, 3, 4, 7, 8, 9] [1, 3, 4, 6, 11, 13] [1, 3, 5, 7, 8, 12] [1, 2, 3, 5, 8, 12] [1, 3, 5, 6, 10, 11] [1, 2, 4, 7, 8, 13] [1, 3, 5, 6, 13, 14] [1, 2, 5, 7, 10, 11] [1, 2, 5, 6, 7, 10] [1, 3, 4, 5, 8, 14] [1, 2, 5, 6, 8, 15] [1, 3, 4, 5, 10, 12] [1, 2, 5, 8, 9, 10] [1, 3, 4, 6, 10, 14] [1, 3, 4, 8, 10, 14] [1, 2, 4, 5, 10, 12] [1, 3, 5, 6, 7, 10] [1, 2, 3, 4, 9, 14] [1, 2, 4, 5, 11, 13] [1, 2, 4, 6, 7, 15] [1, 3, 5, 6, 8, 12] [1, 3, 5, 6, 10, 14] [1, 3, 5, 6, 11, 12] [1, 3, 5, 6, 12, 13] [1, 3, 5, 7, 8, 16] [1, 3, 4, 5, 11, 12] [1, 3, 4, 5, 11, 13] [1, 2, 5, 6, 7, 15] [1, 2, 5, 7, 11, 15] [1, 2, 5, 7, 8, 9] [1, 2, 5, 8, 10, 12] [1, 3, 4, 9, 11, 13] [1, 3, 4, 7, 8, 13] [1, 2, 3, 4, 8, 13] [1, 3, 4, 6, 8, 9] [1, 3, 4, 8, 9, 11] [1, 2, 4, 6, 8, 9] [1, 3, 4, 6, 10, 11] [1, 3, 5, 6, 8, 14] [1, 3, 4, 9, 11, 16] [1, 2, 4, 7, 8, 9] [1, 3, 5, 7, 8, 9] [1, 2, 3, 4, 9, 13] CPU times: user 52 ms, sys: 0 ns, total: 52 ms Wall time: 53 ms 18 new smallest = 6 [1, 3, 5, 7, 8, 10] [1, 2, 5, 6, 8, 9] [1, 2, 5, 6, 9, 11] [1, 3, 4, 7, 9, 14] [1, 3, 5, 7, 9, 10] [1, 3, 5, 6, 8, 9] [1, 2, 5, 7, 8, 10] [1, 3, 4, 6, 11, 12] [1, 3, 4, 7, 8, 10] [1, 3, 4, 8, 9, 14] [1, 3, 4, 7, 8, 9] [1, 3, 5, 6, 13, 14] [1, 2, 5, 7, 10, 11] [1, 3, 4, 5, 8, 14] [1, 3, 4, 6, 10, 14] [1, 3, 4, 8, 10, 14] [1, 2, 5, 8, 9, 10] [1, 2, 3, 4, 9, 14] [1, 2, 4, 5, 11, 13] [1, 3, 5, 6, 8, 12] [1, 3, 5, 6, 11, 12] [1, 3, 5, 6, 12, 13] [1, 3, 4, 5, 11, 13] [1, 2, 5, 7, 11, 15] [1, 2, 5, 7, 8, 9] [1, 2, 5, 8, 10, 12] [1, 3, 4, 9, 11, 13] [1, 3, 4, 8, 9, 11] [1, 3, 4, 6, 8, 9] [1, 2, 4, 6, 8, 9] [1, 3, 4, 9, 11, 16] [1, 2, 4, 7, 8, 9] [1, 3, 5, 7, 8, 9] [1, 2, 3, 4, 9, 13] CPU times: user 0 ns, sys: 0 ns, total: 0 ns Wall time: 1.64 ms 19 new smallest = 7 new smallest = 6 [1, 3, 5, 6, 13, 14] [1, 3, 5, 7, 9, 10] [1, 3, 4, 5, 8, 14] [1, 3, 4, 8, 9, 11] [1, 3, 5, 6, 12, 13] [1, 2, 5, 8, 9, 10] [1, 3, 4, 9, 11, 16] CPU times: user 4 ms, sys: 0 ns, total: 4 ms Wall time: 1.42 ms 20 new smallest = 6 [1, 3, 4, 9, 11, 16] [1, 3, 5, 6, 13, 14] [1, 3, 5, 7, 9, 10] [1, 3, 4, 8, 9, 11] [1, 2, 5, 8, 9, 10] CPU times: user 0 ns, sys: 0 ns, total: 0 ns Wall time: 400 µs
for n in range(20, 25):
print(n+1)
%time upgrade(cmap, n, n+1)
21 new smallest = 7 considering 1 considering 2 considering 3 considering 4 [1, 3, 4, 7, 9, 12, 13] [1, 2, 3, 4, 7, 12, 17] [1, 2, 4, 5, 11, 13, 19] [1, 2, 5, 8, 10, 13, 17] [1, 2, 3, 4, 8, 13, 16] [1, 2, 4, 5, 6, 13, 15] [1, 3, 5, 6, 7, 9, 14] [1, 2, 4, 7, 9, 10, 11] [1, 2, 4, 7, 9, 12, 13] [1, 3, 4, 7, 9, 12, 16] [1, 3, 5, 6, 11, 13, 15] [1, 2, 5, 7, 10, 11, 19] [1, 3, 5, 6, 10, 11, 18] [1, 3, 4, 7, 8, 9, 12] [1, 3, 5, 7, 9, 10, 20] [1, 3, 4, 7, 8, 12, 17] [1, 2, 4, 7, 8, 11, 13] [1, 3, 4, 9, 11, 12, 16] [1, 3, 4, 6, 7, 15, 16] [1, 3, 5, 7, 8, 12, 18] [1, 2, 5, 6, 9, 10, 12] [1, 3, 4, 9, 11, 16, 20] [1, 3, 5, 6, 13, 14, 20] [1, 2, 3, 4, 9, 12, 17] [1, 2, 4, 5, 8, 10, 17] [1, 2, 5, 7, 8, 10, 14] [1, 2, 4, 7, 8, 13, 17] [1, 3, 4, 9, 10, 12, 14] [1, 3, 5, 6, 10, 14, 18] [1, 3, 4, 5, 8, 13, 15] [1, 3, 5, 7, 8, 16, 17] [1, 3, 4, 9, 10, 12, 13] [1, 2, 5, 7, 10, 11, 12] [1, 2, 4, 7, 9, 10, 14] [1, 3, 4, 5, 8, 14, 16] [1, 2, 5, 7, 8, 9, 19] [1, 3, 4, 5, 9, 10, 16] [1, 2, 5, 8, 10, 12, 19] [1, 2, 3, 5, 8, 12, 16] [1, 3, 4, 6, 7, 12, 17] [1, 3, 4, 8, 10, 11, 13] [1, 2, 5, 8, 9, 10, 20] [1, 2, 4, 6, 8, 9, 19] [1, 3, 4, 6, 10, 13, 15] [1, 3, 5, 7, 8, 14, 15] [1, 3, 5, 6, 13, 15, 17] [1, 3, 4, 9, 11, 13, 18] [1, 3, 4, 8, 9, 11, 20] [1, 2, 5, 7, 9, 12, 13] [1, 2, 5, 7, 10, 12, 16] [1, 3, 4, 6, 10, 11, 18] [1, 2, 5, 6, 8, 12, 13] [1, 2, 5, 7, 10, 11, 17] [1, 3, 4, 5, 7, 13, 14] [1, 3, 4, 8, 9, 11, 12] [1, 2, 5, 6, 8, 10, 11] [1, 3, 4, 5, 9, 10, 12] [1, 3, 4, 6, 7, 15, 17] [1, 3, 4, 5, 10, 11, 14] [1, 3, 5, 6, 8, 12, 16] [1, 3, 5, 7, 8, 12, 13] [1, 2, 4, 5, 9, 10, 12] [1, 2, 4, 5, 7, 13, 14] [1, 3, 5, 6, 8, 12, 13] [1, 3, 4, 6, 7, 14, 15] [1, 2, 4, 5, 11, 14, 16] [1, 2, 3, 4, 9, 13, 18] [1, 3, 4, 5, 11, 13, 16] [1, 2, 4, 5, 9, 12, 15] [1, 2, 4, 6, 7, 14, 15] [1, 2, 3, 4, 9, 13, 17] [1, 2, 4, 7, 8, 13, 18] [1, 3, 4, 7, 9, 10, 14] [1, 2, 4, 6, 9, 10, 15] [1, 3, 5, 6, 9, 10, 16] [1, 2, 5, 8, 11, 13, 15] [1, 3, 4, 6, 10, 14, 18] [1, 2, 5, 6, 8, 15, 18] [1, 3, 4, 7, 9, 14, 19] [1, 3, 4, 8, 9, 11, 17] [1, 3, 5, 7, 8, 10, 14] [1, 2, 3, 5, 8, 12, 18] [1, 3, 5, 6, 13, 14, 18] [1, 3, 4, 5, 8, 14, 17] [1, 3, 4, 5, 8, 10, 16] [1, 3, 5, 6, 10, 14, 15] [1, 2, 5, 6, 8, 9, 19] [1, 3, 4, 7, 9, 14, 16] [1, 3, 4, 8, 9, 11, 13] [1, 2, 4, 5, 9, 10, 16] [1, 2, 3, 4, 8, 11, 17] [1, 2, 3, 4, 9, 12, 16] [1, 2, 4, 6, 9, 14, 15] [1, 3, 4, 6, 10, 14, 15] [1, 3, 4, 9, 10, 12, 17] [1, 2, 5, 6, 7, 15, 18] [1, 2, 4, 7, 9, 11, 17] [1, 2, 4, 7, 10, 12, 14] [1, 2, 5, 7, 9, 10, 11] [1, 3, 4, 7, 9, 10, 11] [1, 2, 5, 8, 10, 11, 12] [1, 3, 4, 5, 6, 13, 15] [1, 2, 4, 5, 10, 12, 17] [1, 2, 4, 6, 9, 10, 11] [1, 2, 5, 6, 7, 14, 17] [1, 3, 4, 5, 9, 11, 16] [1, 2, 4, 7, 8, 10, 11] [1, 3, 5, 6, 12, 13, 15] [1, 3, 4, 7, 9, 12, 17] [1, 2, 3, 4, 9, 13, 19] [1, 3, 5, 6, 12, 14, 16] [1, 2, 5, 6, 7, 13, 15] [1, 2, 3, 5, 9, 10, 16] [1, 3, 5, 6, 7, 15, 16] [1, 2, 3, 4, 8, 13, 17] [1, 2, 4, 7, 8, 12, 17] [1, 2, 5, 7, 11, 15, 19] [1, 3, 4, 5, 8, 14, 20] [1, 3, 5, 6, 10, 11, 13] [1, 2, 3, 4, 8, 13, 18] [1, 3, 4, 5, 6, 9, 16] [1, 2, 5, 8, 9, 12, 14] [1, 2, 5, 8, 9, 10, 11] [1, 3, 4, 7, 9, 15, 17] [1, 3, 5, 6, 13, 15, 16] [1, 2, 5, 6, 7, 12, 14] [1, 3, 4, 8, 9, 10, 11] [1, 3, 5, 7, 8, 10, 16] [1, 3, 5, 6, 12, 13, 20] [1, 3, 5, 6, 7, 12, 15] [1, 2, 4, 6, 8, 10, 13] [1, 3, 5, 6, 13, 14, 15] [1, 3, 4, 5, 7, 12, 17] [1, 3, 4, 9, 10, 11, 13] [1, 3, 5, 7, 8, 17, 18] [1, 2, 5, 6, 8, 13, 15] [1, 3, 4, 6, 9, 10, 17] [1, 3, 5, 6, 8, 15, 16] [1, 3, 4, 9, 11, 16, 17] [1, 2, 5, 7, 10, 13, 14] [1, 3, 5, 6, 8, 13, 14] [1, 2, 5, 6, 8, 14, 16] [1, 2, 5, 8, 9, 11, 13] [1, 3, 5, 7, 8, 13, 16] [1, 2, 4, 5, 6, 12, 15] [1, 2, 3, 4, 6, 10, 15] [1, 2, 5, 6, 7, 11, 14] [1, 2, 4, 7, 8, 9, 19] [1, 3, 4, 7, 8, 10, 11] [1, 2, 5, 7, 11, 14, 15] [1, 3, 4, 6, 9, 10, 11] [1, 2, 4, 6, 7, 14, 17] [1, 3, 4, 8, 10, 14, 18] [1, 2, 4, 5, 6, 13, 16] [1, 2, 5, 6, 7, 15, 17] [1, 3, 4, 6, 8, 10, 11] [1, 3, 5, 7, 9, 10, 11] [1, 2, 5, 8, 9, 10, 16] [1, 3, 5, 7, 8, 10, 11] [1, 3, 4, 9, 10, 15, 17] [1, 3, 5, 6, 9, 10, 11] [1, 2, 4, 5, 10, 11, 17] [1, 3, 4, 5, 8, 11, 17] [1, 2, 5, 7, 10, 11, 14] [1, 3, 5, 7, 9, 10, 12] [1, 2, 3, 4, 9, 14, 17] [1, 3, 4, 8, 10, 13, 15] [1, 3, 5, 6, 9, 10, 12] [1, 3, 5, 7, 8, 9, 12] [1, 2, 3, 4, 5, 11, 16] [1, 2, 5, 8, 10, 14, 16] [1, 3, 4, 6, 7, 13, 14] [1, 3, 5, 6, 7, 14, 15] [1, 2, 4, 6, 9, 14, 17] [1, 3, 4, 6, 7, 12, 14] [1, 2, 5, 6, 8, 15, 17] [1, 3, 5, 6, 8, 14, 18] [1, 3, 4, 8, 10, 11, 17] [1, 3, 5, 6, 8, 10, 16] [1, 3, 5, 7, 9, 10, 16] [1, 3, 4, 6, 10, 15, 17] [1, 3, 4, 8, 9, 11, 18] [1, 3, 4, 7, 8, 13, 18] [1, 3, 4, 8, 10, 11, 14] [1, 3, 4, 9, 11, 16, 18] [1, 3, 4, 7, 8, 13, 15] [1, 3, 4, 6, 10, 15, 16] [1, 3, 4, 7, 8, 10, 18] [1, 2, 3, 4, 5, 11, 17] [1, 3, 4, 8, 10, 11, 16] [1, 3, 5, 6, 8, 14, 15] [1, 2, 5, 8, 9, 10, 12] [1, 2, 5, 7, 8, 10, 19] [1, 3, 4, 8, 9, 10, 12] [1, 3, 4, 7, 8, 12, 14] [1, 2, 5, 6, 9, 10, 11] [1, 2, 5, 8, 9, 10, 13] [1, 2, 5, 7, 8, 10, 11] [1, 2, 5, 7, 10, 11, 18] [1, 3, 4, 5, 10, 12, 18] [1, 2, 5, 6, 9, 11, 19] [1, 3, 5, 6, 8, 10, 11] [1, 3, 4, 8, 10, 15, 17] [1, 2, 4, 6, 8, 10, 11] [1, 3, 4, 6, 7, 10, 15] [1, 2, 5, 7, 9, 12, 15] [1, 2, 4, 6, 7, 15, 18] [1, 2, 4, 6, 7, 13, 14] [1, 2, 4, 5, 6, 9, 15] [1, 3, 4, 6, 7, 14, 16] [1, 2, 5, 7, 8, 9, 12] [1, 3, 5, 6, 7, 13, 14] [1, 2, 5, 6, 7, 14, 16] [1, 2, 5, 8, 11, 12, 13] [1, 2, 4, 7, 10, 11, 15] [1, 2, 4, 6, 7, 15, 16] [1, 2, 5, 6, 7, 13, 16] [1, 3, 4, 6, 7, 13, 15] [1, 2, 3, 4, 9, 14, 19] [1, 3, 4, 6, 9, 11, 15] [1, 2, 5, 7, 9, 10, 12] [1, 3, 4, 6, 10, 11, 15] [1, 3, 4, 7, 8, 11, 13] [1, 3, 5, 6, 8, 12, 18] [1, 3, 4, 7, 9, 10, 12] [1, 3, 4, 6, 11, 13, 17] [1, 3, 5, 6, 7, 10, 18] [1, 2, 4, 5, 9, 11, 17] [1, 2, 5, 8, 9, 10, 19] [1, 2, 3, 4, 9, 14, 18] [1, 2, 4, 7, 8, 9, 12] [1, 3, 5, 6, 8, 11, 15] [1, 3, 5, 7, 8, 14, 17] [1, 2, 4, 7, 10, 11, 12] [1, 3, 4, 9, 10, 12, 16] [1, 2, 3, 4, 5, 10, 16] [1, 2, 3, 4, 8, 12, 17] [1, 2, 5, 6, 7, 12, 15] [1, 2, 3, 5, 6, 13, 15] [1, 3, 5, 6, 13, 14, 16] [1, 3, 5, 7, 9, 10, 14] [1, 3, 5, 7, 9, 11, 12] [1, 3, 5, 6, 7, 11, 14] [1, 3, 5, 6, 12, 14, 15] [1, 3, 5, 7, 8, 13, 14] [1, 3, 4, 9, 11, 15, 17] [1, 2, 5, 6, 9, 13, 15] [1, 2, 3, 5, 7, 10, 16] [1, 3, 5, 6, 10, 13, 16] [1, 3, 5, 7, 8, 15, 16] [1, 3, 4, 6, 8, 13, 14] [1, 3, 5, 7, 8, 10, 18] [1, 2, 4, 6, 9, 10, 17] [1, 3, 5, 7, 9, 10, 18] [1, 3, 4, 9, 10, 11, 16] [1, 3, 4, 6, 8, 12, 13] [1, 2, 5, 6, 9, 12, 14] CPU times: user 344 ms, sys: 0 ns, total: 344 ms Wall time: 346 ms 22 new smallest = 7 [1, 3, 4, 7, 9, 12, 13] [1, 2, 4, 5, 11, 13, 19] [1, 2, 5, 8, 10, 13, 17] [1, 2, 4, 7, 9, 10, 11] [1, 2, 4, 7, 9, 12, 13] [1, 3, 5, 6, 11, 13, 15] [1, 2, 5, 7, 10, 11, 19] [1, 3, 5, 6, 10, 11, 18] [1, 2, 4, 7, 8, 11, 13] [1, 3, 4, 9, 11, 12, 16] [1, 3, 4, 6, 7, 15, 16] [1, 2, 5, 6, 9, 10, 12] [1, 3, 4, 9, 11, 16, 20] [1, 2, 4, 5, 8, 10, 17] [1, 2, 5, 7, 8, 10, 14] [1, 3, 4, 9, 10, 12, 14] [1, 3, 5, 7, 8, 16, 17] [1, 3, 4, 9, 10, 12, 13] [1, 2, 5, 7, 10, 11, 12] [1, 3, 4, 5, 8, 14, 16] [1, 2, 5, 8, 10, 12, 19] [1, 3, 4, 8, 10, 11, 13] [1, 2, 5, 8, 9, 10, 20] [1, 3, 5, 7, 8, 14, 15] [1, 3, 5, 6, 13, 15, 17] [1, 3, 4, 9, 11, 13, 18] [1, 3, 4, 8, 9, 11, 20] [1, 2, 5, 7, 9, 12, 13] [1, 2, 5, 7, 10, 12, 16] [1, 3, 4, 6, 10, 11, 18] [1, 2, 5, 7, 10, 11, 17] [1, 3, 5, 6, 8, 12, 16] [1, 3, 4, 8, 9, 11, 12] [1, 2, 5, 6, 8, 10, 11] [1, 3, 4, 5, 9, 10, 12] [1, 3, 4, 6, 7, 15, 17] [1, 3, 4, 5, 10, 11, 14] [1, 2, 4, 5, 9, 10, 12] [1, 3, 4, 6, 7, 14, 15] [1, 2, 4, 5, 11, 14, 16] [1, 2, 3, 4, 9, 13, 18] [1, 3, 4, 5, 11, 13, 16] [1, 2, 4, 6, 7, 14, 15] [1, 2, 3, 4, 9, 13, 17] [1, 2, 4, 7, 8, 13, 18] [1, 3, 5, 6, 9, 10, 16] [1, 2, 5, 8, 11, 13, 15] [1, 3, 4, 6, 10, 14, 18] [1, 3, 4, 7, 9, 14, 19] [1, 3, 4, 8, 9, 11, 17] [1, 3, 5, 7, 8, 10, 14] [1, 3, 4, 5, 8, 14, 17] [1, 3, 4, 8, 9, 11, 13] [1, 2, 3, 4, 8, 11, 17] [1, 3, 4, 9, 10, 12, 17] [1, 2, 5, 6, 7, 15, 18] [1, 2, 4, 7, 9, 11, 17] [1, 2, 4, 7, 10, 12, 14] [1, 2, 5, 7, 9, 10, 11] [1, 3, 4, 7, 9, 10, 11] [1, 2, 5, 8, 10, 11, 12] [1, 2, 4, 5, 10, 12, 17] [1, 2, 4, 6, 9, 10, 11] [1, 2, 5, 6, 7, 14, 17] [1, 3, 4, 5, 9, 11, 16] [1, 2, 4, 7, 8, 10, 11] [1, 2, 3, 4, 9, 13, 19] [1, 3, 5, 6, 12, 14, 16] [1, 2, 5, 6, 7, 13, 15] [1, 3, 5, 6, 7, 15, 16] [1, 2, 5, 7, 11, 15, 19] [1, 3, 4, 5, 8, 14, 20] [1, 3, 5, 6, 10, 11, 13] [1, 2, 3, 4, 8, 13, 18] [1, 3, 4, 5, 6, 9, 16] [1, 2, 5, 8, 9, 12, 14] [1, 3, 4, 7, 9, 15, 17] [1, 3, 5, 6, 13, 15, 16] [1, 2, 5, 8, 9, 10, 11] [1, 3, 4, 8, 9, 10, 11] [1, 3, 5, 6, 7, 12, 15] [1, 3, 4, 5, 7, 12, 17] [1, 3, 4, 9, 10, 11, 13] [1, 3, 5, 7, 8, 17, 18] [1, 3, 5, 6, 8, 15, 16] [1, 3, 4, 9, 11, 16, 17] [1, 3, 5, 6, 8, 13, 14] [1, 2, 5, 6, 8, 14, 16] [1, 2, 5, 8, 9, 11, 13] [1, 2, 5, 6, 7, 11, 14] [1, 3, 4, 7, 8, 10, 11] [1, 2, 5, 7, 11, 14, 15] [1, 3, 4, 6, 9, 10, 11] [1, 3, 4, 8, 10, 14, 18] [1, 2, 4, 5, 6, 13, 16] [1, 2, 5, 6, 7, 15, 17] [1, 3, 4, 6, 8, 10, 11] [1, 3, 5, 7, 9, 10, 11] [1, 3, 5, 7, 8, 10, 11] [1, 3, 5, 6, 9, 10, 11] [1, 2, 4, 5, 10, 11, 17] [1, 3, 4, 5, 8, 11, 17] [1, 2, 5, 7, 10, 11, 14] [1, 3, 5, 7, 9, 10, 12] [1, 2, 3, 4, 5, 11, 16] [1, 2, 5, 8, 10, 14, 16] [1, 3, 5, 6, 7, 14, 15] [1, 2, 5, 6, 8, 15, 17] [1, 3, 5, 6, 8, 14, 18] [1, 3, 4, 8, 10, 11, 17] [1, 3, 5, 6, 8, 10, 16] [1, 3, 4, 8, 9, 11, 18] [1, 3, 4, 7, 8, 13, 18] [1, 3, 4, 8, 10, 11, 14] [1, 3, 4, 9, 11, 16, 18] [1, 3, 4, 7, 8, 13, 15] [1, 3, 4, 6, 10, 15, 16] [1, 3, 4, 7, 8, 10, 18] [1, 3, 4, 8, 10, 11, 16] [1, 3, 5, 6, 8, 14, 15] [1, 2, 5, 8, 9, 10, 12] [1, 3, 4, 8, 9, 10, 12] [1, 3, 4, 7, 8, 12, 14] [1, 2, 5, 6, 9, 10, 11] [1, 2, 5, 8, 9, 10, 13] [1, 2, 5, 7, 8, 10, 11] [1, 2, 5, 7, 10, 11, 18] [1, 3, 4, 5, 10, 12, 18] [1, 2, 5, 6, 9, 11, 19] [1, 3, 5, 6, 8, 10, 11] [1, 2, 4, 6, 8, 10, 11] [1, 3, 4, 6, 7, 10, 15] [1, 2, 5, 7, 9, 12, 15] [1, 2, 4, 6, 7, 15, 18] [1, 3, 4, 6, 7, 14, 16] [1, 2, 5, 8, 11, 12, 13] [1, 2, 5, 6, 7, 14, 16] [1, 3, 5, 6, 9, 10, 12] [1, 2, 4, 7, 10, 11, 15] [1, 2, 4, 6, 7, 15, 16] [1, 2, 5, 6, 7, 13, 16] [1, 3, 4, 6, 7, 13, 15] [1, 2, 3, 4, 9, 14, 19] [1, 3, 4, 6, 9, 11, 15] [1, 2, 5, 7, 9, 10, 12] [1, 3, 4, 6, 10, 11, 15] [1, 3, 4, 7, 8, 11, 13] [1, 3, 4, 7, 9, 10, 12] [1, 3, 4, 6, 11, 13, 17] [1, 2, 4, 5, 9, 11, 17] [1, 2, 3, 4, 9, 14, 18] [1, 3, 5, 6, 8, 11, 15] [1, 3, 5, 7, 8, 14, 17] [1, 2, 4, 7, 10, 11, 12] [1, 3, 4, 9, 10, 12, 16] [1, 2, 5, 6, 7, 12, 15] [1, 3, 5, 6, 13, 14, 16] [1, 3, 5, 7, 9, 11, 12] [1, 3, 5, 6, 7, 11, 14] [1, 3, 5, 7, 8, 13, 14] [1, 3, 4, 9, 11, 15, 17] [1, 2, 5, 6, 9, 13, 15] [1, 3, 5, 6, 10, 13, 16] [1, 3, 5, 7, 8, 15, 16] [1, 3, 4, 6, 8, 13, 14] [1, 3, 4, 9, 10, 11, 16] [1, 2, 3, 4, 5, 11, 17] CPU times: user 4 ms, sys: 0 ns, total: 4 ms Wall time: 4.66 ms 23 new smallest = 8 new smallest = 7 [1, 2, 4, 5, 11, 13, 19] [1, 2, 5, 8, 10, 13, 17] [1, 3, 4, 7, 8, 13, 15] [1, 3, 5, 6, 8, 14, 15] [1, 3, 5, 6, 10, 11, 18] [1, 3, 4, 9, 10, 11, 13] [1, 3, 5, 7, 8, 17, 18] [1, 3, 5, 6, 8, 15, 16] [1, 2, 5, 8, 11, 13, 15] [1, 2, 5, 8, 9, 10, 13] [1, 2, 5, 7, 10, 11, 18] [1, 3, 4, 5, 10, 12, 18] [1, 3, 4, 7, 9, 14, 19] [1, 3, 4, 9, 11, 12, 16] [1, 3, 4, 6, 7, 15, 16] [1, 3, 4, 9, 11, 16, 20] [1, 3, 4, 6, 7, 14, 16] [1, 2, 5, 8, 11, 12, 13] [1, 2, 5, 6, 7, 14, 16] [1, 2, 5, 6, 7, 15, 17] [1, 2, 4, 6, 7, 15, 16] [1, 2, 5, 6, 7, 13, 16] [1, 2, 3, 4, 9, 14, 19] [1, 3, 4, 9, 10, 12, 14] [1, 3, 5, 7, 8, 16, 17] [1, 3, 4, 6, 11, 13, 17] [1, 3, 4, 9, 10, 12, 13] [1, 2, 3, 4, 9, 14, 18] [1, 2, 5, 7, 10, 11, 12] [1, 3, 5, 6, 8, 11, 15] [1, 2, 4, 7, 10, 11, 12] [1, 2, 5, 6, 7, 15, 18] [1, 3, 4, 8, 10, 11, 13] [1, 2, 5, 8, 10, 11, 12] [1, 3, 5, 7, 8, 14, 15] [1, 3, 5, 6, 13, 15, 17] [1, 3, 5, 7, 9, 11, 12] [1, 2, 5, 6, 7, 14, 17] [1, 3, 4, 8, 9, 11, 20] [1, 2, 5, 6, 8, 15, 17] [1, 2, 5, 7, 10, 12, 16] [1, 2, 3, 4, 9, 13, 19] [1, 3, 5, 6, 8, 14, 18] [1, 3, 4, 8, 9, 11, 12] [1, 3, 4, 6, 7, 15, 17] [1, 3, 5, 6, 7, 15, 16] [1, 3, 5, 6, 10, 13, 16] [1, 3, 5, 7, 8, 15, 16] [1, 3, 4, 5, 8, 14, 20] [1, 3, 5, 6, 10, 11, 13] [1, 2, 5, 8, 9, 12, 14] CPU times: user 4 ms, sys: 0 ns, total: 4 ms Wall time: 3.31 ms 24 new smallest = 7 [1, 2, 4, 5, 11, 13, 19] [1, 3, 5, 6, 10, 11, 18] [1, 3, 5, 7, 8, 17, 18] [1, 3, 4, 9, 10, 11, 13] [1, 3, 5, 6, 8, 15, 16] [1, 2, 5, 8, 11, 13, 15] [1, 3, 4, 5, 10, 12, 18] [1, 3, 4, 9, 11, 12, 16] [1, 3, 4, 9, 11, 16, 20] [1, 2, 5, 8, 11, 12, 13] [1, 2, 5, 6, 7, 15, 17] [1, 3, 4, 9, 10, 12, 14] [1, 3, 5, 7, 8, 16, 17] [1, 3, 4, 6, 11, 13, 17] [1, 3, 4, 9, 10, 12, 13] [1, 2, 5, 7, 10, 11, 12] [1, 2, 4, 7, 10, 11, 12] [1, 2, 5, 6, 7, 15, 18] [1, 3, 4, 8, 10, 11, 13] [1, 2, 5, 8, 10, 11, 12] [1, 3, 5, 7, 9, 11, 12] [1, 2, 5, 6, 7, 14, 17] [1, 3, 4, 8, 9, 11, 20] [1, 2, 5, 7, 10, 12, 16] [1, 3, 5, 6, 8, 14, 18] [1, 3, 4, 8, 9, 11, 12] [1, 3, 4, 6, 7, 15, 17] [1, 3, 5, 7, 8, 15, 16] [1, 3, 4, 5, 8, 14, 20] [1, 3, 5, 6, 10, 11, 13] [1, 2, 5, 8, 9, 12, 14] CPU times: user 0 ns, sys: 0 ns, total: 0 ns Wall time: 1 ms 25 new smallest = 8 new smallest = 7 [1, 3, 5, 7, 8, 16, 17] [1, 3, 4, 9, 10, 12, 13] [1, 3, 4, 9, 11, 12, 16] [1, 3, 4, 9, 11, 16, 20] [1, 2, 5, 6, 7, 15, 18] [1, 2, 5, 8, 11, 12, 13] [1, 3, 4, 5, 8, 14, 20] [1, 3, 5, 7, 8, 17, 18] CPU times: user 0 ns, sys: 0 ns, total: 0 ns Wall time: 828 µs
for n in range(25, 30):
print(n+1)
%time upgrade(cmap, n, n+1)
26 new smallest = 8 new smallest = 7 [1, 2, 5, 8, 11, 12, 13] [1, 3, 4, 9, 10, 12, 13] [1, 3, 5, 7, 8, 17, 18] CPU times: user 4 ms, sys: 0 ns, total: 4 ms Wall time: 332 µs 27 new smallest = 8 considering 1 considering 2 considering 3 considering 4 [1, 3, 4, 9, 11, 12, 16, 17] [1, 2, 5, 7, 8, 11, 16, 18] [1, 2, 5, 6, 7, 8, 17, 19] [1, 2, 5, 7, 10, 11, 14, 16] [1, 2, 3, 4, 9, 13, 18, 23] [1, 3, 4, 9, 11, 13, 16, 20] [1, 3, 4, 9, 11, 15, 16, 20] [1, 3, 5, 6, 10, 13, 16, 24] [1, 3, 4, 5, 11, 13, 14, 20] [1, 3, 5, 6, 8, 10, 17, 18] [1, 3, 5, 6, 8, 9, 18, 19] [1, 3, 4, 6, 9, 11, 16, 20] [1, 3, 4, 8, 10, 11, 17, 23] [1, 2, 4, 5, 9, 12, 15, 21] [1, 2, 4, 7, 8, 13, 18, 23] [1, 2, 5, 6, 7, 14, 17, 25] [1, 2, 3, 4, 9, 13, 18, 21] [1, 2, 5, 8, 11, 13, 14, 15] [1, 2, 5, 7, 10, 13, 14, 15] [1, 3, 4, 9, 10, 11, 16, 23] [1, 3, 4, 8, 9, 11, 13, 14] [1, 2, 5, 6, 8, 13, 17, 19] [1, 3, 4, 6, 11, 13, 14, 20] [1, 3, 5, 6, 7, 11, 12, 20] [1, 3, 4, 9, 11, 16, 20, 25] [1, 2, 4, 7, 9, 12, 13, 23] [1, 2, 5, 8, 9, 12, 14, 25] [1, 2, 4, 5, 10, 12, 13, 17] [1, 2, 5, 7, 10, 13, 14, 20] [1, 2, 4, 5, 6, 12, 14, 21] [1, 2, 5, 6, 8, 12, 13, 22] [1, 3, 5, 7, 8, 16, 17, 26] [1, 2, 4, 5, 9, 12, 13, 18] [1, 2, 4, 6, 7, 9, 17, 18] [1, 2, 4, 7, 9, 11, 17, 23] [1, 2, 4, 6, 8, 11, 18, 19] [1, 2, 5, 7, 11, 13, 16, 18] [1, 2, 3, 4, 9, 14, 19, 23] [1, 2, 4, 6, 7, 8, 16, 19] [1, 3, 4, 9, 10, 12, 13, 23] [1, 2, 5, 8, 11, 14, 15, 16] [1, 3, 4, 8, 9, 12, 13, 15] [1, 3, 4, 5, 11, 12, 14, 16] [1, 3, 5, 7, 8, 10, 18, 19] [1, 2, 5, 6, 9, 11, 19, 21] [1, 3, 4, 8, 10, 11, 16, 22] [1, 2, 5, 6, 7, 15, 18, 20] [1, 2, 5, 7, 11, 12, 14, 15] [1, 2, 5, 7, 8, 10, 15, 19] [1, 3, 4, 5, 9, 11, 16, 23] [1, 2, 4, 6, 8, 9, 19, 20] [1, 3, 4, 5, 10, 12, 18, 22] [1, 2, 5, 7, 9, 12, 13, 14] [1, 3, 4, 9, 11, 12, 13, 16] [1, 3, 5, 6, 7, 12, 16, 20] [1, 2, 4, 7, 8, 11, 13, 23] [1, 3, 5, 6, 10, 14, 17, 20] [1, 3, 5, 7, 9, 10, 20, 21] [1, 2, 5, 6, 9, 13, 16, 18] [1, 3, 4, 5, 11, 12, 13, 16] [1, 3, 5, 6, 8, 10, 16, 22] [1, 3, 4, 9, 10, 12, 14, 15] [1, 3, 5, 7, 8, 13, 16, 22] [1, 2, 5, 8, 11, 12, 13, 25] [1, 2, 4, 5, 9, 10, 16, 22] [1, 3, 4, 9, 11, 13, 18, 22] [1, 3, 4, 9, 10, 12, 13, 17] [1, 2, 3, 4, 9, 13, 19, 24] [1, 3, 4, 9, 11, 12, 16, 25] [1, 3, 4, 5, 8, 14, 20, 26] [1, 2, 5, 6, 7, 14, 17, 20] [1, 3, 4, 9, 11, 14, 15, 18] [1, 2, 5, 8, 9, 10, 16, 22] [1, 2, 4, 7, 9, 11, 16, 17] [1, 2, 3, 4, 5, 11, 17, 22] [1, 3, 4, 9, 10, 11, 12, 16] [1, 3, 4, 6, 10, 12, 13, 17] [1, 3, 4, 5, 6, 9, 16, 23] [1, 3, 4, 5, 7, 8, 17, 19] [1, 3, 4, 6, 8, 12, 13, 19] [1, 3, 5, 6, 12, 14, 15, 22] [1, 2, 3, 5, 6, 13, 15, 22] [1, 3, 4, 9, 10, 13, 14, 21] [1, 2, 5, 7, 10, 12, 16, 25] [1, 3, 4, 5, 7, 12, 17, 22] [1, 2, 4, 6, 8, 9, 18, 19] [1, 2, 4, 5, 6, 9, 15, 21] [1, 2, 3, 4, 5, 11, 16, 21] [1, 3, 5, 7, 8, 14, 18, 19] [1, 2, 4, 6, 8, 9, 19, 22] [1, 2, 5, 6, 7, 15, 18, 21] [1, 3, 4, 9, 11, 16, 17, 23] [1, 3, 5, 7, 8, 16, 18, 19] [1, 3, 5, 7, 8, 17, 18, 20] [1, 2, 5, 7, 8, 10, 17, 21] [1, 2, 4, 7, 10, 12, 14, 23] [1, 2, 5, 7, 11, 13, 14, 16] [1, 3, 5, 6, 11, 12, 14, 21] [1, 3, 4, 5, 8, 13, 14, 20] [1, 2, 4, 7, 8, 11, 17, 19] [1, 2, 3, 4, 9, 14, 18, 22] [1, 2, 5, 8, 10, 13, 14, 15] [1, 3, 4, 9, 11, 12, 16, 23] [1, 3, 4, 5, 8, 11, 17, 23] [1, 3, 4, 7, 8, 13, 15, 24] [1, 3, 4, 8, 9, 11, 17, 23] [1, 3, 4, 6, 8, 9, 17, 18] [1, 3, 4, 5, 11, 13, 16, 20] [1, 3, 4, 7, 9, 12, 13, 20] [1, 3, 4, 9, 11, 13, 14, 18] [1, 2, 5, 6, 7, 15, 17, 20] [1, 3, 4, 9, 10, 11, 13, 16] [1, 2, 5, 8, 9, 12, 13, 18] [1, 2, 5, 8, 11, 14, 16, 18] [1, 3, 4, 6, 7, 10, 15, 23] [1, 3, 5, 6, 10, 12, 13, 15] [1, 3, 4, 9, 10, 12, 13, 26] [1, 2, 5, 8, 10, 13, 17, 22] [1, 2, 5, 8, 10, 13, 17, 19] [1, 3, 5, 6, 7, 12, 15, 20] [1, 3, 5, 6, 13, 15, 17, 24] [1, 3, 5, 7, 8, 9, 18, 19] [1, 3, 5, 7, 9, 10, 17, 18] [1, 3, 4, 6, 11, 12, 15, 19] [1, 2, 5, 6, 7, 8, 17, 20] [1, 2, 5, 6, 8, 9, 17, 19] [1, 2, 5, 7, 9, 12, 14, 20] [1, 3, 4, 8, 10, 11, 15, 16] [1, 3, 5, 6, 8, 10, 16, 17] [1, 3, 4, 7, 8, 12, 13, 15] [1, 3, 5, 7, 8, 10, 19, 20] [1, 2, 5, 7, 11, 12, 13, 20] [1, 2, 4, 5, 11, 13, 19, 23] [1, 2, 4, 5, 11, 13, 14, 19] [1, 2, 4, 7, 10, 12, 13, 14] [1, 2, 5, 6, 8, 9, 18, 20] [1, 3, 4, 8, 9, 14, 16, 18] [1, 3, 5, 6, 8, 12, 18, 22] [1, 3, 4, 9, 11, 16, 20, 23] [1, 2, 4, 5, 10, 13, 14, 21] [1, 3, 4, 5, 11, 12, 15, 20] [1, 3, 5, 6, 13, 14, 20, 21] [1, 3, 4, 5, 6, 10, 13, 21] [1, 2, 4, 6, 8, 11, 18, 21] [1, 3, 5, 6, 10, 11, 13, 24] [1, 3, 4, 7, 8, 9, 16, 18] [1, 3, 5, 7, 9, 10, 16, 17] [1, 2, 5, 8, 11, 13, 15, 25] [1, 3, 4, 9, 10, 15, 17, 22] [1, 3, 4, 7, 9, 11, 16, 17] [1, 3, 5, 6, 8, 9, 19, 20] [1, 3, 4, 5, 8, 14, 20, 22] [1, 3, 5, 6, 10, 11, 13, 22] [1, 2, 5, 8, 11, 12, 13, 16] [1, 3, 5, 7, 8, 12, 18, 22] [1, 3, 5, 7, 8, 17, 18, 19] [1, 2, 5, 8, 10, 11, 12, 25] [1, 2, 5, 8, 9, 12, 13, 14] [1, 3, 4, 9, 10, 12, 13, 15] [1, 3, 5, 6, 12, 13, 20, 22] [1, 2, 5, 8, 10, 11, 13, 17] [1, 2, 5, 8, 9, 11, 15, 16] [1, 2, 5, 8, 9, 12, 15, 17] [1, 3, 5, 6, 11, 13, 14, 20] [1, 2, 5, 8, 11, 12, 13, 26] [1, 2, 5, 8, 9, 11, 13, 14] [1, 2, 4, 7, 10, 13, 14, 15] [1, 3, 4, 8, 10, 12, 13, 19] [1, 3, 4, 7, 8, 13, 17, 19] [1, 3, 4, 9, 11, 12, 16, 26] [1, 2, 5, 7, 11, 12, 14, 20] [1, 3, 4, 6, 9, 10, 17, 21] [1, 3, 4, 9, 11, 16, 21, 22] [1, 3, 5, 6, 12, 13, 20, 21] [1, 3, 5, 6, 13, 14, 21, 22] [1, 3, 5, 7, 8, 17, 18, 24] [1, 3, 4, 9, 10, 15, 17, 19] [1, 3, 5, 6, 12, 13, 15, 22] [1, 3, 4, 8, 9, 13, 14, 16] [1, 3, 5, 6, 8, 14, 18, 22] [1, 3, 4, 9, 10, 12, 16, 23] [1, 3, 5, 6, 10, 12, 13, 21] [1, 2, 5, 8, 10, 12, 13, 17] [1, 3, 4, 5, 10, 11, 12, 15] [1, 3, 4, 5, 7, 13, 15, 20] [1, 3, 5, 7, 8, 16, 17, 19] [1, 2, 5, 8, 10, 12, 13, 19] [1, 2, 5, 6, 8, 9, 19, 21] [1, 2, 4, 7, 10, 11, 12, 25] [1, 3, 4, 6, 7, 10, 15, 20] [1, 3, 5, 6, 8, 12, 13, 22] [1, 3, 4, 8, 9, 11, 21, 23] [1, 3, 5, 7, 8, 17, 19, 20] [1, 2, 4, 5, 6, 12, 15, 21] [1, 3, 4, 5, 9, 10, 12, 22] [1, 2, 3, 4, 5, 11, 17, 23] [1, 3, 4, 7, 9, 12, 13, 23] [1, 2, 3, 4, 5, 11, 16, 23] [1, 3, 4, 9, 11, 12, 13, 15] [1, 3, 5, 6, 8, 14, 17, 21] [1, 3, 4, 6, 11, 13, 14, 17] [1, 2, 5, 7, 9, 12, 13, 18] [1, 2, 3, 5, 9, 12, 13, 18] [1, 2, 4, 7, 10, 11, 12, 15] [1, 2, 5, 6, 7, 15, 17, 25] [1, 3, 4, 8, 10, 12, 13, 15] [1, 3, 5, 6, 7, 10, 18, 21] [1, 2, 5, 7, 8, 10, 16, 17] [1, 3, 4, 6, 10, 15, 16, 23] [1, 3, 4, 9, 11, 16, 20, 26] [1, 3, 4, 9, 10, 13, 15, 18] [1, 3, 5, 6, 11, 12, 16, 20] [1, 3, 4, 7, 8, 12, 17, 19] [1, 3, 4, 9, 10, 14, 16, 18] [1, 3, 5, 6, 11, 13, 15, 22] [1, 3, 5, 6, 9, 12, 13, 14] [1, 3, 4, 9, 11, 16, 17, 20] [1, 2, 5, 6, 9, 12, 13, 14] [1, 3, 5, 6, 7, 9, 17, 18] [1, 2, 5, 8, 11, 12, 14, 16] [1, 3, 4, 8, 9, 10, 15, 18] [1, 3, 4, 9, 11, 12, 14, 15] [1, 2, 5, 8, 11, 12, 13, 15] [1, 2, 5, 7, 11, 14, 16, 19] [1, 3, 5, 7, 8, 17, 18, 26] [1, 3, 4, 5, 8, 14, 20, 23] [1, 3, 4, 9, 11, 12, 15, 16] [1, 2, 4, 5, 11, 12, 14, 16] [1, 2, 4, 7, 10, 13, 15, 17] [1, 2, 5, 8, 10, 13, 17, 24] [1, 2, 3, 4, 5, 10, 16, 22] [1, 2, 5, 7, 10, 12, 16, 20] [1, 3, 4, 6, 11, 12, 14, 15] [1, 3, 5, 7, 8, 9, 16, 19] [1, 3, 4, 9, 10, 11, 13, 14] [1, 2, 5, 7, 10, 12, 13, 14] [1, 3, 4, 6, 7, 9, 17, 18] [1, 3, 4, 5, 10, 11, 14, 22] [1, 2, 4, 6, 9, 12, 13, 14] [1, 2, 5, 7, 10, 12, 15, 16] [1, 3, 4, 7, 8, 9, 18, 20] [1, 3, 5, 7, 9, 10, 17, 20] [1, 2, 5, 8, 10, 12, 17, 21] [1, 2, 5, 6, 7, 8, 16, 19] [1, 3, 4, 6, 10, 11, 13, 14] [1, 3, 4, 8, 10, 11, 13, 24] [1, 2, 5, 6, 7, 10, 17, 20] [1, 3, 5, 6, 11, 12, 15, 19] [1, 2, 5, 7, 10, 11, 12, 15] [1, 2, 4, 6, 7, 12, 15, 19] [1, 3, 5, 6, 9, 10, 16, 18] [1, 3, 4, 6, 10, 13, 14, 21] [1, 2, 5, 7, 9, 12, 13, 22] [1, 3, 5, 6, 12, 13, 15, 17] [1, 2, 5, 7, 10, 11, 12, 25] [1, 3, 5, 6, 8, 12, 18, 19] [1, 2, 3, 4, 8, 13, 18, 23] [1, 3, 5, 7, 8, 12, 15, 18] [1, 3, 5, 7, 9, 10, 21, 22] [1, 3, 5, 6, 8, 12, 19, 20] [1, 2, 5, 6, 7, 10, 18, 21] [1, 2, 4, 5, 8, 10, 17, 22] [1, 3, 4, 6, 11, 13, 17, 21] [1, 2, 5, 8, 10, 14, 17, 21] [1, 3, 5, 6, 13, 14, 18, 22] [1, 2, 4, 6, 8, 9, 18, 21] [1, 3, 4, 5, 8, 14, 19, 21] [1, 3, 4, 9, 10, 11, 16, 20] [1, 2, 4, 5, 10, 11, 13, 14] [1, 2, 3, 4, 9, 13, 18, 22] [1, 2, 4, 5, 10, 13, 14, 20] [1, 3, 4, 8, 10, 13, 14, 15] [1, 3, 4, 9, 10, 11, 13, 24] [1, 3, 4, 8, 9, 10, 14, 17] [1, 3, 5, 6, 13, 14, 18, 19] [1, 3, 4, 6, 10, 11, 12, 15] [1, 2, 5, 6, 8, 10, 16, 17] [1, 2, 5, 7, 11, 12, 13, 16] [1, 2, 3, 4, 9, 14, 18, 24] [1, 2, 5, 7, 11, 12, 13, 14] [1, 2, 5, 6, 8, 9, 16, 18] [1, 3, 4, 7, 8, 10, 18, 20] [1, 3, 5, 6, 13, 14, 19, 20] [1, 3, 5, 7, 9, 10, 18, 21] [1, 2, 5, 7, 11, 14, 15, 22] [1, 2, 5, 7, 11, 12, 15, 20] [1, 3, 5, 6, 8, 14, 18, 24] [1, 3, 5, 7, 8, 12, 18, 19] [1, 2, 3, 4, 5, 11, 16, 22] [1, 3, 4, 6, 9, 10, 13, 21] [1, 2, 4, 5, 11, 14, 16, 22] [1, 3, 4, 7, 8, 13, 18, 20] [1, 2, 3, 5, 9, 10, 16, 22] [1, 2, 4, 7, 10, 11, 15, 23] [1, 3, 4, 9, 10, 12, 13, 14] [1, 2, 3, 5, 8, 12, 18, 22] [1, 3, 4, 8, 10, 11, 13, 17] [1, 3, 4, 8, 9, 12, 13, 19] [1, 3, 4, 9, 10, 12, 17, 22] [1, 3, 5, 6, 9, 10, 15, 17] [1, 2, 4, 5, 10, 12, 17, 21] [1, 2, 3, 4, 9, 14, 19, 24] [1, 2, 5, 6, 9, 11, 18, 20] [1, 2, 4, 7, 9, 12, 13, 14] [1, 3, 4, 9, 10, 12, 14, 24] [1, 3, 4, 5, 10, 11, 14, 23] [1, 3, 4, 9, 10, 12, 13, 24] [1, 3, 5, 7, 9, 10, 19, 20] [1, 2, 5, 8, 10, 13, 14, 17] [1, 3, 5, 6, 8, 11, 15, 19] [1, 2, 5, 8, 10, 11, 12, 15] [1, 3, 4, 5, 8, 12, 13, 19] [1, 3, 4, 6, 7, 8, 17, 19] [1, 3, 4, 7, 9, 12, 13, 14] [1, 3, 5, 7, 8, 12, 13, 15] [1, 3, 4, 9, 11, 16, 21, 23] [1, 3, 5, 6, 11, 13, 14, 18] [1, 2, 4, 6, 7, 12, 13, 21] [1, 3, 5, 7, 8, 10, 17, 18] [1, 2, 5, 8, 10, 12, 13, 14] [1, 2, 5, 6, 7, 9, 17, 20] [1, 3, 5, 7, 8, 9, 17, 18] [1, 3, 4, 6, 7, 9, 16, 20] [1, 2, 3, 4, 8, 11, 17, 23] [1, 3, 5, 6, 12, 13, 17, 21] [1, 3, 4, 6, 10, 12, 13, 21] [1, 3, 5, 6, 7, 10, 12, 20] [1, 2, 5, 8, 11, 12, 13, 19] [1, 2, 5, 6, 7, 10, 17, 19] [1, 3, 4, 7, 8, 9, 19, 21] [1, 3, 4, 6, 10, 12, 13, 15] [1, 2, 3, 4, 9, 13, 17, 23] [1, 2, 4, 5, 7, 8, 17, 19] [1, 3, 5, 6, 12, 14, 16, 22] [1, 2, 3, 4, 9, 13, 19, 23] [1, 3, 5, 7, 9, 11, 13, 14] [1, 2, 4, 5, 11, 13, 19, 25] [1, 3, 5, 6, 8, 9, 17, 18] [1, 3, 4, 6, 8, 9, 18, 19] [1, 3, 4, 9, 10, 11, 14, 16] [1, 2, 5, 6, 8, 12, 13, 21] [1, 3, 4, 5, 8, 14, 17, 23] [1, 3, 5, 7, 8, 12, 13, 22] [1, 2, 5, 8, 10, 13, 17, 23] [1, 3, 4, 9, 11, 12, 13, 18] [1, 3, 4, 9, 11, 12, 14, 18] [1, 3, 4, 7, 9, 14, 19, 24] [1, 3, 4, 9, 11, 12, 14, 16] [1, 3, 4, 9, 11, 16, 20, 22] [1, 3, 5, 6, 10, 11, 13, 14] [1, 2, 5, 7, 10, 11, 13, 14] [1, 2, 5, 8, 11, 12, 13, 14] [1, 2, 5, 6, 7, 15, 18, 25] [1, 2, 5, 6, 7, 15, 18, 26] [1, 2, 4, 6, 8, 9, 17, 18] [1, 3, 5, 7, 8, 17, 18, 22] [1, 2, 5, 7, 8, 10, 13, 17] [1, 3, 4, 5, 8, 10, 16, 22] [1, 3, 4, 8, 10, 11, 13, 14] [1, 2, 3, 5, 7, 10, 16, 22] [1, 3, 5, 7, 8, 10, 16, 17] [1, 3, 4, 8, 10, 11, 14, 23] [1, 3, 5, 6, 11, 12, 14, 15] [1, 3, 4, 6, 8, 9, 19, 20] [1, 3, 4, 6, 10, 13, 15, 21] [1, 3, 4, 5, 11, 13, 16, 22] [1, 3, 4, 6, 10, 11, 15, 23] [1, 3, 4, 6, 11, 13, 17, 24] [1, 3, 5, 6, 8, 11, 15, 24] [1, 3, 4, 9, 11, 16, 18, 23] [1, 3, 4, 5, 10, 11, 13, 14] [1, 2, 5, 8, 10, 13, 16, 17] [1, 3, 4, 9, 10, 13, 15, 17] [1, 2, 4, 5, 6, 13, 16, 23] [1, 3, 4, 7, 8, 10, 19, 21] [1, 3, 5, 7, 8, 9, 19, 20] [1, 3, 4, 9, 11, 12, 16, 22] [1, 2, 4, 5, 9, 11, 17, 23] [1, 2, 3, 4, 9, 14, 18, 23] [1, 3, 4, 5, 11, 12, 15, 21] [1, 3, 5, 6, 11, 12, 19, 21] [1, 2, 5, 8, 11, 12, 13, 22] [1, 2, 4, 7, 10, 12, 13, 17] [1, 3, 4, 7, 8, 13, 18, 23] [1, 2, 5, 6, 7, 10, 18, 20] [1, 2, 4, 6, 7, 8, 17, 20] [1, 2, 4, 7, 10, 13, 14, 18] [1, 3, 4, 5, 8, 14, 16, 22] [1, 3, 4, 7, 8, 10, 17, 19] [1, 3, 5, 7, 8, 10, 16, 22] [1, 3, 4, 7, 8, 9, 17, 19] [1, 3, 5, 7, 9, 10, 18, 19] [1, 3, 5, 7, 8, 9, 15, 18] [1, 3, 4, 9, 10, 12, 13, 18] [1, 3, 5, 6, 8, 14, 18, 19] [1, 3, 4, 7, 9, 14, 17, 18] [1, 3, 5, 6, 11, 12, 13, 15] [1, 3, 4, 7, 8, 10, 18, 23] [1, 3, 5, 6, 11, 12, 14, 16] CPU times: user 6.02 s, sys: 44 ms, total: 6.06 s Wall time: 6.06 s 28 new smallest = 8 [1, 3, 4, 9, 11, 12, 16, 17] [1, 3, 4, 5, 10, 11, 14, 23] [1, 3, 4, 9, 10, 12, 13, 24] [1, 3, 4, 9, 10, 14, 16, 18] [1, 3, 5, 6, 11, 13, 15, 22] [1, 3, 5, 6, 9, 12, 13, 14] [1, 3, 5, 7, 9, 10, 19, 20] [1, 3, 4, 9, 11, 16, 17, 20] [1, 2, 5, 6, 9, 12, 13, 14] [1, 2, 5, 8, 10, 13, 14, 17] [1, 3, 4, 7, 9, 12, 13, 14] [1, 3, 5, 7, 8, 12, 13, 15] [1, 2, 5, 8, 11, 12, 14, 16] [1, 2, 5, 7, 10, 11, 14, 16] [1, 3, 4, 8, 9, 10, 15, 18] [1, 3, 4, 9, 11, 12, 14, 15] [1, 3, 5, 6, 13, 15, 17, 24] [1, 2, 5, 8, 11, 12, 13, 15] [1, 2, 5, 7, 11, 14, 16, 19] [1, 3, 4, 5, 8, 14, 20, 23] [1, 3, 5, 6, 11, 13, 14, 18] [1, 2, 4, 6, 7, 12, 13, 21] [1, 3, 4, 9, 11, 12, 15, 16] [1, 3, 5, 7, 8, 9, 18, 19] [1, 3, 5, 7, 8, 10, 17, 18] [1, 3, 4, 5, 11, 13, 14, 20] [1, 2, 5, 8, 10, 12, 13, 14] [1, 3, 5, 6, 8, 10, 17, 18] [1, 3, 5, 6, 8, 9, 18, 19] [1, 2, 4, 5, 11, 12, 14, 16] [1, 3, 5, 7, 9, 10, 17, 18] [1, 3, 4, 8, 10, 11, 17, 23] [1, 2, 4, 7, 10, 13, 15, 17] [1, 2, 5, 6, 7, 8, 17, 20] [1, 2, 5, 6, 8, 9, 17, 19] [1, 2, 5, 6, 7, 14, 17, 25] [1, 2, 5, 8, 11, 13, 14, 15] [1, 2, 5, 7, 10, 13, 14, 15] [1, 2, 5, 7, 10, 12, 16, 20] [1, 3, 4, 6, 11, 12, 14, 15] [1, 3, 4, 8, 9, 11, 13, 14] [1, 2, 3, 4, 8, 11, 17, 23] [1, 2, 5, 7, 9, 12, 14, 20] [1, 3, 4, 6, 11, 13, 14, 20] [1, 3, 5, 7, 8, 9, 16, 19] [1, 3, 4, 9, 10, 11, 13, 14] [1, 3, 4, 9, 11, 16, 20, 25] [1, 2, 5, 7, 10, 12, 13, 14] [1, 3, 4, 5, 10, 11, 14, 22] [1, 3, 4, 7, 8, 12, 13, 15] [1, 2, 5, 8, 9, 12, 14, 25] [1, 3, 5, 7, 8, 10, 19, 20] [1, 2, 4, 6, 9, 12, 13, 14] [1, 2, 5, 7, 10, 13, 14, 20] [1, 2, 5, 7, 10, 12, 15, 16] [1, 3, 4, 7, 8, 9, 19, 21] [1, 2, 4, 5, 6, 12, 14, 21] [1, 2, 4, 5, 11, 13, 19, 23] [1, 2, 4, 5, 11, 13, 14, 19] [1, 3, 4, 7, 8, 9, 18, 20] [1, 2, 5, 6, 8, 12, 13, 22] [1, 3, 4, 6, 10, 12, 13, 15] [1, 2, 4, 7, 10, 12, 13, 14] [1, 3, 4, 8, 9, 14, 16, 18] [1, 2, 5, 6, 8, 9, 18, 20] [1, 3, 5, 6, 8, 12, 18, 22] [1, 2, 4, 7, 9, 11, 17, 23] [1, 2, 4, 5, 10, 13, 14, 21] [1, 3, 4, 6, 10, 11, 13, 14] [1, 2, 3, 4, 9, 14, 19, 23] [1, 3, 5, 6, 12, 14, 16, 22] [1, 2, 3, 4, 9, 13, 19, 23] [1, 3, 5, 7, 9, 11, 13, 14] [1, 3, 4, 8, 10, 11, 13, 24] [1, 2, 5, 8, 11, 14, 15, 16] [1, 3, 4, 8, 9, 12, 13, 15] [1, 3, 5, 6, 13, 14, 20, 21] [1, 3, 4, 6, 8, 9, 18, 19] [1, 3, 4, 5, 11, 12, 14, 16] [1, 3, 5, 7, 8, 10, 18, 19] [1, 2, 5, 6, 9, 11, 19, 21] [1, 3, 4, 9, 10, 11, 14, 16] [1, 2, 5, 7, 11, 12, 14, 15] [1, 3, 4, 5, 8, 14, 17, 23] [1, 3, 5, 6, 9, 10, 16, 18] [1, 2, 5, 8, 11, 13, 15, 25] [1, 3, 4, 5, 9, 11, 16, 23] [1, 3, 4, 6, 10, 13, 14, 21] [1, 2, 4, 6, 8, 9, 19, 20] [1, 2, 5, 8, 10, 13, 17, 23] [1, 3, 4, 7, 9, 11, 16, 17] [1, 3, 5, 6, 8, 9, 19, 20] [1, 3, 5, 6, 12, 13, 15, 17] [1, 3, 4, 5, 10, 12, 18, 22] [1, 2, 5, 7, 9, 12, 13, 14] [1, 3, 4, 9, 11, 12, 14, 18] [1, 3, 4, 7, 9, 14, 19, 24] [1, 3, 4, 9, 11, 12, 13, 16] [1, 3, 4, 5, 8, 14, 20, 22] [1, 3, 5, 6, 10, 11, 13, 22] [1, 3, 5, 6, 7, 12, 16, 20] [1, 3, 4, 9, 11, 12, 14, 16] [1, 2, 5, 8, 11, 12, 13, 16] [1, 3, 5, 6, 10, 11, 13, 14] [1, 2, 5, 7, 10, 11, 13, 14] [1, 3, 5, 6, 10, 14, 17, 20] [1, 2, 5, 8, 11, 12, 13, 14] [1, 3, 5, 7, 9, 10, 21, 22] [1, 3, 5, 6, 8, 12, 19, 20] [1, 2, 5, 6, 7, 10, 18, 21] [1, 2, 5, 6, 7, 15, 18, 26] [1, 3, 5, 7, 9, 10, 20, 21] [1, 2, 5, 8, 9, 12, 13, 14] [1, 3, 4, 6, 11, 13, 17, 21] [1, 3, 4, 9, 10, 12, 13, 15] [1, 3, 4, 5, 11, 12, 13, 16] [1, 3, 5, 6, 8, 10, 16, 22] [1, 3, 5, 6, 12, 13, 20, 22] [1, 3, 4, 9, 10, 12, 14, 15] [1, 2, 5, 8, 10, 11, 13, 17] [1, 3, 5, 6, 11, 13, 14, 20] [1, 2, 5, 8, 11, 12, 13, 26] [1, 2, 5, 8, 9, 11, 13, 14] [1, 2, 5, 8, 10, 14, 17, 21] [1, 3, 5, 6, 13, 14, 18, 22] [1, 2, 3, 4, 9, 13, 19, 24] [1, 2, 4, 7, 9, 12, 13, 14] [1, 3, 4, 9, 11, 12, 16, 25] [1, 2, 4, 7, 10, 13, 14, 15] [1, 3, 4, 5, 8, 14, 20, 26] [1, 2, 5, 6, 7, 14, 17, 20] [1, 3, 4, 8, 10, 11, 13, 14] [1, 3, 4, 9, 11, 12, 16, 26] [1, 3, 4, 9, 11, 14, 15, 18] [1, 2, 5, 7, 11, 12, 14, 20] [1, 3, 4, 8, 10, 11, 14, 23] [1, 3, 5, 6, 11, 12, 14, 15] [1, 2, 4, 7, 9, 11, 16, 17] [1, 3, 4, 6, 8, 9, 19, 20] [1, 2, 3, 4, 5, 11, 17, 22] [1, 3, 4, 9, 10, 11, 12, 16] [1, 3, 4, 5, 8, 14, 19, 21] [1, 3, 4, 6, 10, 13, 15, 21] [1, 2, 4, 5, 10, 11, 13, 14] [1, 3, 5, 6, 13, 14, 21, 22] [1, 3, 4, 5, 6, 9, 16, 23] [1, 2, 4, 5, 10, 13, 14, 20] [1, 3, 4, 8, 10, 13, 14, 15] [1, 3, 4, 9, 10, 11, 13, 24] [1, 3, 4, 9, 10, 15, 17, 19] [1, 3, 5, 6, 12, 13, 15, 22] [1, 3, 4, 8, 9, 13, 14, 16] [1, 3, 5, 6, 12, 14, 15, 22] [1, 3, 4, 8, 9, 10, 14, 17] [1, 2, 3, 5, 6, 13, 15, 22] [1, 3, 4, 9, 10, 13, 14, 21] [1, 2, 5, 7, 10, 12, 16, 25] [1, 2, 4, 6, 8, 9, 18, 19] [1, 3, 5, 6, 13, 14, 18, 19] [1, 3, 5, 6, 8, 14, 18, 22] [1, 3, 4, 9, 10, 12, 16, 23] [1, 3, 5, 7, 8, 14, 18, 19] [1, 2, 5, 7, 11, 12, 13, 16] [1, 2, 4, 6, 8, 9, 19, 22] [1, 2, 5, 6, 7, 15, 18, 21] [1, 3, 4, 6, 11, 13, 17, 24] [1, 2, 3, 4, 9, 14, 18, 24] [1, 3, 4, 9, 11, 16, 17, 23] [1, 2, 5, 7, 11, 12, 13, 14] [1, 3, 4, 9, 10, 13, 15, 18] [1, 3, 4, 5, 7, 13, 15, 20] [1, 2, 5, 6, 8, 9, 19, 21] [1, 3, 4, 5, 10, 11, 13, 14] [1, 3, 5, 7, 8, 17, 18, 20] [1, 3, 4, 7, 8, 10, 18, 20] [1, 3, 5, 6, 8, 12, 13, 22] [1, 2, 5, 7, 8, 10, 17, 21] [1, 3, 4, 9, 10, 13, 15, 17] [1, 2, 4, 7, 10, 12, 14, 23] [1, 3, 5, 6, 13, 14, 19, 20] [1, 3, 5, 7, 8, 17, 19, 20] [1, 2, 4, 5, 6, 13, 16, 23] [1, 3, 5, 7, 9, 10, 18, 21] [1, 2, 5, 7, 11, 13, 14, 16] [1, 2, 5, 7, 11, 14, 15, 22] [1, 3, 5, 6, 8, 14, 18, 24] [1, 2, 3, 4, 5, 11, 17, 23] [1, 3, 5, 6, 11, 12, 14, 21] [1, 3, 4, 7, 8, 10, 19, 21] [1, 3, 5, 7, 8, 9, 19, 20] [1, 3, 5, 6, 11, 12, 14, 16] [1, 2, 3, 4, 5, 11, 16, 23] [1, 3, 4, 9, 11, 12, 13, 15] [1, 3, 5, 6, 8, 14, 17, 21] [1, 3, 4, 5, 8, 13, 14, 20] [1, 2, 4, 7, 8, 11, 17, 19] [1, 3, 4, 6, 11, 13, 14, 17] [1, 2, 3, 4, 9, 14, 18, 22] [1, 2, 5, 8, 10, 13, 14, 15] [1, 3, 4, 9, 11, 12, 16, 23] [1, 3, 4, 9, 11, 12, 16, 22] [1, 2, 4, 5, 9, 11, 17, 23] [1, 2, 3, 4, 9, 14, 18, 23] [1, 2, 4, 5, 11, 14, 16, 22] [1, 3, 4, 5, 8, 11, 17, 23] [1, 3, 4, 7, 8, 13, 15, 24] [1, 3, 4, 7, 8, 13, 18, 20] [1, 3, 4, 9, 10, 12, 13, 14] [1, 3, 4, 8, 9, 11, 17, 23] [1, 2, 5, 6, 7, 10, 18, 20] [1, 2, 4, 6, 7, 8, 17, 20] [1, 2, 4, 7, 10, 13, 14, 18] [1, 3, 4, 5, 8, 14, 16, 22] [1, 3, 4, 7, 8, 9, 17, 19] [1, 3, 5, 7, 9, 10, 18, 19] [1, 3, 4, 8, 10, 12, 13, 15] [1, 3, 5, 6, 7, 10, 18, 21] [1, 3, 4, 8, 10, 11, 13, 17] [1, 3, 4, 9, 11, 13, 14, 18] [1, 3, 4, 8, 9, 12, 13, 19] [1, 3, 4, 9, 10, 12, 13, 18] [1, 3, 5, 6, 8, 14, 18, 19] [1, 3, 4, 7, 9, 14, 17, 18] [1, 3, 5, 6, 11, 12, 13, 15] [1, 2, 5, 8, 11, 14, 16, 18] [1, 3, 4, 7, 8, 10, 18, 23] [1, 2, 3, 4, 9, 14, 19, 24] [1, 3, 5, 6, 10, 12, 13, 15] [1, 3, 5, 6, 11, 12, 16, 20] [1, 3, 4, 9, 10, 12, 14, 24] CPU times: user 12 ms, sys: 0 ns, total: 12 ms Wall time: 9.31 ms 29 new smallest = 8 [1, 3, 4, 9, 11, 12, 16, 17] [1, 3, 5, 7, 9, 10, 19, 20] [1, 3, 5, 7, 9, 10, 20, 21] [1, 3, 4, 9, 11, 16, 17, 20] [1, 3, 4, 7, 8, 10, 19, 21] [1, 3, 4, 5, 11, 12, 13, 16] [1, 3, 4, 9, 10, 12, 14, 15] [1, 2, 5, 6, 8, 9, 19, 21] [1, 2, 5, 8, 11, 14, 15, 16] [1, 3, 4, 9, 11, 12, 14, 15] [1, 3, 5, 6, 13, 15, 17, 24] [1, 2, 5, 7, 8, 10, 17, 21] [1, 2, 5, 8, 10, 14, 17, 21] [1, 2, 4, 5, 6, 13, 16, 23] [1, 3, 5, 6, 11, 13, 14, 18] [1, 3, 4, 9, 11, 12, 16, 25] [1, 2, 4, 7, 10, 13, 14, 15] [1, 3, 5, 7, 8, 10, 18, 19] [1, 3, 4, 5, 8, 14, 20, 26] [1, 2, 5, 7, 11, 13, 14, 16] [1, 3, 4, 9, 11, 12, 16, 26] [1, 3, 4, 9, 11, 14, 15, 18] [1, 3, 5, 6, 11, 12, 14, 15] [1, 2, 5, 7, 11, 14, 15, 22] [1, 3, 5, 6, 8, 14, 18, 24] [1, 3, 5, 7, 8, 9, 19, 20] [1, 3, 5, 6, 8, 14, 17, 21] [1, 2, 5, 7, 11, 12, 14, 15] [1, 2, 5, 8, 10, 13, 14, 15] [1, 3, 4, 6, 8, 9, 19, 20] [1, 3, 4, 5, 8, 14, 19, 21] [1, 2, 5, 8, 11, 13, 14, 15] [1, 2, 5, 7, 10, 13, 14, 15] [1, 3, 4, 6, 11, 12, 14, 15] [1, 3, 4, 5, 6, 9, 16, 23] [1, 3, 4, 8, 10, 13, 14, 15] [1, 2, 5, 7, 9, 12, 14, 20] [1, 2, 4, 6, 8, 9, 19, 20] [1, 3, 4, 9, 10, 15, 17, 19] [1, 3, 5, 6, 12, 13, 15, 17] [1, 3, 5, 6, 8, 9, 19, 20] [1, 3, 4, 8, 9, 13, 14, 16] [1, 3, 5, 7, 9, 10, 18, 19] [1, 3, 5, 6, 12, 14, 15, 22] [1, 3, 4, 9, 11, 12, 14, 18] [1, 3, 4, 9, 11, 16, 20, 25] [1, 3, 4, 9, 11, 12, 13, 16] [1, 3, 4, 9, 11, 13, 14, 18] [1, 3, 5, 7, 8, 10, 19, 20] [1, 2, 5, 8, 11, 12, 13, 16] [1, 3, 4, 7, 8, 9, 19, 21] [1, 3, 4, 7, 8, 9, 18, 20] [1, 2, 5, 8, 11, 14, 16, 18] [1, 2, 5, 6, 8, 9, 18, 20] [1, 3, 5, 7, 9, 10, 21, 22] [1, 2, 5, 7, 11, 12, 13, 16] CPU times: user 4 ms, sys: 0 ns, total: 4 ms Wall time: 5.6 ms 30 new smallest = 9 new smallest = 8 [1, 3, 5, 7, 9, 10, 19, 20] [1, 3, 5, 7, 9, 10, 20, 21] [1, 3, 4, 9, 10, 12, 14, 15] [1, 2, 5, 6, 8, 9, 19, 21] [1, 2, 5, 8, 11, 14, 15, 16] [1, 3, 4, 9, 11, 12, 14, 15] [1, 3, 5, 6, 13, 15, 17, 24] [1, 2, 5, 7, 11, 13, 14, 16] [1, 2, 4, 7, 10, 13, 14, 15] [1, 3, 4, 5, 8, 14, 20, 26] [1, 2, 5, 7, 11, 14, 15, 22] [1, 3, 5, 6, 8, 14, 18, 24] [1, 3, 4, 9, 11, 12, 16, 26] [1, 3, 4, 9, 11, 14, 15, 18] [1, 3, 5, 6, 11, 12, 14, 15] [1, 2, 5, 7, 11, 12, 14, 15] [1, 2, 5, 8, 10, 13, 14, 15] [1, 2, 5, 8, 11, 13, 14, 15] [1, 2, 5, 7, 10, 13, 14, 15] [1, 3, 4, 6, 11, 12, 14, 15] [1, 3, 4, 8, 10, 13, 14, 15] [1, 3, 4, 9, 10, 15, 17, 19] [1, 3, 5, 6, 12, 13, 15, 17] [1, 3, 4, 8, 9, 13, 14, 16] [1, 3, 5, 6, 12, 14, 15, 22] [1, 3, 4, 9, 11, 12, 14, 18] [1, 3, 5, 7, 8, 10, 19, 20] [1, 3, 4, 7, 8, 9, 19, 21] [1, 2, 5, 8, 11, 14, 16, 18] [1, 3, 5, 7, 9, 10, 21, 22] CPU times: user 0 ns, sys: 0 ns, total: 0 ns Wall time: 1.36 ms
n = 30
print(n+1)
%time upgrade(cmap, n, n+1)
31 new smallest = 9 new smallest = 8 [1, 2, 5, 8, 11, 14, 15, 16] [1, 3, 4, 5, 8, 14, 20, 26] [1, 3, 5, 7, 9, 10, 21, 22] [1, 3, 5, 7, 9, 10, 20, 21] CPU times: user 0 ns, sys: 0 ns, total: 0 ns Wall time: 811 µs
n = 31
print(n+1)
%time upgrade(cmap, n, n+1)
32 new smallest = 8 [1, 2, 5, 8, 11, 14, 15, 16] [1, 3, 5, 7, 9, 10, 21, 22] CPU times: user 0 ns, sys: 0 ns, total: 0 ns Wall time: 190 µs
n = 32
print(n+1)
%time upgrade(cmap, n, n+1)
33 new smallest = 9 considering 1 considering 2 considering 3 considering 4 [1, 2, 5, 8, 9, 10, 18, 20, 23] [1, 3, 5, 6, 13, 15, 16, 20, 21] [1, 3, 5, 6, 13, 14, 16, 17, 19] [1, 3, 4, 5, 8, 14, 17, 23, 29] [1, 2, 4, 6, 8, 10, 11, 22, 25] [1, 3, 4, 9, 11, 16, 17, 20, 26] [1, 3, 4, 6, 10, 14, 15, 16, 17] [1, 3, 4, 6, 8, 9, 11, 21, 22] [1, 3, 5, 7, 9, 10, 20, 21, 32] [1, 2, 5, 7, 10, 13, 15, 19, 26] [1, 3, 5, 6, 11, 12, 17, 19, 21] [1, 2, 5, 6, 7, 11, 15, 18, 26] [1, 3, 4, 9, 11, 12, 14, 16, 17] [1, 3, 4, 5, 8, 14, 20, 23, 29] [1, 3, 4, 5, 11, 13, 18, 20, 27] [1, 3, 5, 6, 8, 11, 15, 21, 25] [1, 3, 5, 6, 8, 14, 16, 17, 26] [1, 3, 5, 6, 10, 11, 18, 20, 27] [1, 2, 4, 5, 6, 11, 13, 19, 27] [1, 2, 5, 8, 10, 14, 16, 19, 23] [1, 2, 5, 8, 10, 13, 14, 15, 31] [1, 3, 4, 6, 10, 13, 15, 18, 26] [1, 3, 4, 9, 11, 16, 19, 20, 22] [1, 3, 4, 8, 9, 14, 15, 17, 19] [1, 3, 4, 9, 10, 13, 15, 18, 29] [1, 3, 4, 9, 11, 12, 14, 18, 19] [1, 3, 4, 9, 11, 16, 17, 20, 29] [1, 3, 4, 7, 8, 13, 15, 23, 25] [1, 2, 5, 6, 8, 14, 16, 17, 21] [1, 3, 4, 9, 10, 14, 16, 17, 19] [1, 3, 4, 5, 6, 9, 16, 20, 27] [1, 2, 4, 5, 11, 13, 14, 19, 29] [1, 3, 5, 7, 9, 10, 20, 22, 23] [1, 3, 5, 7, 9, 10, 12, 20, 21] [1, 3, 5, 7, 9, 10, 21, 22, 23] [1, 2, 5, 6, 7, 14, 15, 18, 25] [1, 3, 4, 7, 9, 12, 15, 16, 26] [1, 3, 4, 9, 11, 14, 15, 18, 30] [1, 3, 4, 8, 9, 14, 16, 17, 26] [1, 3, 5, 6, 10, 14, 15, 16, 17] [1, 3, 4, 6, 10, 15, 16, 18, 23] [1, 3, 4, 9, 10, 14, 15, 21, 23] [1, 2, 5, 6, 9, 10, 12, 22, 24] [1, 3, 4, 9, 11, 16, 17, 20, 27] [1, 2, 4, 5, 10, 12, 17, 21, 28] [1, 2, 4, 7, 10, 13, 14, 18, 29] [1, 3, 4, 5, 7, 13, 15, 20, 28] [1, 2, 5, 8, 10, 14, 15, 16, 25] [1, 3, 4, 7, 8, 11, 13, 23, 25] [1, 3, 4, 7, 9, 14, 15, 17, 18] [1, 2, 5, 8, 11, 14, 17, 18, 19] [1, 3, 5, 7, 8, 14, 15, 24, 26] [1, 2, 3, 4, 9, 13, 16, 20, 27] [1, 3, 4, 9, 10, 13, 14, 16, 17] [1, 3, 4, 8, 9, 11, 20, 22, 23] [1, 3, 4, 9, 11, 12, 15, 16, 17] [1, 2, 5, 7, 10, 12, 15, 16, 28] [1, 3, 4, 7, 8, 13, 18, 23, 25] [1, 3, 5, 6, 8, 10, 16, 23, 24] [1, 3, 5, 7, 8, 14, 16, 17, 26] [1, 3, 4, 9, 11, 12, 15, 16, 18] [1, 3, 4, 6, 10, 14, 16, 19, 21] [1, 2, 5, 6, 7, 15, 17, 25, 27] [1, 2, 5, 7, 8, 10, 12, 20, 21] [1, 3, 4, 6, 7, 9, 16, 20, 24] [1, 3, 4, 7, 9, 14, 17, 18, 26] [1, 3, 4, 6, 7, 12, 14, 19, 26] [1, 3, 4, 9, 11, 12, 16, 17, 30] [1, 3, 4, 9, 11, 14, 15, 17, 24] [1, 3, 5, 7, 9, 11, 12, 21, 22] [1, 2, 5, 7, 10, 13, 14, 15, 18] [1, 3, 4, 5, 8, 12, 13, 19, 25] [1, 2, 5, 8, 11, 13, 15, 20, 27] [1, 2, 5, 8, 11, 14, 15, 17, 19] [1, 3, 4, 9, 11, 14, 15, 18, 31] [1, 3, 5, 6, 12, 13, 15, 16, 20] [1, 3, 4, 5, 11, 13, 14, 20, 29] [1, 3, 4, 6, 10, 15, 16, 23, 28] [1, 3, 4, 5, 6, 9, 16, 22, 24] [1, 3, 4, 7, 8, 11, 13, 22, 24] [1, 2, 3, 5, 7, 10, 16, 22, 28] [1, 3, 4, 9, 11, 14, 15, 18, 28] [1, 3, 5, 7, 8, 16, 17, 26, 27] [1, 2, 5, 8, 9, 10, 19, 22, 25] [1, 3, 4, 5, 10, 11, 12, 15, 28] [1, 3, 4, 6, 10, 13, 15, 16, 23] [1, 3, 4, 7, 9, 12, 13, 19, 26] [1, 2, 5, 6, 9, 10, 12, 23, 25] [1, 3, 4, 8, 9, 13, 15, 16, 18] [1, 2, 5, 7, 11, 14, 15, 16, 22] [1, 2, 3, 5, 6, 11, 13, 20, 27] [1, 2, 5, 8, 10, 13, 14, 16, 17] [1, 2, 5, 7, 11, 12, 14, 18, 26] [1, 3, 5, 6, 11, 12, 16, 17, 25] [1, 3, 4, 6, 7, 13, 15, 20, 25] [1, 3, 4, 5, 8, 11, 17, 23, 29] [1, 3, 4, 8, 9, 12, 13, 19, 21] [1, 3, 5, 6, 7, 10, 12, 20, 28] [1, 2, 5, 6, 7, 14, 16, 24, 27] [1, 3, 4, 7, 8, 13, 15, 24, 29] [1, 3, 5, 7, 8, 14, 15, 19, 24] [1, 3, 4, 8, 10, 15, 17, 21, 25] [1, 2, 5, 8, 10, 13, 17, 19, 23] [1, 2, 4, 7, 10, 13, 16, 18, 20] [1, 2, 5, 7, 11, 14, 15, 22, 31] [1, 2, 4, 5, 11, 13, 19, 23, 29] [1, 3, 4, 6, 11, 13, 14, 16, 17] [1, 3, 4, 6, 10, 11, 15, 23, 28] [1, 3, 4, 5, 11, 12, 14, 16, 28] [1, 2, 3, 4, 5, 11, 16, 22, 27] [1, 2, 4, 6, 8, 10, 13, 22, 23] [1, 2, 5, 6, 9, 13, 15, 16, 18] [1, 3, 5, 7, 8, 13, 14, 16, 17] [1, 2, 4, 5, 10, 13, 14, 20, 27] [1, 3, 5, 7, 9, 11, 12, 25, 26] [1, 2, 5, 7, 8, 10, 19, 21, 25] [1, 2, 5, 8, 9, 10, 17, 21, 23] [1, 2, 3, 5, 6, 7, 15, 18, 26] [1, 3, 4, 9, 10, 12, 13, 20, 27] [1, 3, 5, 7, 9, 11, 12, 24, 25] [1, 3, 4, 6, 8, 10, 11, 23, 24] [1, 3, 4, 7, 8, 10, 11, 22, 24] [1, 2, 5, 7, 10, 13, 15, 16, 17] [1, 3, 5, 7, 8, 15, 16, 24, 25] [1, 2, 4, 6, 7, 15, 16, 23, 26] [1, 2, 5, 6, 7, 15, 18, 26, 29] [1, 3, 5, 6, 8, 11, 12, 21, 25] [1, 3, 5, 6, 7, 10, 15, 18, 26] [1, 2, 4, 5, 7, 13, 15, 16, 20] [1, 3, 5, 6, 8, 14, 18, 21, 25] [1, 3, 5, 7, 8, 9, 12, 22, 25] [1, 3, 5, 7, 8, 12, 14, 18, 26] [1, 2, 5, 6, 7, 15, 18, 24, 26] [1, 3, 4, 9, 10, 14, 15, 18, 22] [1, 2, 3, 4, 5, 11, 17, 23, 28] [1, 3, 5, 6, 7, 12, 15, 22, 26] [1, 2, 4, 6, 7, 15, 16, 24, 27] [1, 2, 4, 7, 10, 13, 15, 16, 20] [1, 3, 4, 8, 9, 13, 14, 16, 17] [1, 2, 4, 7, 9, 11, 16, 19, 22] [1, 3, 4, 8, 9, 10, 14, 17, 29] [1, 2, 5, 8, 11, 14, 15, 16, 25] [1, 3, 5, 6, 11, 13, 15, 16, 22] [1, 2, 4, 5, 8, 9, 10, 21, 23] [1, 2, 4, 5, 11, 14, 15, 16, 22] [1, 2, 5, 7, 11, 14, 15, 16, 17] [1, 3, 5, 6, 11, 13, 15, 20, 26] [1, 2, 5, 6, 7, 11, 14, 22, 25] [1, 2, 5, 6, 9, 12, 15, 16, 17] [1, 3, 4, 5, 11, 13, 16, 20, 27] [1, 3, 4, 5, 11, 13, 19, 20, 24] [1, 3, 4, 6, 10, 15, 16, 23, 24] [1, 2, 5, 8, 9, 10, 21, 23, 25] [1, 3, 4, 9, 11, 16, 20, 24, 26] [1, 2, 4, 7, 10, 12, 15, 16, 17] [1, 3, 4, 8, 10, 14, 16, 17, 19] [1, 2, 4, 7, 8, 13, 14, 16, 17] [1, 3, 5, 6, 13, 15, 16, 17, 24] [1, 2, 5, 7, 11, 13, 16, 17, 20] [1, 2, 4, 6, 9, 13, 15, 18, 23] [1, 2, 4, 7, 9, 10, 14, 22, 23] [1, 2, 5, 7, 9, 13, 14, 16, 17] [1, 3, 5, 6, 7, 14, 15, 18, 26] [1, 3, 4, 9, 11, 16, 20, 25, 29] [1, 2, 3, 4, 9, 14, 19, 24, 29] [1, 3, 5, 6, 11, 13, 15, 22, 26] [1, 3, 4, 6, 10, 13, 14, 17, 19] [1, 2, 5, 6, 7, 13, 15, 23, 26] [1, 2, 5, 8, 9, 10, 19, 22, 24] [1, 3, 4, 5, 11, 12, 13, 16, 30] [1, 2, 5, 8, 11, 13, 14, 15, 31] [1, 3, 4, 6, 8, 10, 11, 21, 22] [1, 3, 4, 7, 8, 10, 11, 21, 23] [1, 3, 5, 7, 8, 17, 18, 25, 26] [1, 3, 5, 6, 8, 10, 11, 21, 22] [1, 3, 4, 9, 11, 15, 16, 20, 24] [1, 3, 4, 7, 8, 9, 10, 21, 23] [1, 3, 5, 6, 11, 13, 14, 18, 19] [1, 2, 5, 6, 8, 14, 15, 18, 25] [1, 2, 5, 6, 8, 9, 10, 21, 23] [1, 3, 4, 9, 11, 14, 15, 18, 27] [1, 2, 5, 8, 11, 12, 15, 16, 17] [1, 2, 4, 6, 9, 14, 15, 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[1, 2, 5, 6, 7, 15, 18, 22, 25] [1, 3, 5, 6, 8, 10, 16, 22, 28] [1, 3, 5, 6, 11, 13, 14, 20, 29] [1, 2, 5, 8, 10, 13, 17, 23, 24] [1, 2, 3, 4, 9, 14, 19, 23, 27] [1, 3, 4, 8, 10, 15, 17, 18, 21] [1, 3, 4, 7, 9, 14, 19, 22, 23] [1, 3, 5, 6, 13, 14, 16, 18, 19] [1, 3, 5, 7, 8, 15, 16, 20, 26] [1, 3, 4, 8, 10, 14, 16, 19, 21] [1, 2, 5, 8, 9, 10, 21, 22, 23] [1, 3, 5, 6, 10, 11, 15, 18, 21] [1, 3, 5, 6, 11, 13, 15, 16, 20] [1, 3, 4, 9, 11, 12, 16, 17, 27] [1, 3, 4, 8, 10, 11, 16, 22, 28] [1, 3, 4, 9, 11, 13, 14, 16, 17] [1, 3, 5, 7, 8, 14, 15, 17, 19] [1, 3, 5, 7, 8, 15, 16, 25, 26] [1, 2, 3, 4, 5, 11, 16, 23, 29] [1, 2, 4, 5, 11, 13, 19, 20, 27] [1, 3, 4, 6, 11, 13, 14, 17, 29] [1, 3, 4, 5, 10, 12, 18, 22, 28] [1, 2, 5, 6, 7, 15, 17, 24, 26] [1, 3, 5, 6, 9, 13, 14, 18, 24] [1, 3, 5, 7, 8, 10, 12, 20, 26] [1, 3, 5, 7, 8, 10, 14, 22, 26] [1, 3, 4, 9, 11, 15, 16, 17, 20] [1, 2, 5, 8, 9, 10, 19, 21, 24] [1, 3, 4, 6, 9, 10, 14, 21, 23] [1, 3, 4, 9, 11, 13, 14, 16, 20] [1, 3, 5, 7, 9, 10, 21, 22, 28] [1, 3, 4, 9, 11, 16, 17, 20, 30] [1, 2, 5, 6, 8, 9, 19, 21, 31] [1, 2, 5, 8, 11, 13, 15, 16, 20] [1, 2, 4, 6, 9, 10, 15, 22, 27] [1, 3, 4, 5, 6, 7, 10, 18, 26] [1, 2, 4, 5, 9, 12, 15, 21, 27] [1, 2, 5, 6, 9, 13, 16, 18, 28] [1, 3, 4, 9, 11, 13, 16, 20, 27] [1, 3, 4, 9, 11, 13, 19, 20, 24] [1, 3, 5, 7, 8, 10, 14, 22, 23] [1, 3, 5, 7, 8, 10, 11, 23, 24] [1, 3, 5, 7, 9, 11, 12, 20, 21] [1, 3, 4, 7, 8, 9, 12, 21, 23] [1, 3, 5, 6, 11, 12, 14, 16, 17] [1, 3, 5, 7, 8, 16, 17, 24, 25] [1, 3, 4, 8, 9, 10, 14, 21, 23] [1, 2, 5, 6, 7, 14, 16, 23, 26] [1, 2, 5, 7, 11, 13, 14, 16, 20] [1, 2, 4, 5, 11, 12, 14, 16, 29] [1, 2, 5, 7, 10, 13, 16, 17, 18] [1, 2, 5, 7, 9, 11, 14, 16, 24] [1, 3, 5, 6, 8, 15, 16, 25, 26] [1, 2, 5, 8, 10, 14, 16, 17, 21] [1, 2, 5, 8, 9, 10, 21, 24, 26] [1, 2, 3, 4, 5, 11, 17, 22, 28] [1, 3, 4, 8, 10, 14, 15, 18, 23] [1, 3, 4, 7, 9, 12, 13, 20, 27] [1, 3, 4, 6, 7, 15, 17, 24, 26] [1, 2, 5, 7, 11, 14, 16, 19, 29] [1, 2, 4, 5, 11, 14, 16, 22, 29] [1, 3, 4, 6, 10, 14, 16, 17, 25] [1, 2, 5, 8, 9, 12, 14, 22, 24] [1, 2, 5, 7, 11, 13, 16, 17, 18] [1, 2, 5, 8, 9, 11, 14, 21, 22] [1, 3, 4, 6, 8, 10, 11, 22, 23] [1, 2, 4, 5, 11, 14, 15, 17, 22] [1, 3, 4, 7, 8, 13, 18, 20, 29] [1, 2, 4, 5, 6, 9, 15, 21, 27] [1, 2, 5, 7, 11, 13, 14, 16, 31] [1, 3, 4, 5, 11, 13, 14, 18, 19] [1, 3, 4, 9, 10, 14, 15, 17, 19] [1, 2, 5, 8, 9, 10, 20, 23, 26] [1, 2, 5, 7, 8, 9, 19, 21, 24] [1, 3, 4, 9, 10, 12, 13, 18, 29] [1, 3, 5, 7, 9, 10, 11, 23, 24] [1, 2, 5, 6, 7, 14, 17, 25, 28] [1, 2, 5, 8, 10, 14, 16, 23, 27] [1, 3, 5, 7, 9, 10, 20, 21, 23] [1, 3, 4, 5, 6, 9, 16, 23, 27] [1, 2, 4, 6, 9, 14, 16, 17, 23] [1, 2, 4, 7, 8, 9, 18, 21, 24] [1, 3, 4, 6, 8, 12, 15, 16, 25] [1, 2, 5, 8, 11, 14, 15, 16, 28] [1, 3, 5, 6, 10, 14, 15, 17, 23] [1, 2, 4, 6, 8, 10, 11, 23, 26] [1, 3, 4, 8, 9, 11, 21, 23, 24] [1, 3, 4, 8, 9, 14, 15, 17, 24] [1, 3, 5, 6, 13, 14, 15, 18, 19] [1, 3, 5, 7, 9, 10, 16, 22, 23] [1, 3, 4, 9, 10, 15, 16, 18, 20] [1, 3, 4, 9, 11, 14, 15, 16, 17] [1, 3, 5, 6, 13, 14, 15, 18, 22] [1, 3, 5, 7, 9, 10, 18, 22, 23] [1, 3, 4, 9, 11, 13, 16, 17, 22] [1, 3, 4, 6, 7, 15, 17, 22, 27] [1, 3, 4, 9, 11, 12, 16, 22, 26] [1, 3, 4, 9, 11, 14, 15, 18, 22] [1, 3, 5, 7, 8, 14, 15, 24, 25] [1, 3, 4, 6, 10, 14, 16, 17, 19] [1, 3, 4, 7, 8, 10, 18, 22, 23] [1, 2, 3, 4, 9, 14, 18, 24, 27] [1, 3, 4, 9, 11, 14, 15, 18, 20] [1, 3, 5, 7, 9, 10, 11, 22, 23] [1, 2, 4, 5, 9, 11, 17, 23, 29] [1, 2, 3, 4, 9, 14, 18, 23, 29] [1, 3, 4, 9, 11, 12, 16, 22, 29] [1, 3, 5, 6, 7, 13, 14, 15, 18] [1, 3, 5, 6, 8, 14, 15, 19, 26] [1, 3, 5, 6, 11, 13, 14, 18, 30] [1, 3, 5, 7, 8, 14, 17, 22, 25] [1, 2, 5, 8, 9, 12, 13, 19, 21] [1, 3, 5, 6, 12, 14, 16, 17, 22] [1, 2, 4, 7, 8, 13, 16, 18, 26] [1, 2, 5, 7, 11, 12, 13, 17, 20] [1, 3, 4, 5, 8, 13, 15, 18, 24] [1, 3, 5, 6, 9, 12, 15, 16, 17] [1, 3, 5, 6, 13, 14, 16, 17, 24] [1, 3, 4, 9, 11, 14, 16, 20, 22] [1, 3, 5, 6, 12, 13, 15, 17, 30] [1, 3, 5, 6, 10, 13, 16, 24, 28] [1, 2, 3, 4, 5, 11, 16, 23, 28] [1, 3, 4, 8, 10, 12, 15, 16, 21] [1, 2, 3, 4, 5, 11, 17, 22, 29] [1, 3, 4, 6, 11, 12, 14, 18, 27] [1, 3, 4, 5, 8, 9, 10, 21, 23] [1, 2, 5, 7, 11, 14, 15, 16, 19] [1, 2, 5, 8, 9, 10, 18, 21, 23] [1, 2, 3, 4, 5, 6, 13, 19, 27] [1, 2, 4, 7, 10, 13, 15, 16, 17] [1, 3, 5, 6, 8, 10, 11, 23, 24] [1, 3, 5, 7, 8, 10, 12, 21, 22] [1, 2, 5, 7, 11, 15, 17, 20, 22] [1, 3, 4, 5, 11, 13, 15, 16, 20] [1, 3, 4, 7, 8, 9, 19, 21, 24] [1, 3, 5, 7, 9, 11, 12, 22, 23] [1, 2, 4, 5, 11, 14, 16, 22, 27] [1, 3, 5, 6, 8, 10, 16, 22, 23] [1, 2, 5, 7, 11, 14, 16, 19, 24] [1, 2, 3, 4, 9, 13, 19, 24, 28] [1, 2, 5, 8, 10, 12, 17, 20, 21] [1, 3, 5, 6, 11, 12, 14, 16, 28] [1, 3, 4, 7, 8, 13, 15, 24, 26] [1, 2, 4, 5, 9, 10, 16, 22, 28] [1, 3, 4, 5, 9, 10, 13, 20, 27] [1, 3, 4, 9, 11, 16, 21, 22, 25] [1, 2, 4, 5, 11, 12, 14, 19, 27] [1, 3, 5, 7, 8, 10, 14, 23, 24] [1, 3, 4, 8, 9, 13, 14, 16, 30] [1, 2, 5, 8, 9, 10, 21, 23, 27] [1, 3, 4, 5, 11, 13, 14, 15, 18] [1, 3, 4, 8, 10, 13, 14, 15, 18] [1, 3, 5, 7, 9, 10, 21, 22, 32] [1, 3, 4, 5, 11, 13, 16, 20, 25] [1, 3, 4, 9, 10, 15, 17, 19, 30] [1, 2, 4, 5, 11, 14, 15, 16, 19] [1, 2, 5, 8, 10, 14, 15, 16, 17] [1, 3, 5, 6, 10, 14, 16, 17, 24] [1, 3, 4, 6, 7, 15, 17, 25, 26] [1, 3, 4, 8, 10, 11, 15, 16, 25] [1, 2, 5, 7, 8, 9, 15, 19, 24] [1, 3, 5, 6, 12, 14, 15, 18, 19] [1, 2, 5, 6, 7, 14, 17, 24, 27] [1, 2, 5, 6, 7, 15, 18, 25, 27] [1, 2, 5, 8, 10, 13, 14, 16, 23] [1, 3, 4, 8, 9, 11, 19, 21, 22] [1, 2, 4, 5, 11, 13, 14, 18, 19] [1, 3, 4, 9, 11, 16, 21, 22, 28] [1, 3, 5, 6, 10, 11, 18, 25, 27] [1, 2, 5, 7, 11, 13, 14, 15, 18] [1, 3, 5, 6, 13, 15, 17, 24, 28] [1, 2, 5, 6, 7, 15, 18, 23, 25] [1, 3, 5, 7, 8, 10, 16, 22, 28] [1, 2, 5, 8, 9, 10, 17, 20, 23] [1, 2, 5, 7, 10, 12, 15, 17, 21] [1, 3, 4, 8, 9, 11, 15, 20, 24] [1, 3, 4, 8, 10, 11, 16, 20, 25] [1, 3, 4, 5, 8, 14, 20, 26, 32] [1, 2, 3, 4, 8, 11, 17, 23, 29] [1, 3, 4, 8, 10, 15, 16, 18, 26] [1, 2, 5, 6, 7, 14, 17, 23, 26] [1, 2, 5, 6, 8, 13, 14, 16, 17] [1, 2, 5, 7, 9, 13, 14, 15, 18] [1, 3, 4, 8, 9, 11, 20, 22, 24] [1, 3, 4, 9, 11, 13, 18, 19, 22] [1, 2, 5, 7, 11, 12, 15, 16, 18] [1, 3, 4, 7, 9, 12, 16, 19, 26] [1, 2, 5, 8, 11, 14, 15, 16, 31] [1, 2, 5, 8, 9, 11, 15, 16, 28] [1, 2, 4, 6, 8, 10, 11, 21, 22] [1, 3, 4, 9, 11, 16, 17, 20, 21] [1, 3, 4, 8, 10, 14, 19, 21, 22] [1, 2, 5, 6, 7, 13, 15, 18, 27] [1, 2, 5, 7, 11, 12, 15, 20, 28] [1, 3, 5, 6, 8, 14, 18, 24, 28] [1, 3, 4, 7, 9, 10, 14, 22, 26] [1, 2, 5, 8, 10, 13, 14, 15, 18] [1, 2, 4, 5, 9, 12, 13, 18, 28] [1, 3, 4, 9, 10, 13, 15, 18, 28] [1, 3, 5, 6, 13, 15, 17, 24, 30] [1, 3, 4, 9, 10, 14, 15, 16, 18] [1, 3, 5, 7, 8, 15, 16, 22, 25] [1, 3, 4, 8, 10, 13, 14, 17, 19] [1, 2, 3, 4, 9, 14, 19, 23, 28] [1, 3, 4, 9, 10, 14, 15, 17, 18] [1, 2, 5, 8, 11, 13, 16, 20, 22] [1, 2, 5, 6, 8, 14, 16, 23, 25] [1, 3, 4, 9, 11, 15, 17, 22, 26] [1, 2, 5, 7, 11, 14, 15, 17, 22] [1, 3, 4, 5, 8, 11, 15, 16, 25] [1, 2, 5, 8, 11, 14, 16, 18, 31] [1, 3, 4, 6, 8, 9, 16, 20, 27] [1, 3, 5, 6, 10, 11, 15, 18, 26] [1, 2, 5, 8, 11, 14, 15, 16, 22] [1, 2, 5, 7, 9, 12, 15, 23, 24] [1, 2, 5, 7, 10, 13, 14, 15, 31] [1, 2, 4, 6, 9, 10, 15, 22, 23] [1, 2, 5, 7, 11, 12, 15, 21, 24] [1, 3, 5, 6, 7, 14, 16, 18, 26] [1, 3, 4, 6, 7, 10, 15, 23, 25] [1, 3, 4, 7, 9, 13, 14, 15, 18] [1, 3, 4, 9, 11, 12, 13, 15, 20] [1, 3, 4, 7, 8, 10, 18, 23, 28] [1, 3, 4, 6, 11, 13, 14, 16, 20] [1, 2, 5, 7, 11, 15, 17, 18, 20] [1, 3, 4, 5, 7, 13, 15, 16, 20] [1, 2, 4, 7, 10, 13, 15, 17, 29] [1, 3, 4, 9, 10, 12, 14, 16, 17] [1, 3, 5, 7, 9, 10, 21, 22, 24] [1, 2, 5, 6, 7, 15, 16, 19, 27] [1, 2, 5, 8, 9, 12, 15, 16, 17] [1, 2, 4, 7, 10, 13, 16, 17, 18] [1, 3, 4, 9, 10, 13, 14, 19, 21] [1, 3, 5, 6, 8, 11, 15, 24, 28] [1, 3, 5, 6, 11, 13, 14, 16, 20] [1, 3, 5, 6, 12, 13, 14, 17, 20] [1, 2, 5, 8, 11, 12, 15, 18, 20] [1, 3, 5, 7, 9, 11, 12, 21, 24] [1, 2, 5, 8, 10, 12, 13, 19, 20] [1, 2, 3, 4, 6, 10, 15, 22, 27] [1, 2, 5, 7, 11, 15, 16, 17, 18] [1, 3, 4, 8, 10, 14, 15, 17, 23] [1, 3, 5, 6, 12, 13, 15, 17, 28] [1, 3, 5, 6, 13, 15, 17, 18, 24] [1, 3, 5, 7, 8, 16, 17, 23, 24] [1, 3, 4, 6, 7, 15, 16, 21, 26] [1, 3, 5, 7, 9, 11, 12, 23, 24] [1, 3, 5, 6, 12, 13, 14, 16, 17] [1, 3, 4, 7, 9, 15, 17, 22, 24] [1, 3, 4, 6, 11, 13, 14, 18, 19] [1, 2, 5, 8, 10, 11, 13, 16, 20] [1, 3, 4, 7, 9, 15, 16, 18, 25] [1, 2, 4, 6, 8, 10, 13, 22, 25] [1, 3, 4, 6, 7, 15, 17, 25, 27] [1, 3, 4, 8, 10, 14, 15, 17, 18] [1, 3, 4, 7, 8, 10, 18, 23, 25] [1, 2, 5, 6, 8, 14, 17, 19, 24] [1, 2, 4, 6, 9, 13, 15, 19, 27] [1, 3, 4, 5, 11, 12, 15, 21, 28] [1, 3, 4, 9, 10, 11, 16, 17, 20] [1, 3, 5, 7, 8, 12, 15, 20, 26] [1, 3, 4, 7, 9, 15, 16, 21, 26] [1, 3, 4, 6, 7, 9, 10, 21, 23] [1, 2, 4, 6, 8, 10, 11, 23, 24] [1, 3, 5, 6, 8, 13, 14, 16, 17] [1, 2, 3, 4, 9, 14, 18, 24, 29] [1, 2, 5, 6, 9, 13, 15, 18, 23] [1, 2, 4, 6, 7, 14, 16, 17, 25] [1, 3, 4, 8, 10, 14, 15, 17, 25] [1, 3, 4, 9, 11, 13, 14, 18, 19] [1, 2, 5, 6, 7, 15, 17, 25, 28] [1, 3, 5, 6, 11, 13, 14, 18, 27] [1, 3, 5, 6, 9, 10, 15, 17, 28] [1, 2, 4, 5, 11, 12, 18, 21, 27] [1, 3, 4, 8, 9, 13, 15, 16, 24] [1, 2, 5, 7, 11, 15, 16, 17, 24] [1, 3, 5, 7, 9, 10, 11, 20, 23] [1, 2, 5, 8, 11, 14, 15, 16, 32] [1, 3, 4, 6, 11, 13, 18, 19, 27] [1, 2, 4, 5, 11, 13, 14, 19, 27] [1, 3, 5, 7, 9, 10, 21, 23, 24] [1, 3, 4, 6, 11, 13, 15, 16, 22] [1, 3, 4, 9, 11, 13, 16, 17, 20] [1, 2, 5, 8, 9, 10, 18, 21, 24] [1, 2, 5, 7, 11, 12, 13, 20, 28] [1, 2, 5, 8, 10, 13, 16, 17, 18] [1, 2, 4, 5, 6, 10, 13, 20, 27] [1, 2, 4, 7, 9, 11, 16, 17, 29] [1, 2, 5, 8, 11, 14, 17, 19, 21] [1, 3, 4, 5, 11, 13, 15, 16, 22] [1, 3, 5, 6, 8, 11, 15, 24, 25] [1, 2, 4, 7, 9, 11, 17, 23, 29] [1, 2, 5, 7, 11, 13, 14, 16, 26] [1, 3, 4, 9, 11, 12, 16, 26, 30] [1, 3, 4, 8, 9, 12, 13, 19, 29] [1, 2, 5, 6, 7, 14, 15, 18, 26] [1, 2, 5, 6, 7, 15, 18, 23, 26] [1, 2, 5, 6, 7, 8, 12, 21, 24] [1, 3, 5, 6, 12, 14, 16, 17, 24] [1, 3, 4, 5, 8, 14, 16, 22, 28] [1, 3, 4, 7, 8, 13, 14, 16, 17] [1, 3, 5, 7, 9, 10, 16, 21, 24] [1, 3, 4, 5, 8, 14, 20, 26, 28] [1, 3, 4, 8, 9, 14, 19, 21, 23] [1, 2, 5, 8, 11, 14, 15, 16, 17] [1, 2, 5, 7, 8, 10, 19, 22, 23] [1, 3, 5, 7, 8, 17, 18, 24, 25] [1, 2, 5, 8, 10, 12, 19, 20, 21] [1, 3, 5, 7, 8, 17, 18, 27, 28] [1, 3, 5, 6, 10, 11, 15, 16, 18] [1, 3, 4, 8, 9, 11, 16, 20, 22] [1, 2, 3, 4, 5, 6, 13, 20, 27] [1, 3, 4, 9, 11, 14, 16, 17, 20] [1, 3, 5, 6, 7, 10, 12, 18, 26] [1, 2, 5, 6, 8, 13, 17, 18, 27] [1, 3, 4, 7, 9, 14, 15, 17, 24] [1, 3, 4, 9, 10, 13, 15, 16, 18] [1, 3, 4, 9, 11, 12, 14, 18, 22] [1, 3, 4, 9, 10, 13, 15, 16, 17] [1, 3, 5, 6, 11, 13, 14, 15, 18] [1, 3, 4, 6, 11, 13, 14, 20, 26] [1, 2, 4, 7, 9, 12, 15, 16, 17] [1, 3, 4, 5, 6, 9, 13, 20, 27] [1, 2, 3, 5, 9, 13, 15, 16, 18] [1, 2, 4, 7, 8, 9, 19, 22, 25] [1, 3, 4, 7, 9, 14, 16, 22, 24] [1, 2, 5, 8, 9, 10, 21, 23, 26] [1, 3, 5, 7, 9, 10, 12, 22, 23] [1, 3, 5, 7, 8, 16, 17, 22, 23] [1, 3, 4, 7, 9, 14, 17, 18, 29] [1, 3, 4, 6, 10, 13, 14, 15, 18] [1, 2, 4, 5, 10, 13, 15, 20, 27] [1, 3, 4, 7, 9, 13, 14, 16, 17] [1, 2, 5, 8, 11, 13, 16, 17, 18] [1, 3, 4, 8, 9, 11, 21, 22, 24] [1, 2, 5, 6, 9, 10, 12, 21, 23] [1, 3, 5, 6, 10, 11, 18, 22, 25] [1, 2, 4, 7, 10, 13, 14, 15, 18] [1, 2, 5, 6, 9, 10, 11, 22, 24] [1, 3, 4, 9, 11, 15, 17, 18, 22] [1, 3, 4, 7, 9, 12, 16, 22, 26] [1, 3, 5, 7, 8, 10, 18, 22, 23] [1, 3, 5, 6, 10, 14, 16, 17, 19] [1, 2, 4, 5, 11, 14, 15, 19, 27] [1, 3, 5, 6, 13, 14, 18, 19, 29] [1, 3, 4, 6, 11, 12, 19, 21, 25] [1, 3, 5, 7, 9, 10, 11, 21, 22] [1, 3, 5, 6, 10, 11, 18, 20, 22] [1, 2, 4, 5, 6, 12, 15, 21, 27] [1, 3, 5, 6, 13, 15, 16, 18, 22] [1, 2, 4, 5, 6, 7, 11, 19, 27] [1, 3, 4, 6, 10, 15, 16, 22, 23] [1, 3, 4, 8, 10, 13, 14, 16, 17] [1, 3, 4, 8, 9, 11, 18, 22, 24] [1, 3, 4, 8, 9, 12, 13, 18, 20] [1, 3, 4, 9, 10, 12, 13, 27, 29] [1, 2, 3, 4, 9, 14, 19, 23, 29] [1, 3, 5, 7, 9, 11, 12, 22, 25] [1, 2, 4, 7, 10, 13, 16, 17, 21] [1, 3, 5, 6, 10, 14, 15, 18, 21] [1, 3, 5, 6, 12, 14, 15, 17, 19] [1, 3, 4, 6, 7, 15, 16, 24, 26] [1, 3, 4, 9, 11, 12, 16, 17, 19] [1, 2, 4, 5, 10, 13, 14, 21, 28] [1, 2, 4, 5, 6, 13, 16, 23, 29] [1, 2, 5, 6, 7, 15, 18, 24, 27] [1, 3, 4, 9, 11, 16, 20, 22, 27] CPU times: user 1min 54s, sys: 624 ms, total: 1min 54s Wall time: 1min 54s
n = 33
print(n+1)
%time upgrade(cmap, n, n+1)
34 new smallest = 10 new smallest = 9 [1, 3, 5, 6, 13, 15, 16, 20, 21] [1, 3, 5, 6, 13, 14, 16, 17, 19] [1, 3, 4, 5, 8, 14, 17, 23, 29] [1, 3, 4, 9, 11, 16, 17, 20, 26] [1, 3, 4, 6, 10, 14, 15, 16, 17] [1, 2, 5, 7, 10, 13, 15, 19, 26] [1, 3, 5, 6, 11, 12, 17, 19, 21] [1, 3, 4, 9, 11, 12, 14, 16, 17] [1, 3, 4, 5, 8, 14, 20, 23, 29] [1, 3, 5, 6, 8, 14, 16, 17, 26] [1, 3, 4, 8, 9, 14, 15, 17, 19] [1, 3, 4, 9, 11, 16, 17, 20, 29] [1, 2, 5, 6, 8, 14, 16, 17, 21] [1, 3, 4, 9, 10, 14, 16, 17, 19] [1, 2, 4, 5, 11, 13, 14, 19, 29] [1, 3, 4, 9, 11, 14, 15, 18, 30] [1, 3, 4, 8, 9, 14, 16, 17, 26] [1, 3, 5, 6, 10, 14, 15, 16, 17] [1, 3, 4, 6, 10, 15, 16, 18, 23] [1, 2, 5, 6, 9, 10, 12, 22, 24] [1, 3, 4, 9, 11, 16, 17, 20, 27] [1, 2, 4, 5, 10, 12, 17, 21, 28] [1, 3, 4, 7, 8, 11, 13, 23, 25] [1, 3, 4, 7, 9, 14, 15, 17, 18] [1, 2, 5, 8, 11, 14, 17, 18, 19] [1, 3, 5, 7, 8, 14, 15, 24, 26] [1, 3, 4, 9, 10, 13, 14, 16, 17] [1, 3, 4, 8, 9, 11, 20, 22, 23] [1, 3, 4, 9, 11, 12, 15, 16, 17] [1, 3, 5, 6, 8, 10, 16, 23, 24] [1, 3, 5, 7, 8, 14, 16, 17, 26] [1, 3, 4, 9, 11, 12, 15, 16, 18] [1, 2, 5, 6, 7, 15, 17, 25, 27] [1, 3, 4, 7, 9, 14, 17, 18, 26] [1, 3, 4, 9, 11, 12, 16, 17, 30] [1, 3, 4, 9, 11, 14, 15, 17, 24] [1, 3, 5, 7, 9, 11, 12, 21, 22] [1, 2, 5, 8, 11, 14, 15, 17, 19] [1, 3, 4, 9, 11, 14, 15, 18, 31] [1, 3, 4, 5, 11, 13, 14, 20, 29] [1, 3, 4, 6, 10, 15, 16, 23, 28] [1, 3, 5, 7, 8, 16, 17, 26, 27] [1, 2, 5, 8, 9, 10, 19, 22, 25] [1, 2, 5, 6, 9, 10, 12, 23, 25] [1, 3, 4, 8, 9, 13, 15, 16, 18] [1, 2, 5, 8, 10, 13, 14, 16, 17] [1, 3, 5, 6, 11, 12, 16, 17, 25] [1, 3, 4, 5, 8, 11, 17, 23, 29] [1, 3, 4, 8, 9, 12, 13, 19, 21] [1, 3, 5, 6, 7, 10, 12, 20, 28] [1, 2, 5, 6, 7, 14, 16, 24, 27] [1, 3, 5, 7, 8, 14, 15, 19, 24] [1, 3, 4, 8, 10, 15, 17, 21, 25] [1, 2, 5, 8, 10, 13, 17, 19, 23] [1, 2, 4, 7, 10, 13, 16, 18, 20] [1, 2, 4, 5, 11, 13, 19, 23, 29] [1, 3, 4, 6, 11, 13, 14, 16, 17] [1, 3, 4, 6, 10, 11, 15, 23, 28] [1, 2, 5, 6, 9, 13, 15, 16, 18] [1, 3, 5, 7, 8, 13, 14, 16, 17] [1, 2, 4, 5, 10, 13, 14, 20, 27] [1, 3, 5, 7, 9, 11, 12, 25, 26] [1, 2, 5, 8, 9, 10, 17, 21, 23] [1, 3, 5, 7, 9, 11, 12, 24, 25] [1, 3, 4, 6, 8, 10, 11, 23, 24] [1, 3, 4, 7, 8, 10, 11, 22, 24] [1, 2, 5, 7, 10, 13, 15, 16, 17] [1, 2, 5, 6, 7, 15, 18, 26, 29] [1, 3, 5, 7, 8, 9, 12, 22, 25] [1, 3, 5, 7, 8, 12, 14, 18, 26] [1, 2, 3, 4, 5, 11, 17, 23, 28] [1, 3, 5, 6, 7, 12, 15, 22, 26] [1, 2, 4, 6, 7, 15, 16, 24, 27] [1, 3, 4, 8, 9, 13, 14, 16, 17] [1, 3, 4, 8, 9, 10, 14, 17, 29] [1, 2, 5, 7, 11, 14, 15, 16, 17] [1, 2, 5, 6, 9, 12, 15, 16, 17] [1, 3, 4, 6, 10, 15, 16, 23, 24] [1, 2, 5, 8, 9, 10, 21, 23, 25] [1, 3, 5, 6, 13, 15, 16, 17, 24] [1, 2, 4, 7, 10, 12, 15, 16, 17] [1, 3, 4, 8, 10, 14, 16, 17, 19] [1, 2, 4, 7, 8, 13, 14, 16, 17] [1, 2, 5, 7, 11, 13, 16, 17, 20] [1, 2, 5, 7, 9, 13, 14, 16, 17] [1, 3, 4, 9, 11, 16, 20, 25, 29] [1, 3, 4, 6, 10, 13, 14, 17, 19] [1, 2, 5, 8, 9, 10, 19, 22, 24] [1, 3, 4, 5, 11, 12, 13, 16, 30] [1, 3, 4, 7, 8, 10, 11, 21, 23] [1, 3, 5, 7, 8, 17, 18, 25, 26] [1, 2, 5, 8, 11, 12, 15, 16, 17] [1, 2, 4, 6, 9, 14, 15, 18, 25] [1, 3, 4, 9, 11, 12, 13, 16, 30] [1, 2, 5, 7, 10, 12, 15, 16, 17] [1, 2, 5, 8, 10, 13, 14, 17, 19] [1, 3, 4, 8, 10, 15, 16, 18, 19] [1, 3, 5, 6, 12, 14, 16, 22, 28] [1, 2, 5, 6, 7, 15, 17, 24, 27] [1, 3, 5, 7, 8, 10, 15, 18, 24] [1, 3, 4, 6, 11, 12, 14, 16, 17] [1, 3, 5, 6, 12, 13, 17, 18, 27] [1, 2, 5, 6, 7, 15, 18, 26, 28] [1, 3, 4, 9, 11, 15, 16, 18, 19] [1, 2, 4, 6, 8, 9, 10, 21, 24] [1, 3, 4, 7, 8, 9, 12, 22, 24] [1, 3, 4, 5, 11, 13, 16, 17, 20] [1, 3, 5, 6, 12, 13, 15, 16, 17] [1, 2, 5, 6, 8, 15, 17, 23, 25] [1, 3, 4, 9, 11, 12, 15, 17, 22] [1, 3, 5, 6, 12, 13, 15, 16, 18] [1, 2, 5, 8, 11, 12, 14, 16, 17] [1, 3, 4, 5, 6, 9, 16, 23, 30] [1, 3, 4, 8, 10, 13, 15, 19, 23] [1, 2, 5, 7, 11, 13, 16, 18, 28] [1, 3, 4, 8, 10, 11, 17, 21, 22] [1, 3, 5, 6, 11, 13, 14, 16, 17] [1, 2, 5, 7, 11, 13, 14, 16, 17] [1, 3, 5, 6, 7, 12, 15, 20, 28] [1, 2, 5, 8, 9, 10, 20, 22, 25] [1, 3, 4, 6, 10, 14, 17, 19, 26] [1, 3, 5, 6, 12, 13, 16, 17, 26] [1, 2, 5, 6, 9, 10, 11, 23, 25] [1, 3, 5, 7, 8, 17, 18, 26, 27] [1, 3, 4, 7, 9, 13, 15, 16, 18] [1, 3, 4, 5, 8, 14, 20, 26, 29] [1, 3, 4, 8, 9, 11, 17, 23, 29] [1, 3, 4, 8, 10, 11, 17, 23, 29] [1, 2, 5, 8, 10, 13, 17, 23, 27] [1, 2, 5, 8, 10, 14, 15, 16, 19] [1, 3, 4, 8, 9, 11, 20, 24, 26] [1, 2, 5, 7, 11, 12, 14, 20, 28] [1, 3, 5, 6, 13, 14, 16, 18, 20] [1, 2, 4, 7, 9, 11, 17, 22, 23] [1, 3, 5, 6, 9, 10, 16, 22, 24] [1, 2, 5, 7, 11, 13, 15, 16, 18] [1, 3, 5, 6, 10, 11, 15, 16, 23] [1, 3, 4, 5, 6, 12, 13, 17, 27] [1, 3, 5, 6, 8, 14, 16, 17, 21] [1, 3, 5, 6, 13, 15, 16, 18, 24] [1, 2, 5, 6, 7, 15, 17, 23, 26] [1, 2, 5, 7, 9, 13, 15, 16, 18] [1, 3, 5, 6, 8, 14, 17, 21, 27] [1, 2, 5, 7, 8, 10, 17, 21, 25] [1, 3, 4, 8, 10, 11, 14, 23, 29] [1, 3, 5, 6, 8, 14, 18, 25, 26] [1, 3, 5, 6, 9, 13, 15, 16, 18] [1, 3, 4, 8, 10, 11, 15, 16, 18] [1, 3, 4, 9, 10, 11, 12, 17, 21] [1, 3, 4, 9, 11, 13, 14, 18, 30] [1, 2, 5, 8, 11, 13, 15, 16, 17] [1, 2, 5, 7, 11, 13, 16, 17, 24] [1, 2, 5, 8, 10, 13, 16, 17, 23] [1, 3, 5, 7, 8, 10, 11, 22, 23] [1, 2, 5, 6, 7, 13, 16, 24, 27] [1, 3, 4, 8, 10, 14, 17, 19, 22] [1, 3, 4, 9, 10, 15, 16, 18, 19] [1, 3, 4, 6, 10, 12, 15, 16, 17] [1, 3, 5, 6, 11, 12, 19, 21, 23] [1, 3, 4, 8, 9, 14, 15, 17, 18] [1, 2, 5, 6, 7, 14, 17, 25, 27] [1, 2, 5, 8, 9, 10, 20, 23, 25] [1, 3, 4, 9, 11, 15, 17, 20, 24] [1, 3, 5, 7, 8, 16, 17, 25, 26] [1, 2, 5, 6, 7, 15, 18, 25, 28] [1, 3, 4, 5, 11, 13, 14, 16, 20] [1, 3, 4, 6, 8, 13, 14, 16, 17] [1, 3, 5, 6, 13, 14, 15, 17, 19] [1, 2, 4, 7, 10, 11, 15, 22, 27] [1, 3, 4, 7, 8, 10, 16, 21, 26] [1, 2, 5, 6, 9, 10, 11, 21, 23] [1, 2, 5, 8, 10, 12, 15, 16, 17] [1, 3, 5, 6, 12, 14, 15, 19, 20] [1, 3, 4, 5, 11, 12, 14, 16, 17] [1, 3, 5, 7, 9, 10, 12, 23, 24] [1, 3, 5, 6, 8, 10, 11, 22, 23] [1, 2, 5, 6, 7, 14, 17, 24, 26] [1, 3, 4, 5, 8, 14, 20, 25, 27] [1, 3, 5, 7, 8, 14, 15, 17, 26] [1, 3, 4, 9, 10, 15, 16, 17, 19] [1, 3, 4, 6, 10, 13, 14, 21, 29] [1, 2, 5, 8, 9, 10, 20, 22, 24] [1, 2, 5, 7, 11, 15, 16, 18, 23] [1, 2, 4, 6, 9, 12, 15, 16, 17] [1, 3, 5, 6, 7, 11, 14, 23, 26] [1, 3, 4, 7, 9, 12, 15, 16, 17] [1, 3, 4, 6, 9, 11, 15, 22, 23] [1, 3, 4, 6, 10, 13, 15, 21, 29] [1, 3, 4, 9, 11, 12, 16, 25, 30] [1, 2, 5, 8, 10, 13, 16, 17, 26] [1, 3, 4, 9, 10, 11, 16, 20, 24] [1, 3, 4, 9, 11, 14, 15, 17, 18] [1, 2, 5, 8, 11, 14, 16, 17, 18] [1, 2, 4, 5, 11, 12, 14, 16, 17] [1, 3, 4, 9, 10, 13, 14, 21, 29] [1, 3, 4, 6, 11, 13, 16, 17, 25] [1, 3, 4, 8, 10, 12, 15, 16, 17] [1, 3, 4, 9, 11, 14, 15, 16, 18] [1, 2, 5, 7, 9, 13, 16, 17, 26] [1, 2, 4, 6, 8, 10, 11, 22, 23] [1, 3, 4, 8, 9, 14, 15, 16, 18] [1, 3, 4, 9, 11, 13, 14, 19, 20] [1, 3, 4, 5, 7, 12, 16, 18, 26] [1, 2, 5, 8, 10, 13, 15, 16, 17] [1, 3, 4, 8, 10, 14, 15, 16, 17] [1, 2, 5, 6, 7, 15, 18, 26, 27] [1, 2, 5, 7, 11, 12, 14, 19, 27] [1, 2, 5, 7, 8, 9, 19, 22, 25] [1, 3, 4, 9, 10, 13, 15, 18, 19] [1, 3, 4, 5, 8, 14, 20, 22, 28] [1, 3, 4, 6, 10, 15, 17, 18, 25] [1, 3, 4, 9, 11, 16, 17, 19, 20] [1, 2, 3, 4, 5, 11, 17, 23, 29] [1, 2, 5, 7, 9, 12, 15, 16, 17] [1, 3, 4, 7, 8, 10, 11, 23, 25] [1, 2, 3, 5, 6, 12, 16, 17, 25] [1, 3, 4, 8, 9, 11, 21, 23, 25] [1, 2, 4, 6, 7, 15, 17, 19, 27] [1, 3, 4, 6, 11, 13, 14, 20, 29] [1, 2, 5, 8, 11, 14, 15, 16, 18] [1, 3, 4, 7, 9, 15, 17, 20, 24] [1, 2, 5, 8, 11, 14, 15, 16, 19] [1, 2, 3, 4, 5, 11, 17, 22, 27] [1, 3, 4, 9, 11, 12, 16, 18, 22] [1, 3, 4, 6, 7, 9, 16, 20, 27] [1, 3, 4, 6, 7, 10, 15, 23, 28] [1, 3, 5, 7, 8, 16, 17, 23, 26] [1, 3, 4, 9, 11, 12, 14, 18, 30] [1, 2, 5, 6, 7, 11, 14, 23, 26] [1, 3, 5, 6, 12, 13, 15, 17, 18] [1, 3, 5, 6, 11, 12, 19, 21, 28] [1, 3, 5, 6, 11, 12, 18, 20, 22] [1, 2, 5, 8, 9, 10, 21, 24, 27] [1, 3, 4, 9, 10, 13, 14, 20, 22] [1, 3, 4, 9, 11, 16, 20, 25, 30] [1, 3, 5, 6, 8, 14, 18, 22, 28] [1, 3, 5, 7, 9, 10, 12, 21, 22] [1, 3, 5, 6, 8, 10, 16, 22, 28] [1, 3, 5, 6, 11, 13, 14, 20, 29] [1, 2, 5, 8, 10, 13, 17, 23, 24] [1, 3, 5, 6, 13, 14, 16, 18, 19] [1, 3, 4, 8, 10, 15, 17, 18, 21] [1, 3, 5, 7, 8, 15, 16, 20, 26] [1, 3, 4, 9, 11, 12, 16, 17, 27] [1, 3, 4, 9, 11, 13, 14, 16, 17] [1, 3, 5, 7, 8, 14, 15, 17, 19] [1, 3, 5, 7, 8, 15, 16, 25, 26] [1, 2, 3, 4, 5, 11, 16, 23, 29] [1, 3, 4, 6, 11, 13, 14, 17, 29] [1, 3, 4, 5, 10, 12, 18, 22, 28] [1, 2, 5, 6, 7, 15, 17, 24, 26] [1, 3, 5, 7, 8, 10, 12, 20, 26] [1, 3, 5, 7, 8, 10, 14, 22, 26] [1, 3, 4, 9, 11, 15, 16, 17, 20] [1, 2, 5, 8, 9, 10, 19, 21, 24] [1, 3, 4, 9, 11, 13, 14, 16, 20] [1, 3, 4, 9, 11, 16, 17, 20, 30] [1, 2, 5, 6, 9, 13, 16, 18, 28] [1, 3, 5, 7, 8, 10, 11, 23, 24] [1, 3, 5, 6, 11, 12, 14, 16, 17] [1, 3, 5, 7, 8, 16, 17, 24, 25] [1, 2, 5, 7, 11, 13, 14, 16, 20] [1, 2, 4, 5, 11, 12, 14, 16, 29] [1, 2, 5, 7, 10, 13, 16, 17, 18] [1, 3, 5, 6, 8, 15, 16, 25, 26] [1, 2, 5, 8, 10, 14, 16, 17, 21] [1, 2, 5, 8, 9, 10, 21, 24, 26] [1, 2, 3, 4, 5, 11, 17, 22, 28] [1, 3, 4, 7, 9, 12, 13, 20, 27] [1, 3, 4, 6, 7, 15, 17, 24, 26] [1, 2, 5, 7, 11, 14, 16, 19, 29] [1, 2, 4, 5, 11, 14, 16, 22, 29] [1, 3, 4, 6, 10, 14, 16, 17, 25] [1, 2, 5, 8, 9, 12, 14, 22, 24] [1, 2, 5, 7, 11, 13, 16, 17, 18] [1, 3, 4, 6, 8, 10, 11, 22, 23] [1, 2, 4, 5, 11, 14, 15, 17, 22] [1, 3, 4, 9, 10, 14, 15, 17, 19] [1, 2, 5, 8, 9, 10, 20, 23, 26] [1, 3, 5, 7, 9, 10, 11, 23, 24] [1, 2, 5, 6, 7, 14, 17, 25, 28] [1, 2, 4, 6, 9, 14, 16, 17, 23] [1, 3, 5, 6, 10, 14, 15, 17, 23] [1, 2, 4, 6, 8, 10, 11, 23, 26] [1, 3, 4, 8, 9, 11, 21, 23, 24] [1, 3, 4, 8, 9, 14, 15, 17, 24] [1, 3, 5, 6, 13, 14, 15, 18, 19] [1, 3, 4, 9, 10, 15, 16, 18, 20] [1, 3, 4, 9, 11, 14, 15, 16, 17] [1, 3, 4, 9, 11, 13, 16, 17, 22] [1, 3, 4, 6, 7, 15, 17, 22, 27] [1, 3, 4, 9, 11, 12, 16, 22, 26] [1, 3, 4, 6, 10, 14, 16, 17, 19] [1, 3, 4, 9, 11, 14, 15, 18, 20] [1, 3, 5, 7, 9, 10, 11, 22, 23] [1, 2, 4, 5, 9, 11, 17, 23, 29] [1, 3, 4, 9, 11, 12, 16, 22, 29] [1, 3, 5, 6, 8, 14, 15, 19, 26] [1, 3, 5, 7, 8, 14, 17, 22, 25] [1, 2, 5, 8, 9, 12, 13, 19, 21] [1, 3, 5, 6, 12, 14, 16, 17, 22] [1, 2, 4, 7, 8, 13, 16, 18, 26] [1, 2, 5, 7, 11, 12, 13, 17, 20] [1, 3, 5, 6, 9, 12, 15, 16, 17] [1, 3, 5, 6, 13, 14, 16, 17, 24] [1, 3, 4, 9, 11, 14, 16, 20, 22] [1, 3, 5, 6, 12, 13, 15, 17, 30] [1, 3, 5, 6, 10, 13, 16, 24, 28] [1, 2, 3, 4, 5, 11, 16, 23, 28] [1, 2, 3, 4, 5, 11, 17, 22, 29] [1, 2, 5, 7, 11, 14, 15, 16, 19] [1, 2, 4, 7, 10, 13, 15, 16, 17] [1, 3, 5, 6, 8, 10, 11, 23, 24] [1, 3, 5, 7, 8, 10, 12, 21, 22] [1, 2, 5, 7, 11, 15, 17, 20, 22] [1, 3, 5, 7, 9, 11, 12, 22, 23] [1, 2, 5, 8, 10, 12, 17, 20, 21] [1, 3, 5, 6, 11, 12, 14, 16, 28] [1, 3, 4, 7, 8, 13, 15, 24, 26] [1, 3, 4, 9, 11, 16, 21, 22, 25] [1, 3, 5, 7, 8, 10, 14, 23, 24] [1, 3, 4, 8, 9, 13, 14, 16, 30] [1, 3, 4, 9, 10, 15, 17, 19, 30] [1, 2, 4, 5, 11, 14, 15, 16, 19] [1, 2, 5, 8, 10, 14, 15, 16, 17] [1, 3, 5, 6, 10, 14, 16, 17, 24] [1, 3, 4, 6, 7, 15, 17, 25, 26] [1, 2, 5, 7, 8, 9, 15, 19, 24] [1, 3, 5, 6, 12, 14, 15, 18, 19] [1, 2, 5, 6, 7, 14, 17, 24, 27] [1, 2, 5, 6, 7, 15, 18, 25, 27] [1, 3, 5, 6, 13, 15, 17, 24, 28] [1, 2, 5, 8, 9, 10, 17, 20, 23] [1, 2, 5, 7, 10, 12, 15, 17, 21] [1, 3, 4, 8, 10, 15, 16, 18, 26] [1, 3, 4, 5, 8, 14, 20, 26, 32] [1, 2, 3, 4, 8, 11, 17, 23, 29] [1, 2, 5, 6, 7, 14, 17, 23, 26] [1, 2, 5, 6, 8, 13, 14, 16, 17] [1, 2, 5, 7, 11, 12, 15, 16, 18] [1, 3, 4, 9, 11, 16, 17, 20, 21] [1, 2, 5, 6, 7, 13, 15, 18, 27] [1, 3, 5, 6, 8, 14, 18, 24, 28] [1, 3, 5, 6, 13, 15, 17, 24, 30] [1, 3, 4, 9, 10, 14, 15, 16, 18] [1, 3, 4, 8, 10, 13, 14, 17, 19] [1, 3, 4, 9, 10, 14, 15, 17, 18] [1, 3, 4, 9, 11, 15, 17, 22, 26] [1, 2, 5, 7, 11, 14, 15, 17, 22] [1, 2, 5, 8, 11, 14, 16, 18, 31] [1, 3, 5, 6, 7, 14, 16, 18, 26] [1, 3, 4, 6, 11, 13, 14, 16, 20] [1, 2, 5, 7, 11, 15, 17, 18, 20] [1, 2, 4, 7, 10, 13, 15, 17, 29] [1, 3, 4, 9, 10, 12, 14, 16, 17] [1, 3, 5, 7, 9, 10, 21, 22, 24] [1, 2, 5, 6, 7, 15, 16, 19, 27] [1, 2, 5, 8, 9, 12, 15, 16, 17] [1, 2, 4, 7, 10, 13, 16, 17, 18] [1, 3, 4, 9, 10, 13, 14, 19, 21] [1, 3, 5, 6, 8, 11, 15, 24, 28] [1, 3, 5, 6, 11, 13, 14, 16, 20] [1, 3, 5, 6, 12, 13, 14, 17, 20] [1, 2, 5, 7, 11, 15, 16, 17, 18] [1, 3, 4, 8, 10, 14, 15, 17, 23] [1, 3, 5, 6, 12, 13, 15, 17, 28] [1, 3, 5, 6, 13, 15, 17, 18, 24] [1, 3, 5, 7, 8, 16, 17, 23, 24] [1, 3, 5, 7, 9, 11, 12, 23, 24] [1, 3, 5, 6, 12, 13, 14, 16, 17] [1, 3, 4, 7, 9, 15, 17, 22, 24] [1, 3, 4, 7, 9, 15, 16, 18, 25] [1, 3, 4, 6, 7, 15, 17, 25, 27] [1, 3, 4, 8, 10, 14, 15, 17, 18] [1, 2, 5, 6, 8, 14, 17, 19, 24] [1, 2, 4, 6, 9, 13, 15, 19, 27] [1, 3, 4, 9, 10, 11, 16, 17, 20] [1, 3, 5, 7, 8, 12, 15, 20, 26] [1, 2, 4, 6, 8, 10, 11, 23, 24] [1, 3, 5, 6, 8, 13, 14, 16, 17] [1, 2, 4, 6, 7, 14, 16, 17, 25] [1, 3, 4, 8, 10, 14, 15, 17, 25] [1, 2, 5, 6, 7, 15, 17, 25, 28] [1, 3, 5, 6, 9, 10, 15, 17, 28] [1, 2, 5, 7, 11, 15, 16, 17, 24] [1, 3, 5, 7, 9, 10, 11, 20, 23] [1, 2, 5, 8, 11, 14, 15, 16, 32] [1, 3, 5, 7, 9, 10, 21, 23, 24] [1, 3, 4, 9, 11, 13, 16, 17, 20] [1, 2, 5, 8, 9, 10, 18, 21, 24] [1, 2, 5, 8, 10, 13, 16, 17, 18] [1, 2, 4, 7, 9, 11, 16, 17, 29] [1, 2, 5, 8, 11, 14, 17, 19, 21] [1, 2, 4, 7, 9, 11, 17, 23, 29] [1, 3, 4, 9, 11, 12, 16, 26, 30] [1, 3, 5, 6, 12, 14, 16, 17, 24] [1, 3, 4, 7, 8, 13, 14, 16, 17] [1, 3, 5, 7, 9, 10, 16, 21, 24] [1, 3, 4, 5, 8, 14, 20, 26, 28] [1, 2, 5, 8, 11, 14, 15, 16, 17] [1, 3, 5, 7, 8, 17, 18, 24, 25] [1, 3, 5, 7, 8, 17, 18, 27, 28] [1, 3, 5, 6, 10, 11, 15, 16, 18] [1, 3, 4, 9, 11, 14, 16, 17, 20] [1, 2, 5, 6, 8, 13, 17, 18, 27] [1, 3, 4, 7, 9, 14, 15, 17, 24] [1, 3, 4, 9, 10, 13, 15, 16, 18] [1, 3, 4, 9, 11, 12, 14, 18, 22] [1, 3, 4, 9, 10, 13, 15, 16, 17] [1, 3, 4, 6, 11, 13, 14, 20, 26] [1, 2, 4, 7, 9, 12, 15, 16, 17] [1, 2, 3, 5, 9, 13, 15, 16, 18] [1, 2, 4, 7, 8, 9, 19, 22, 25] [1, 2, 5, 8, 9, 10, 21, 23, 26] [1, 3, 5, 7, 9, 10, 12, 22, 23] [1, 3, 5, 7, 8, 16, 17, 22, 23] [1, 3, 4, 7, 9, 14, 17, 18, 29] [1, 3, 4, 7, 9, 13, 14, 16, 17] [1, 2, 5, 8, 11, 13, 16, 17, 18] [1, 2, 5, 6, 9, 10, 11, 22, 24] [1, 3, 4, 9, 11, 15, 17, 18, 22] [1, 3, 4, 7, 9, 12, 16, 22, 26] [1, 3, 5, 6, 10, 14, 16, 17, 19] [1, 2, 4, 5, 11, 14, 15, 19, 27] [1, 3, 5, 6, 13, 14, 18, 19, 29] [1, 3, 5, 6, 13, 15, 16, 18, 22] [1, 2, 4, 5, 6, 7, 11, 19, 27] [1, 3, 4, 8, 10, 13, 14, 16, 17] [1, 3, 5, 7, 9, 11, 12, 22, 25] [1, 2, 4, 7, 10, 13, 16, 17, 21] [1, 3, 5, 6, 12, 14, 15, 17, 19] [1, 3, 4, 9, 11, 12, 16, 17, 19] [1, 2, 4, 5, 10, 13, 14, 21, 28] [1, 2, 4, 5, 6, 13, 16, 23, 29] [1, 2, 5, 6, 7, 15, 18, 24, 27] CPU times: user 24 ms, sys: 0 ns, total: 24 ms Wall time: 21.4 ms
n = 34
print(n+1)
%time upgrade(cmap, n, n+1)
35 new smallest = 9 [1, 3, 4, 7, 8, 10, 11, 23, 25] [1, 3, 4, 5, 8, 14, 20, 26, 32] [1, 3, 5, 6, 12, 13, 17, 18, 27] [1, 3, 5, 6, 13, 15, 16, 20, 21] [1, 3, 5, 6, 13, 14, 16, 17, 19] [1, 3, 4, 6, 11, 13, 14, 20, 29] [1, 3, 4, 9, 11, 16, 17, 20, 26] [1, 2, 5, 6, 7, 15, 18, 26, 28] [1, 3, 4, 9, 11, 15, 16, 18, 19] [1, 3, 4, 7, 9, 15, 17, 20, 24] [1, 2, 5, 8, 11, 14, 15, 16, 19] [1, 3, 4, 6, 7, 10, 15, 23, 28] [1, 3, 5, 6, 13, 15, 17, 24, 30] [1, 3, 4, 5, 6, 9, 16, 23, 30] [1, 3, 4, 9, 10, 14, 15, 17, 18] [1, 2, 5, 7, 11, 13, 16, 18, 28] [1, 2, 5, 6, 8, 14, 16, 17, 21] [1, 3, 4, 9, 11, 15, 17, 22, 26] [1, 3, 4, 9, 10, 14, 16, 17, 19] [1, 3, 5, 6, 12, 13, 15, 17, 18] [1, 3, 5, 6, 7, 12, 15, 20, 28] [1, 2, 5, 8, 9, 10, 20, 22, 25] [1, 2, 5, 8, 9, 10, 21, 24, 27] [1, 3, 4, 9, 10, 13, 14, 20, 22] [1, 3, 4, 8, 9, 14, 16, 17, 26] [1, 2, 5, 6, 9, 10, 11, 23, 25] [1, 3, 5, 7, 8, 17, 18, 26, 27] [1, 3, 5, 6, 11, 13, 14, 20, 29] [1, 3, 5, 6, 13, 14, 16, 18, 19] [1, 3, 4, 8, 10, 15, 17, 18, 21] [1, 3, 5, 7, 8, 15, 16, 20, 26] [1, 2, 5, 7, 11, 15, 17, 18, 20] [1, 2, 5, 6, 7, 15, 16, 19, 27] [1, 2, 4, 7, 10, 13, 16, 17, 18] [1, 3, 4, 7, 9, 14, 15, 17, 18] [1, 2, 5, 8, 11, 14, 17, 18, 19] [1, 2, 5, 8, 10, 13, 17, 23, 27] [1, 3, 4, 9, 10, 13, 14, 19, 21] [1, 3, 5, 6, 8, 11, 15, 24, 28] [1, 2, 5, 8, 10, 14, 15, 16, 19] [1, 3, 4, 6, 11, 13, 14, 17, 29] [1, 3, 4, 8, 9, 11, 20, 24, 26] [1, 2, 5, 7, 11, 15, 16, 17, 18] [1, 3, 5, 6, 13, 15, 17, 18, 24] [1, 3, 5, 7, 9, 11, 12, 23, 24] [1, 2, 5, 7, 11, 12, 14, 20, 28] [1, 3, 4, 9, 11, 15, 16, 17, 20] [1, 3, 4, 8, 10, 14, 15, 17, 18] [1, 3, 5, 6, 8, 14, 16, 17, 21] [1, 3, 4, 7, 9, 14, 17, 18, 26] [1, 3, 4, 9, 11, 14, 15, 17, 24] [1, 3, 5, 7, 8, 12, 15, 20, 26] [1, 2, 4, 6, 8, 10, 11, 23, 24] [1, 3, 5, 7, 8, 10, 11, 23, 24] [1, 3, 4, 9, 11, 14, 15, 18, 31] [1, 3, 5, 6, 8, 14, 17, 21, 27] [1, 3, 4, 8, 10, 14, 15, 17, 25] [1, 2, 5, 7, 8, 10, 17, 21, 25] [1, 2, 5, 6, 7, 15, 17, 25, 28] [1, 2, 5, 7, 11, 15, 16, 17, 24] [1, 2, 5, 7, 10, 13, 16, 17, 18] [1, 2, 5, 7, 11, 13, 16, 17, 24] [1, 3, 5, 7, 8, 16, 17, 26, 27] [1, 2, 5, 8, 9, 10, 19, 22, 25] [1, 2, 5, 8, 10, 14, 16, 17, 21] [1, 2, 5, 6, 9, 10, 12, 23, 25] [1, 2, 5, 8, 9, 10, 21, 24, 26] [1, 2, 5, 7, 11, 14, 16, 19, 29] [1, 3, 5, 6, 7, 10, 12, 20, 28] [1, 3, 4, 6, 10, 14, 16, 17, 25] [1, 2, 5, 7, 11, 13, 16, 17, 18] [1, 3, 4, 8, 10, 15, 17, 21, 25] [1, 2, 5, 8, 10, 13, 16, 17, 18] [1, 3, 4, 9, 10, 15, 16, 18, 19] [1, 3, 5, 6, 11, 12, 19, 21, 23] [1, 2, 5, 8, 11, 14, 17, 19, 21] [1, 3, 4, 8, 9, 14, 15, 17, 18] [1, 2, 5, 8, 9, 10, 20, 23, 25] [1, 2, 5, 8, 9, 10, 20, 23, 26] [1, 3, 4, 9, 11, 12, 16, 26, 30] [1, 3, 4, 9, 11, 15, 17, 20, 24] [1, 3, 5, 7, 9, 10, 11, 23, 24] [1, 3, 5, 7, 9, 11, 12, 25, 26] [1, 2, 5, 6, 7, 14, 17, 25, 28] [1, 2, 5, 6, 7, 15, 18, 25, 28] [1, 3, 5, 7, 9, 11, 12, 24, 25] [1, 3, 4, 6, 8, 10, 11, 23, 24] [1, 3, 4, 7, 8, 10, 11, 22, 24] [1, 3, 4, 8, 9, 11, 21, 23, 24] [1, 3, 4, 9, 10, 15, 16, 18, 20] [1, 2, 5, 6, 7, 15, 18, 26, 29] [1, 3, 5, 7, 8, 17, 18, 24, 25] [1, 3, 4, 9, 11, 13, 16, 17, 22] [1, 3, 4, 9, 11, 12, 16, 22, 26] [1, 3, 5, 6, 12, 14, 15, 19, 20] [1, 3, 4, 6, 10, 14, 16, 17, 19] [1, 3, 5, 7, 9, 10, 12, 23, 24] [1, 3, 4, 9, 11, 14, 15, 18, 20] [1, 3, 5, 7, 8, 17, 18, 27, 28] [1, 2, 5, 6, 8, 13, 17, 18, 27] [1, 3, 4, 5, 8, 14, 20, 25, 27] [1, 3, 4, 9, 10, 15, 16, 17, 19] [1, 3, 4, 6, 10, 13, 14, 21, 29] [1, 3, 5, 6, 12, 13, 15, 17, 30] [1, 2, 5, 8, 9, 10, 21, 23, 26] [1, 2, 5, 8, 9, 10, 21, 23, 25] [1, 3, 5, 7, 9, 10, 12, 22, 23] [1, 3, 4, 8, 10, 14, 16, 17, 19] [1, 3, 4, 6, 10, 13, 15, 21, 29] [1, 2, 5, 7, 11, 14, 15, 16, 19] [1, 3, 5, 6, 8, 10, 11, 23, 24] [1, 2, 5, 7, 11, 15, 17, 20, 22] [1, 3, 5, 7, 9, 11, 12, 22, 23] [1, 3, 4, 7, 9, 14, 17, 18, 29] [1, 3, 4, 9, 10, 11, 16, 20, 24] [1, 3, 4, 9, 11, 14, 15, 17, 18] [1, 2, 5, 8, 11, 13, 16, 17, 18] [1, 2, 5, 8, 11, 14, 16, 17, 18] [1, 2, 5, 6, 9, 10, 11, 22, 24] [1, 3, 4, 9, 11, 15, 17, 18, 22] [1, 3, 4, 7, 9, 12, 16, 22, 26] [1, 3, 4, 9, 10, 13, 14, 21, 29] [1, 3, 4, 5, 11, 12, 13, 16, 30] [1, 3, 5, 6, 10, 14, 16, 17, 19] [1, 3, 5, 6, 13, 14, 18, 19, 29] [1, 3, 5, 6, 13, 15, 16, 18, 22] [1, 3, 5, 7, 8, 17, 18, 25, 26] [1, 2, 5, 7, 9, 13, 16, 17, 26] [1, 2, 4, 5, 11, 14, 15, 16, 19] [1, 3, 4, 8, 10, 15, 16, 18, 19] [1, 3, 4, 9, 11, 12, 16, 17, 19] [1, 2, 4, 5, 10, 13, 14, 21, 28] [1, 3, 4, 6, 10, 15, 17, 18, 25] [1, 2, 4, 5, 6, 13, 16, 23, 29] [1, 3, 4, 9, 11, 16, 17, 19, 20] CPU times: user 24 ms, sys: 0 ns, total: 24 ms Wall time: 23.5 ms
n = 35
print(n+1)
%time upgrade(cmap, n, n+1)
36 new smallest = 9 [1, 3, 4, 7, 8, 10, 11, 23, 25] [1, 3, 4, 9, 10, 15, 16, 17, 19] [1, 3, 4, 5, 8, 14, 20, 26, 32] [1, 3, 5, 6, 12, 13, 17, 18, 27] [1, 3, 5, 6, 12, 13, 15, 17, 30] [1, 2, 5, 7, 11, 15, 17, 18, 20] [1, 2, 5, 7, 11, 14, 16, 19, 29] [1, 3, 4, 8, 10, 15, 17, 18, 21] [1, 3, 5, 6, 13, 15, 16, 20, 21] [1, 3, 5, 6, 13, 14, 16, 17, 19] [1, 2, 4, 7, 10, 13, 16, 17, 18] [1, 3, 4, 7, 9, 14, 15, 17, 18] [1, 3, 4, 9, 11, 16, 17, 20, 26] [1, 2, 5, 6, 7, 15, 18, 26, 28] [1, 2, 5, 8, 11, 14, 17, 18, 19] [1, 3, 4, 9, 11, 15, 16, 18, 19] [1, 2, 5, 8, 10, 13, 17, 23, 27] [1, 3, 5, 6, 8, 11, 15, 24, 28] [1, 2, 5, 7, 11, 13, 16, 17, 18] [1, 3, 4, 8, 10, 15, 17, 21, 25] [1, 3, 4, 8, 10, 14, 16, 17, 19] [1, 3, 4, 6, 10, 13, 15, 21, 29] [1, 2, 5, 7, 11, 15, 16, 17, 18] [1, 2, 5, 8, 10, 13, 16, 17, 18] [1, 3, 5, 6, 13, 15, 17, 18, 24] [1, 3, 5, 7, 9, 11, 12, 23, 24] [1, 3, 4, 9, 10, 15, 16, 18, 19] [1, 3, 4, 7, 9, 14, 17, 18, 29] [1, 2, 5, 8, 11, 14, 17, 19, 21] [1, 3, 4, 8, 9, 14, 15, 17, 18] [1, 3, 4, 9, 10, 11, 16, 20, 24] [1, 3, 4, 9, 11, 14, 15, 17, 18] [1, 2, 5, 8, 11, 13, 16, 17, 18] [1, 2, 5, 8, 11, 14, 16, 17, 18] [1, 3, 4, 9, 11, 15, 16, 17, 20] [1, 3, 4, 9, 11, 15, 17, 18, 22] [1, 2, 5, 8, 9, 10, 20, 23, 26] [1, 3, 5, 6, 10, 14, 16, 17, 19] [1, 3, 5, 7, 9, 11, 12, 25, 26] [1, 3, 4, 8, 10, 14, 15, 17, 18] [1, 3, 5, 6, 13, 14, 18, 19, 29] [1, 2, 5, 6, 7, 15, 18, 25, 28] [1, 3, 5, 6, 13, 15, 16, 18, 22] [1, 3, 5, 7, 8, 17, 18, 25, 26] [1, 3, 5, 7, 9, 11, 12, 24, 25] [1, 3, 5, 6, 13, 15, 17, 24, 30] [1, 3, 4, 5, 6, 9, 16, 23, 30] [1, 3, 4, 7, 9, 14, 17, 18, 26] [1, 2, 5, 8, 9, 10, 21, 23, 26] [1, 3, 4, 9, 10, 15, 16, 18, 20] [1, 3, 4, 9, 10, 14, 15, 17, 18] [1, 2, 5, 7, 11, 13, 16, 18, 28] [1, 2, 5, 6, 7, 15, 18, 26, 29] [1, 3, 5, 7, 8, 17, 18, 24, 25] [1, 3, 4, 9, 11, 14, 15, 18, 31] [1, 3, 4, 9, 10, 14, 16, 17, 19] [1, 3, 5, 6, 12, 13, 15, 17, 18] [1, 3, 4, 6, 10, 14, 16, 17, 19] [1, 3, 5, 7, 9, 10, 12, 23, 24] [1, 2, 5, 8, 9, 10, 21, 24, 27] [1, 3, 4, 9, 10, 13, 14, 20, 22] [1, 3, 4, 9, 11, 14, 15, 18, 20] [1, 2, 5, 6, 9, 10, 11, 23, 25] [1, 3, 5, 7, 8, 17, 18, 26, 27] [1, 3, 5, 7, 8, 17, 18, 27, 28] [1, 3, 4, 8, 10, 15, 16, 18, 19] [1, 2, 5, 7, 10, 13, 16, 17, 18] [1, 2, 5, 6, 8, 13, 17, 18, 27] [1, 3, 4, 9, 11, 12, 16, 17, 19] [1, 3, 4, 6, 10, 15, 17, 18, 25] [1, 2, 4, 5, 6, 13, 16, 23, 29] [1, 3, 4, 9, 11, 16, 17, 19, 20] [1, 3, 5, 6, 13, 14, 16, 18, 19] [1, 3, 5, 7, 8, 15, 16, 20, 26] [1, 2, 5, 8, 9, 10, 21, 24, 26] CPU times: user 8 ms, sys: 0 ns, total: 8 ms Wall time: 7.78 ms
n = 36
print(n+1)
%time upgrade(cmap, n, n+1)
37 new smallest = 10 new smallest = 9 [1, 3, 5, 7, 9, 11, 12, 24, 25] [1, 3, 5, 6, 13, 15, 17, 24, 30] [1, 3, 4, 5, 8, 14, 20, 26, 32] [1, 2, 5, 8, 9, 10, 21, 24, 27] [1, 2, 5, 7, 11, 15, 17, 18, 20] [1, 3, 4, 8, 10, 15, 16, 18, 19] [1, 3, 5, 6, 13, 15, 16, 20, 21] [1, 3, 4, 9, 11, 15, 16, 17, 20] [1, 3, 4, 9, 11, 15, 17, 18, 22] [1, 3, 5, 6, 13, 15, 16, 18, 22] [1, 3, 4, 9, 11, 16, 17, 20, 26] [1, 2, 5, 8, 11, 14, 17, 18, 19] [1, 2, 5, 8, 10, 13, 17, 23, 27] [1, 3, 4, 9, 11, 15, 16, 18, 19] [1, 3, 4, 9, 11, 16, 17, 19, 20] [1, 3, 5, 7, 9, 11, 12, 25, 26] [1, 3, 5, 6, 13, 14, 18, 19, 29] [1, 3, 5, 6, 13, 14, 16, 18, 19] [1, 3, 4, 9, 10, 15, 16, 18, 19] [1, 3, 5, 6, 13, 15, 17, 18, 24] CPU times: user 4 ms, sys: 0 ns, total: 4 ms Wall time: 2.88 ms
n = 37
print(n+1)
%time upgrade(cmap, n, n+1)
38 new smallest = 10 new smallest = 9 [1, 2, 5, 7, 11, 15, 17, 18, 20] [1, 3, 4, 8, 10, 15, 16, 18, 19] [1, 3, 4, 9, 10, 15, 16, 18, 19] [1, 2, 5, 8, 11, 14, 17, 18, 19] [1, 3, 4, 9, 11, 15, 16, 18, 19] [1, 3, 5, 6, 13, 14, 18, 19, 29] [1, 3, 5, 7, 9, 11, 12, 25, 26] [1, 3, 4, 9, 11, 16, 17, 19, 20] [1, 3, 5, 6, 13, 14, 16, 18, 19] [1, 3, 5, 6, 13, 15, 16, 18, 22] CPU times: user 4 ms, sys: 0 ns, total: 4 ms Wall time: 2.88 ms
n = 38
print(n+1)
%time upgrade(cmap, n, n+1)
39 new smallest = 10 new smallest = 9 [1, 3, 4, 9, 11, 16, 17, 19, 20] CPU times: user 4 ms, sys: 0 ns, total: 4 ms Wall time: 3.24 ms
n = 39
print(n+1)
%time upgrade(cmap, n, n+1)
40 new smallest = 9 [1, 3, 4, 9, 11, 16, 17, 19, 20] CPU times: user 0 ns, sys: 0 ns, total: 0 ns Wall time: 140 µs
n = 40
print(n+1)
%time upgrade(cmap, n, n+1)
41 new smallest = 10 considering 1 considering 2 considering 3 considering 4 [1, 3, 4, 9, 11, 16, 18, 19, 21, 22] [1, 2, 5, 8, 11, 12, 13, 24, 26, 28] [1, 3, 5, 6, 11, 12, 19, 21, 23, 36] [1, 2, 4, 5, 6, 7, 11, 19, 27, 35] [1, 3, 5, 7, 9, 10, 19, 20, 28, 31] [1, 3, 4, 8, 10, 14, 18, 19, 22, 31] [1, 3, 4, 8, 10, 14, 19, 20, 22, 27] [1, 3, 5, 6, 11, 12, 16, 19, 25, 28] [1, 2, 5, 7, 11, 13, 17, 18, 20, 21] [1, 3, 4, 7, 8, 10, 19, 21, 29, 31] [1, 3, 5, 6, 12, 14, 15, 19, 20, 36] [1, 3, 4, 9, 10, 12, 13, 27, 29, 34] [1, 3, 5, 7, 9, 10, 21, 22, 32, 33] [1, 3, 4, 9, 11, 15, 17, 20, 21, 24] [1, 3, 4, 9, 11, 16, 17, 19, 20, 22] [1, 3, 5, 6, 13, 14, 15, 19, 22, 26] [1, 3, 4, 7, 8, 11, 12, 14, 27, 29] [1, 3, 5, 6, 9, 13, 17, 19, 20, 22] [1, 2, 5, 8, 10, 11, 13, 17, 27, 31] [1, 2, 3, 5, 9, 13, 17, 19, 20, 22] [1, 3, 5, 6, 13, 15, 17, 18, 20, 26] [1, 3, 4, 8, 9, 11, 16, 20, 26, 30] [1, 2, 5, 7, 11, 15, 17, 20, 22, 36] [1, 3, 5, 6, 7, 10, 12, 18, 26, 34] [1, 2, 5, 7, 10, 13, 15, 19, 26, 30] [1, 2, 5, 7, 11, 13, 17, 18, 19, 22] [1, 2, 4, 7, 8, 13, 18, 19, 22, 26] [1, 3, 5, 6, 13, 14, 18, 21, 24, 27] [1, 3, 4, 6, 10, 14, 17, 19, 20, 31] [1, 3, 4, 9, 11, 16, 20, 25, 30, 34] [1, 3, 4, 7, 8, 11, 12, 13, 26, 28] [1, 3, 5, 6, 13, 15, 16, 19, 20, 22] [1, 3, 4, 9, 11, 15, 17, 20, 24, 35] [1, 3, 4, 8, 10, 15, 17, 18, 23, 29] [1, 3, 5, 6, 7, 10, 12, 20, 28, 36] [1, 3, 4, 5, 11, 13, 17, 18, 19, 22] [1, 3, 5, 6, 10, 11, 13, 25, 27, 28] [1, 3, 4, 7, 8, 9, 19, 21, 30, 32] [1, 3, 4, 9, 11, 16, 19, 21, 25, 30] [1, 3, 4, 9, 11, 16, 17, 19, 20, 24] [1, 3, 5, 6, 13, 15, 16, 17, 24, 35] [1, 2, 5, 8, 11, 13, 16, 19, 20, 21] [1, 2, 5, 7, 10, 13, 15, 19, 26, 35] [1, 3, 5, 7, 8, 10, 12, 20, 26, 34] [1, 3, 5, 7, 9, 10, 20, 21, 31, 32] [1, 2, 4, 7, 10, 13, 16, 19, 20, 21] [1, 3, 5, 7, 9, 10, 21, 22, 31, 32] [1, 2, 5, 8, 10, 14, 17, 20, 21, 31] [1, 3, 5, 6, 13, 14, 16, 17, 22, 24] [1, 3, 4, 7, 8, 13, 17, 19, 20, 28] [1, 3, 5, 6, 13, 15, 16, 17, 19, 24] [1, 3, 5, 6, 11, 13, 14, 18, 27, 34] [1, 2, 5, 8, 10, 12, 17, 18, 20, 31] [1, 2, 5, 7, 11, 13, 17, 19, 20, 22] [1, 3, 4, 6, 10, 14, 18, 19, 20, 21] [1, 2, 5, 7, 10, 11, 12, 25, 26, 29] [1, 3, 5, 7, 9, 10, 18, 19, 30, 31] [1, 3, 5, 7, 8, 15, 17, 19, 20, 26] [1, 3, 4, 7, 9, 11, 16, 19, 20, 30] [1, 3, 5, 6, 13, 15, 17, 24, 30, 35] [1, 2, 5, 8, 11, 13, 15, 25, 26, 27] [1, 3, 4, 9, 11, 16, 18, 19, 20, 22] [1, 2, 4, 5, 11, 14, 15, 19, 27, 35] [1, 2, 5, 6, 8, 10, 15, 19, 20, 31] [1, 3, 4, 8, 9, 10, 15, 18, 29, 31] [1, 3, 5, 6, 13, 14, 15, 19, 22, 25] [1, 3, 4, 9, 11, 16, 17, 20, 21, 35] [1, 3, 4, 6, 10, 14, 18, 20, 25, 27] [1, 3, 4, 7, 8, 11, 12, 13, 27, 29] [1, 3, 4, 9, 11, 16, 17, 18, 20, 30] [1, 3, 4, 9, 11, 16, 17, 19, 20, 32] [1, 3, 5, 6, 13, 15, 17, 18, 23, 24] [1, 3, 4, 6, 11, 13, 17, 18, 20, 21] [1, 3, 4, 9, 11, 12, 16, 24, 26, 30] [1, 3, 5, 7, 9, 11, 13, 14, 28, 29] [1, 3, 4, 8, 9, 10, 15, 18, 28, 31] [1, 3, 4, 9, 11, 16, 17, 19, 20, 30] [1, 3, 5, 6, 8, 12, 19, 20, 28, 29] [1, 3, 4, 9, 11, 16, 17, 19, 20, 25] [1, 2, 5, 6, 9, 10, 12, 13, 27, 29] [1, 2, 5, 8, 11, 12, 13, 27, 28, 29] [1, 3, 5, 6, 11, 13, 15, 20, 26, 33] [1, 3, 4, 6, 10, 14, 19, 20, 27, 32] [1, 3, 5, 7, 8, 10, 18, 19, 30, 31] [1, 2, 5, 8, 11, 14, 17, 19, 20, 21] [1, 3, 5, 7, 9, 10, 20, 21, 29, 30] [1, 3, 4, 9, 10, 11, 13, 24, 27, 28] [1, 3, 4, 9, 11, 12, 16, 20, 26, 30] [1, 3, 5, 7, 9, 10, 20, 21, 32, 33] [1, 2, 5, 7, 10, 11, 12, 25, 28, 29] [1, 3, 5, 7, 8, 12, 14, 18, 26, 34] [1, 3, 4, 7, 8, 10, 18, 20, 29, 31] [1, 3, 4, 5, 11, 13, 17, 19, 20, 24] [1, 3, 4, 9, 10, 13, 14, 21, 27, 29] [1, 3, 5, 7, 8, 13, 17, 19, 20, 28] [1, 3, 5, 7, 9, 10, 19, 20, 31, 32] [1, 3, 4, 9, 11, 16, 19, 20, 25, 33] [1, 3, 4, 6, 10, 12, 17, 18, 20, 21] [1, 2, 4, 5, 7, 13, 16, 18, 23, 33] [1, 3, 4, 9, 10, 12, 13, 23, 28, 30] [1, 3, 4, 9, 11, 15, 17, 18, 20, 24] [1, 2, 5, 7, 10, 13, 16, 19, 20, 21] [1, 3, 4, 9, 11, 12, 16, 26, 30, 36] [1, 3, 4, 9, 11, 15, 17, 18, 22, 23] [1, 2, 5, 6, 7, 10, 18, 20, 29, 31] [1, 3, 4, 7, 9, 15, 17, 19, 20, 24] [1, 3, 4, 9, 11, 12, 16, 24, 25, 27] [1, 3, 4, 5, 11, 13, 16, 20, 25, 34] [1, 3, 4, 6, 8, 12, 17, 19, 20, 29] [1, 2, 5, 6, 9, 11, 19, 21, 28, 30] [1, 3, 5, 6, 13, 15, 17, 18, 22, 23] [1, 3, 5, 6, 12, 13, 15, 18, 22, 26] [1, 2, 5, 8, 9, 12, 14, 25, 26, 27] [1, 3, 5, 6, 8, 12, 19, 20, 29, 33] [1, 2, 5, 7, 11, 15, 17, 20, 21, 28] [1, 3, 5, 6, 10, 13, 16, 24, 25, 33] [1, 3, 4, 9, 11, 14, 15, 17, 24, 36] [1, 3, 4, 9, 11, 16, 17, 19, 20, 38] [1, 2, 4, 6, 9, 10, 17, 19, 20, 31] [1, 3, 4, 7, 9, 15, 17, 20, 21, 24] [1, 3, 4, 9, 11, 13, 18, 19, 21, 32] [1, 2, 5, 7, 8, 11, 17, 20, 21, 28] [1, 3, 4, 5, 6, 9, 16, 23, 30, 37] [1, 3, 5, 6, 10, 11, 12, 16, 25, 28] [1, 3, 4, 9, 10, 12, 13, 22, 27, 29] [1, 2, 5, 8, 11, 13, 17, 19, 22, 29] [1, 3, 5, 7, 9, 10, 20, 21, 28, 29] [1, 3, 4, 7, 8, 9, 19, 21, 31, 33] [1, 3, 4, 9, 11, 13, 17, 18, 19, 22] [1, 3, 4, 9, 11, 15, 17, 18, 19, 22] [1, 2, 4, 5, 10, 13, 14, 21, 28, 35] [1, 3, 5, 6, 13, 14, 16, 18, 20, 21] [1, 3, 5, 6, 10, 13, 16, 23, 24, 25] [1, 3, 5, 6, 13, 15, 17, 18, 24, 35] [1, 2, 5, 8, 11, 14, 17, 20, 22, 24] [1, 2, 5, 8, 10, 12, 17, 18, 20, 21] [1, 2, 5, 7, 11, 15, 17, 20, 21, 22] [1, 3, 4, 9, 11, 16, 20, 26, 27, 30] [1, 3, 4, 7, 8, 9, 18, 20, 30, 32] [1, 3, 5, 6, 13, 14, 16, 20, 21, 25] [1, 3, 5, 6, 13, 14, 21, 23, 25, 27] [1, 3, 4, 8, 10, 11, 13, 24, 28, 30] [1, 3, 4, 6, 10, 15, 16, 18, 23, 34] [1, 2, 5, 8, 11, 13, 17, 18, 19, 22] [1, 3, 4, 6, 11, 12, 17, 18, 20, 21] [1, 3, 4, 9, 10, 12, 13, 21, 26, 28] [1, 3, 4, 6, 11, 13, 18, 20, 21, 24] [1, 3, 4, 9, 11, 16, 17, 20, 30, 34] [1, 2, 5, 8, 11, 14, 16, 19, 20, 21] [1, 2, 5, 8, 10, 12, 18, 19, 20, 33] [1, 3, 4, 9, 11, 16, 17, 20, 30, 35] [1, 3, 4, 9, 11, 15, 17, 18, 20, 21] [1, 2, 5, 8, 10, 12, 13, 18, 27, 33] [1, 3, 4, 9, 11, 12, 17, 18, 20, 21] [1, 2, 5, 8, 10, 12, 15, 18, 20, 29] [1, 3, 4, 8, 9, 10, 14, 17, 29, 32] [1, 3, 5, 6, 13, 15, 16, 18, 22, 26] [1, 3, 4, 5, 11, 12, 18, 19, 21, 23] [1, 3, 4, 8, 10, 15, 17, 18, 20, 21] [1, 3, 5, 6, 10, 14, 15, 19, 22, 25] [1, 3, 4, 9, 11, 12, 17, 19, 20, 24] [1, 3, 5, 6, 11, 12, 18, 19, 21, 23] [1, 2, 4, 7, 10, 11, 14, 19, 25, 30] [1, 3, 5, 6, 13, 15, 16, 20, 21, 38] [1, 2, 4, 5, 7, 12, 14, 18, 27, 33] [1, 3, 4, 7, 8, 10, 19, 21, 29, 34] [1, 3, 4, 8, 10, 14, 18, 20, 25, 27] [1, 3, 5, 6, 12, 14, 16, 17, 23, 24] [1, 3, 5, 6, 13, 15, 17, 20, 21, 26] [1, 3, 4, 6, 9, 10, 17, 20, 22, 32] [1, 3, 4, 9, 10, 15, 17, 18, 20, 21] [1, 2, 5, 7, 11, 15, 19, 20, 21, 22] [1, 3, 5, 7, 9, 10, 21, 22, 33, 34] [1, 3, 5, 7, 8, 12, 15, 20, 26, 36] [1, 2, 5, 8, 10, 14, 16, 19, 20, 21] [1, 2, 5, 8, 11, 13, 15, 24, 25, 26] [1, 2, 4, 5, 10, 13, 14, 20, 27, 34] [1, 3, 5, 7, 8, 10, 19, 20, 30, 31] [1, 3, 4, 9, 11, 12, 17, 19, 24, 28] [1, 2, 5, 7, 11, 15, 16, 17, 24, 36] [1, 2, 5, 7, 11, 15, 17, 19, 20, 22] [1, 3, 5, 6, 13, 15, 17, 18, 20, 24] [1, 2, 5, 8, 11, 14, 17, 20, 21, 22] [1, 3, 4, 9, 11, 13, 17, 19, 20, 24] [1, 2, 4, 6, 9, 13, 15, 19, 27, 35] [1, 3, 4, 9, 11, 16, 17, 18, 20, 21] [1, 3, 5, 7, 8, 10, 12, 13, 27, 28] [1, 3, 4, 9, 11, 16, 18, 19, 22, 23] [1, 3, 4, 8, 9, 11, 17, 19, 20, 32] [1, 3, 4, 9, 11, 13, 18, 19, 21, 22] [1, 2, 4, 5, 11, 14, 17, 18, 19, 22] [1, 2, 5, 8, 10, 13, 16, 19, 20, 21] [1, 2, 5, 6, 8, 9, 19, 21, 30, 32] [1, 2, 4, 5, 10, 12, 18, 20, 25, 29] [1, 3, 4, 9, 10, 14, 16, 19, 20, 27] [1, 3, 5, 7, 9, 11, 13, 14, 26, 27] [1, 2, 5, 8, 11, 14, 17, 18, 19, 22] [1, 3, 5, 6, 8, 15, 17, 18, 22, 23] [1, 2, 5, 8, 10, 12, 18, 20, 25, 29] [1, 3, 4, 5, 6, 7, 10, 18, 26, 34] [1, 2, 4, 5, 8, 10, 17, 20, 21, 31] [1, 3, 4, 8, 10, 11, 13, 24, 26, 30] [1, 2, 5, 6, 9, 11, 18, 20, 28, 30] [1, 2, 4, 7, 10, 11, 12, 25, 27, 29] [1, 3, 4, 9, 11, 16, 17, 19, 20, 21] [1, 3, 4, 9, 10, 12, 13, 24, 26, 28] [1, 2, 5, 8, 11, 14, 17, 18, 19, 39] [1, 2, 4, 6, 8, 10, 12, 13, 27, 28] [1, 3, 5, 7, 8, 10, 18, 21, 27, 33] [1, 3, 4, 8, 9, 10, 15, 18, 19, 31] [1, 3, 5, 6, 13, 15, 17, 23, 24, 30] [1, 2, 5, 8, 10, 13, 17, 19, 27, 31] [1, 3, 4, 9, 11, 16, 19, 20, 26, 30] [1, 3, 5, 6, 13, 15, 17, 19, 20, 26] [1, 3, 4, 6, 11, 13, 14, 20, 26, 35] [1, 2, 5, 7, 9, 13, 14, 16, 24, 34] [1, 3, 5, 6, 13, 15, 17, 24, 28, 35] [1, 3, 5, 6, 13, 15, 16, 18, 22, 36] [1, 3, 5, 7, 8, 17, 19, 20, 24, 30] [1, 3, 5, 7, 8, 15, 17, 18, 22, 23] [1, 3, 4, 8, 10, 12, 13, 19, 27, 33] [1, 3, 5, 7, 8, 14, 17, 19, 22, 32] [1, 3, 4, 5, 8, 14, 20, 25, 27, 33] [1, 3, 4, 8, 10, 11, 13, 20, 24, 28] [1, 3, 5, 6, 12, 13, 18, 19, 21, 23] [1, 3, 4, 8, 9, 11, 17, 19, 20, 24] [1, 3, 4, 6, 10, 13, 15, 18, 26, 34] [1, 3, 4, 9, 10, 15, 17, 20, 21, 24] [1, 2, 5, 8, 11, 12, 13, 26, 28, 30] [1, 3, 4, 8, 10, 12, 17, 18, 20, 21] [1, 3, 4, 9, 11, 13, 16, 20, 25, 26] [1, 3, 4, 5, 8, 11, 15, 16, 25, 34] [1, 2, 5, 7, 11, 15, 17, 18, 20, 21] [1, 3, 5, 6, 13, 15, 16, 20, 21, 33] [1, 2, 5, 8, 11, 12, 13, 26, 27, 28] [1, 3, 4, 5, 8, 14, 20, 26, 31, 33] [1, 3, 5, 6, 13, 15, 17, 22, 23, 28] [1, 3, 4, 6, 11, 12, 14, 18, 27, 34] [1, 3, 5, 6, 13, 15, 17, 18, 24, 25] [1, 3, 4, 8, 10, 15, 17, 18, 21, 37] [1, 3, 4, 7, 9, 15, 17, 20, 24, 29] [1, 2, 5, 8, 11, 12, 13, 27, 29, 31] [1, 3, 5, 6, 8, 15, 16, 20, 21, 33] [1, 3, 5, 6, 10, 14, 18, 20, 21, 23] [1, 3, 4, 9, 10, 12, 13, 26, 28, 30] [1, 3, 4, 5, 10, 12, 17, 18, 20, 21] [1, 3, 5, 7, 9, 10, 18, 21, 28, 31] [1, 3, 5, 7, 9, 10, 21, 22, 30, 31] [1, 2, 5, 8, 10, 11, 12, 25, 27, 29] [1, 2, 5, 7, 11, 15, 19, 21, 22, 24] [1, 2, 4, 5, 11, 13, 18, 20, 26, 30] [1, 3, 4, 5, 8, 14, 17, 22, 24, 32] [1, 3, 4, 9, 10, 11, 12, 16, 26, 30] [1, 3, 5, 7, 8, 16, 18, 20, 21, 30] [1, 3, 4, 8, 10, 11, 13, 25, 27, 31] [1, 3, 5, 6, 13, 15, 16, 18, 20, 21] [1, 3, 5, 6, 12, 14, 15, 19, 20, 22] [1, 3, 5, 6, 11, 12, 17, 18, 20, 21] [1, 2, 5, 7, 10, 11, 13, 18, 27, 28] [1, 3, 4, 9, 11, 13, 18, 19, 22, 30] [1, 2, 5, 7, 11, 12, 14, 18, 26, 34] [1, 3, 4, 7, 9, 12, 13, 20, 27, 34] [1, 3, 4, 9, 10, 12, 13, 25, 27, 29] [1, 3, 5, 7, 9, 11, 13, 14, 27, 28] [1, 3, 5, 6, 8, 10, 12, 13, 27, 28] [1, 2, 4, 5, 11, 12, 18, 19, 21, 23] [1, 3, 4, 8, 10, 14, 18, 19, 20, 21] [1, 3, 4, 8, 10, 11, 14, 19, 26, 31] [1, 3, 4, 9, 11, 16, 17, 19, 20, 37] [1, 3, 5, 6, 12, 14, 16, 17, 24, 34] [1, 2, 5, 8, 10, 14, 17, 18, 19, 22] [1, 3, 4, 8, 10, 14, 18, 23, 25, 30] [1, 3, 4, 5, 8, 14, 20, 26, 32, 38] [1, 3, 4, 6, 11, 13, 18, 19, 21, 22] [1, 3, 5, 6, 13, 15, 16, 18, 24, 35] [1, 3, 5, 6, 8, 12, 19, 20, 29, 30] [1, 3, 4, 6, 10, 14, 16, 19, 20, 21] [1, 3, 4, 8, 9, 11, 12, 22, 27, 29] [1, 3, 5, 6, 8, 15, 16, 18, 20, 21] [1, 3, 5, 6, 13, 15, 16, 20, 21, 23] [1, 3, 4, 7, 9, 15, 17, 18, 20, 24] [1, 3, 4, 9, 11, 15, 17, 18, 22, 37] [1, 2, 5, 6, 8, 15, 16, 18, 20, 21] [1, 3, 4, 7, 9, 15, 17, 18, 19, 22] [1, 3, 4, 9, 10, 12, 13, 25, 27, 32] [1, 3, 5, 7, 9, 10, 12, 13, 27, 28] [1, 3, 5, 6, 7, 15, 16, 19, 22, 33] [1, 3, 4, 7, 9, 15, 17, 20, 24, 35] [1, 3, 4, 6, 10, 13, 15, 21, 29, 37] [1, 3, 4, 9, 10, 12, 13, 24, 29, 31] [1, 3, 4, 8, 10, 11, 13, 24, 28, 29] [1, 2, 5, 7, 10, 12, 16, 25, 28, 29] [1, 2, 5, 7, 11, 15, 18, 20, 23, 32] [1, 3, 4, 9, 11, 15, 17, 19, 20, 24] [1, 3, 5, 6, 12, 13, 18, 19, 27, 29] [1, 3, 5, 6, 13, 15, 16, 18, 22, 23] [1, 3, 4, 9, 10, 12, 16, 18, 23, 28] [1, 3, 5, 6, 13, 15, 16, 19, 20, 21] [1, 3, 4, 6, 10, 14, 19, 20, 26, 31] [1, 3, 4, 6, 10, 14, 18, 20, 21, 23] [1, 2, 5, 6, 7, 11, 15, 18, 26, 33] [1, 2, 5, 7, 11, 14, 17, 18, 19, 22] [1, 2, 4, 7, 8, 13, 15, 16, 23, 33] [1, 3, 4, 8, 10, 15, 16, 19, 20, 33] [1, 2, 4, 5, 6, 13, 16, 23, 29, 36] [1, 2, 5, 7, 11, 15, 17, 18, 20, 24] [1, 3, 5, 7, 9, 11, 13, 14, 29, 30] [1, 3, 4, 9, 11, 13, 18, 20, 21, 24] [1, 2, 5, 6, 7, 15, 18, 22, 26, 33] [1, 2, 5, 7, 11, 15, 18, 19, 20, 21] [1, 3, 4, 6, 10, 14, 18, 20, 23, 25] [1, 3, 4, 7, 9, 15, 17, 20, 21, 30] [1, 2, 5, 7, 11, 15, 17, 18, 20, 39] [1, 3, 4, 9, 10, 12, 17, 18, 20, 21] [1, 3, 5, 7, 9, 10, 20, 21, 30, 31] [1, 2, 5, 7, 11, 15, 19, 21, 24, 26] [1, 3, 4, 9, 11, 16, 19, 20, 22, 34] [1, 3, 4, 9, 11, 15, 16, 17, 20, 38] [1, 3, 4, 8, 10, 14, 18, 20, 23, 25] [1, 2, 5, 7, 10, 12, 16, 25, 29, 33] [1, 2, 5, 8, 11, 12, 13, 25, 27, 29] [1, 3, 5, 6, 12, 13, 19, 20, 22, 24] [1, 3, 4, 8, 10, 14, 18, 20, 21, 23] [1, 2, 5, 7, 9, 13, 15, 18, 20, 32] [1, 3, 4, 9, 10, 15, 16, 21, 23, 25] [1, 2, 5, 6, 8, 9, 18, 20, 30, 32] [1, 2, 5, 7, 8, 10, 17, 21, 30, 31] [1, 2, 4, 6, 8, 9, 19, 20, 29, 32] [1, 3, 4, 8, 10, 14, 17, 18, 19, 22] [1, 2, 5, 7, 9, 13, 17, 19, 20, 22] [1, 3, 5, 7, 9, 11, 12, 14, 26, 27] [1, 3, 5, 6, 10, 14, 18, 19, 20, 21] [1, 3, 4, 9, 11, 12, 14, 18, 26, 30] [1, 3, 4, 8, 9, 11, 12, 17, 27, 29] [1, 3, 4, 9, 11, 13, 16, 19, 20, 21] [1, 2, 4, 6, 8, 9, 19, 20, 30, 33] [1, 3, 4, 9, 11, 16, 17, 19, 20, 40] [1, 3, 4, 8, 10, 14, 18, 21, 23, 30] [1, 3, 4, 9, 11, 16, 19, 20, 22, 33] [1, 3, 5, 6, 13, 15, 16, 18, 22, 38] [1, 3, 4, 9, 10, 12, 13, 26, 28, 33] [1, 3, 5, 6, 13, 14, 18, 20, 21, 24] [1, 2, 5, 8, 10, 12, 17, 20, 21, 34] [1, 3, 5, 7, 9, 11, 12, 14, 27, 28] [1, 2, 5, 7, 11, 15, 17, 18, 20, 34] [1, 3, 4, 5, 7, 13, 15, 16, 20, 34] [1, 3, 5, 7, 9, 11, 12, 13, 27, 28] [1, 2, 5, 7, 8, 10, 13, 17, 27, 31] [1, 3, 4, 5, 8, 11, 15, 16, 24, 33] [1, 3, 4, 8, 10, 14, 16, 19, 20, 21] [1, 3, 4, 9, 10, 15, 17, 18, 19, 22] [1, 3, 4, 8, 9, 11, 12, 25, 27, 32] [1, 2, 5, 8, 9, 11, 13, 23, 27, 28] [1, 2, 5, 7, 11, 12, 14, 20, 28, 36] [1, 3, 4, 9, 11, 15, 16, 19, 20, 22] [1, 3, 5, 6, 13, 15, 17, 24, 30, 37] [1, 3, 4, 8, 9, 11, 12, 25, 27, 29] [1, 2, 5, 6, 8, 9, 19, 21, 31, 33] [1, 2, 5, 7, 11, 12, 14, 19, 27, 35] [1, 2, 5, 6, 9, 10, 12, 13, 26, 28] [1, 3, 4, 6, 10, 15, 16, 23, 25, 33] [1, 3, 5, 7, 9, 10, 20, 21, 29, 32] [1, 3, 5, 7, 8, 15, 16, 18, 20, 21] [1, 3, 4, 6, 8, 10, 12, 13, 27, 28] [1, 3, 5, 7, 8, 15, 17, 18, 20, 24] [1, 2, 4, 5, 9, 12, 13, 18, 28, 34] [1, 3, 5, 6, 13, 15, 17, 20, 23, 26] [1, 2, 4, 6, 8, 9, 19, 22, 28, 31] [1, 3, 4, 6, 10, 14, 16, 19, 20, 27] [1, 3, 5, 7, 8, 14, 17, 18, 19, 22] [1, 3, 5, 6, 12, 13, 17, 19, 20, 22] [1, 3, 4, 9, 11, 15, 17, 20, 24, 27] [1, 2, 5, 7, 11, 13, 16, 19, 20, 21] [1, 2, 4, 5, 10, 12, 17, 18, 20, 21] [1, 3, 5, 6, 11, 13, 15, 20, 23, 26] [1, 3, 4, 9, 11, 16, 17, 19, 24, 28] [1, 2, 5, 7, 11, 15, 16, 17, 21, 24] [1, 3, 5, 6, 13, 15, 17, 18, 24, 37] [1, 3, 4, 9, 10, 15, 16, 18, 20, 21] [1, 2, 4, 7, 8, 12, 14, 15, 24, 33] [1, 2, 4, 7, 9, 10, 15, 19, 26, 30] [1, 3, 4, 6, 11, 13, 18, 20, 24, 28] [1, 3, 5, 7, 9, 10, 19, 20, 30, 31] [1, 3, 5, 7, 8, 10, 19, 20, 31, 32] [1, 3, 4, 9, 11, 15, 17, 18, 22, 38] [1, 3, 4, 9, 11, 16, 17, 20, 26, 38] [1, 2, 5, 7, 11, 15, 16, 18, 23, 35] [1, 2, 5, 6, 8, 15, 17, 18, 22, 23] [1, 3, 4, 9, 10, 12, 13, 24, 26, 31] [1, 3, 5, 7, 8, 14, 18, 20, 21, 30] [1, 3, 5, 6, 13, 15, 17, 24, 25, 30] [1, 3, 4, 9, 11, 13, 17, 18, 20, 21] [1, 3, 4, 9, 10, 12, 13, 27, 29, 31] CPU times: user 9h 56min 8s, sys: 57.9 s, total: 9h 57min 6s Wall time: 9h 56min 49s
n = 41
print(n+1)
%time upgrade(cmap, n, n+1)
42 new smallest = 10 [1, 3, 4, 9, 11, 16, 18, 19, 21, 22] [1, 3, 5, 6, 11, 12, 19, 21, 23, 36] [1, 3, 5, 7, 9, 10, 20, 21, 32, 33] [1, 3, 4, 6, 10, 13, 15, 21, 29, 37] [1, 2, 4, 5, 6, 7, 11, 19, 27, 35] [1, 3, 5, 7, 8, 12, 14, 18, 26, 34] [1, 3, 4, 9, 11, 13, 18, 19, 21, 22] [1, 3, 4, 9, 10, 12, 13, 24, 29, 31] [1, 3, 4, 8, 10, 14, 19, 20, 22, 27] [1, 2, 5, 8, 10, 13, 16, 19, 20, 21] [1, 3, 4, 9, 10, 13, 14, 21, 27, 29] [1, 2, 5, 6, 8, 9, 19, 21, 30, 32] [1, 3, 5, 7, 9, 10, 19, 20, 31, 32] [1, 3, 4, 8, 10, 11, 13, 24, 28, 29] [1, 2, 5, 7, 11, 13, 17, 18, 20, 21] [1, 3, 4, 7, 8, 10, 19, 21, 29, 31] [1, 3, 4, 9, 11, 16, 19, 20, 25, 33] [1, 3, 4, 6, 10, 12, 17, 18, 20, 21] [1, 3, 5, 6, 12, 13, 18, 19, 27, 29] [1, 3, 4, 9, 10, 12, 13, 23, 28, 30] [1, 3, 5, 6, 13, 15, 16, 19, 20, 21] [1, 3, 4, 9, 11, 15, 17, 18, 20, 24] [1, 3, 5, 6, 12, 14, 15, 19, 20, 36] [1, 2, 5, 7, 10, 13, 16, 19, 20, 21] [1, 2, 4, 5, 8, 10, 17, 20, 21, 31] [1, 3, 4, 9, 11, 12, 16, 26, 30, 36] [1, 3, 4, 6, 10, 14, 18, 20, 21, 23] [1, 3, 4, 9, 10, 12, 13, 27, 29, 34] [1, 2, 5, 6, 9, 11, 19, 21, 28, 30] [1, 3, 4, 9, 11, 16, 17, 19, 20, 21] [1, 3, 5, 7, 9, 10, 21, 22, 32, 33] [1, 3, 5, 7, 8, 10, 18, 21, 27, 33] [1, 3, 4, 9, 11, 15, 17, 20, 21, 24] [1, 3, 4, 9, 11, 16, 17, 19, 20, 22] [1, 2, 4, 5, 6, 13, 16, 23, 29, 36] [1, 2, 5, 7, 11, 15, 17, 20, 21, 28] [1, 2, 5, 7, 11, 15, 17, 18, 20, 24] [1, 3, 5, 7, 9, 11, 13, 14, 29, 30] [1, 3, 4, 9, 11, 13, 18, 20, 21, 24] [1, 3, 4, 9, 11, 16, 17, 19, 20, 38] [1, 3, 4, 7, 9, 15, 17, 20, 21, 24] [1, 3, 5, 6, 9, 13, 17, 19, 20, 22] [1, 3, 4, 9, 11, 13, 18, 19, 21, 32] [1, 2, 5, 7, 8, 11, 17, 20, 21, 28] [1, 3, 4, 5, 6, 9, 16, 23, 30, 37] [1, 2, 5, 8, 10, 11, 13, 17, 27, 31] [1, 3, 4, 9, 10, 12, 13, 22, 27, 29] [1, 2, 5, 7, 11, 15, 18, 19, 20, 21] [1, 2, 3, 5, 9, 13, 17, 19, 20, 22] [1, 2, 5, 8, 11, 13, 17, 19, 22, 29] [1, 3, 5, 7, 9, 10, 20, 21, 28, 29] [1, 3, 4, 9, 11, 16, 19, 20, 26, 30] [1, 3, 4, 7, 8, 9, 19, 21, 31, 33] [1, 3, 4, 7, 9, 15, 17, 20, 21, 30] [1, 3, 5, 6, 13, 15, 16, 18, 22, 36] [1, 3, 4, 8, 9, 11, 16, 20, 26, 30] [1, 2, 4, 5, 10, 13, 14, 21, 28, 35] [1, 3, 5, 6, 13, 14, 16, 18, 20, 21] [1, 2, 5, 7, 11, 15, 17, 20, 22, 36] [1, 3, 5, 6, 13, 15, 17, 18, 24, 35] [1, 2, 5, 8, 11, 14, 17, 20, 22, 24] [1, 3, 4, 9, 10, 12, 13, 27, 29, 31] [1, 3, 5, 6, 12, 13, 18, 19, 21, 23] [1, 3, 4, 9, 10, 12, 17, 18, 20, 21] [1, 2, 5, 8, 10, 12, 17, 18, 20, 21] [1, 3, 4, 9, 10, 15, 17, 20, 21, 24] [1, 2, 5, 8, 11, 12, 13, 26, 28, 30] [1, 3, 5, 7, 9, 10, 20, 21, 30, 31] [1, 3, 4, 8, 10, 12, 17, 18, 20, 21] [1, 2, 5, 7, 11, 15, 19, 21, 24, 26] [1, 3, 4, 9, 11, 16, 19, 20, 22, 34] [1, 3, 4, 9, 11, 15, 16, 17, 20, 38] [1, 2, 5, 7, 11, 15, 17, 20, 21, 22] [1, 3, 5, 6, 13, 14, 18, 21, 24, 27] [1, 2, 5, 8, 11, 12, 13, 25, 27, 29] [1, 3, 5, 6, 12, 13, 19, 20, 22, 24] [1, 3, 4, 9, 11, 13, 16, 20, 25, 26] [1, 3, 4, 9, 11, 16, 20, 26, 27, 30] [1, 3, 4, 5, 8, 11, 15, 16, 25, 34] [1, 3, 5, 6, 13, 15, 16, 19, 20, 22] [1, 3, 5, 6, 13, 14, 16, 20, 21, 25] [1, 3, 5, 6, 13, 14, 21, 23, 25, 27] [1, 2, 5, 7, 11, 15, 17, 18, 20, 21] [1, 3, 5, 6, 13, 15, 16, 20, 21, 33] [1, 3, 4, 8, 10, 14, 18, 20, 21, 23] [1, 3, 4, 9, 10, 15, 16, 21, 23, 25] [1, 3, 5, 6, 7, 10, 12, 20, 28, 36] [1, 2, 5, 7, 8, 10, 17, 21, 30, 31] [1, 3, 4, 7, 8, 9, 19, 21, 30, 32] [1, 2, 5, 7, 9, 13, 17, 19, 20, 22] [1, 3, 4, 9, 11, 16, 19, 21, 25, 30] [1, 3, 4, 6, 11, 12, 17, 18, 20, 21] [1, 3, 5, 6, 10, 14, 18, 19, 20, 21] [1, 3, 4, 9, 11, 12, 14, 18, 26, 30] [1, 3, 4, 9, 10, 12, 13, 21, 26, 28] [1, 3, 4, 6, 11, 13, 18, 20, 21, 24] [1, 3, 4, 9, 11, 13, 16, 19, 20, 21] [1, 2, 5, 8, 11, 14, 16, 19, 20, 21] [1, 2, 4, 6, 8, 9, 19, 20, 30, 33] [1, 2, 5, 8, 11, 13, 16, 19, 20, 21] [1, 3, 4, 8, 10, 14, 18, 21, 23, 30] [1, 3, 4, 9, 11, 15, 17, 18, 20, 21] [1, 3, 4, 9, 11, 16, 19, 20, 22, 33] [1, 3, 5, 6, 13, 15, 17, 18, 24, 25] [1, 2, 5, 7, 10, 13, 15, 19, 26, 35] [1, 3, 5, 7, 8, 10, 12, 20, 26, 34] [1, 3, 4, 9, 10, 12, 13, 26, 28, 33] [1, 3, 4, 8, 10, 15, 17, 18, 21, 37] [1, 3, 5, 7, 9, 10, 20, 21, 31, 32] [1, 2, 4, 7, 10, 13, 16, 19, 20, 21] [1, 2, 5, 8, 11, 12, 13, 27, 29, 31] [1, 3, 5, 6, 8, 15, 16, 20, 21, 33] [1, 3, 5, 7, 9, 10, 21, 22, 31, 32] [1, 3, 5, 6, 10, 14, 18, 20, 21, 23] [1, 3, 5, 6, 13, 14, 18, 20, 21, 24] [1, 3, 4, 9, 11, 12, 17, 18, 20, 21] [1, 2, 5, 8, 10, 12, 17, 20, 21, 34] [1, 3, 4, 9, 10, 12, 13, 26, 28, 30] [1, 3, 5, 7, 9, 11, 12, 14, 27, 28] [1, 3, 4, 5, 10, 12, 17, 18, 20, 21] [1, 3, 5, 7, 9, 10, 18, 21, 28, 31] [1, 3, 5, 7, 9, 10, 21, 22, 30, 31] [1, 3, 4, 8, 9, 10, 14, 17, 29, 32] [1, 3, 5, 6, 13, 15, 16, 18, 22, 26] [1, 3, 4, 5, 11, 12, 18, 19, 21, 23] [1, 2, 5, 8, 10, 14, 17, 20, 21, 31] [1, 3, 4, 8, 10, 15, 17, 18, 20, 21] [1, 2, 5, 7, 11, 15, 19, 21, 22, 24] [1, 3, 4, 8, 10, 14, 16, 19, 20, 21] [1, 2, 5, 7, 11, 12, 14, 20, 28, 36] [1, 3, 5, 6, 11, 12, 18, 19, 21, 23] [1, 3, 4, 9, 11, 15, 16, 19, 20, 22] [1, 3, 5, 6, 13, 15, 17, 24, 30, 37] [1, 2, 5, 6, 8, 9, 19, 21, 31, 33] [1, 3, 4, 9, 10, 11, 12, 16, 26, 30] [1, 3, 5, 6, 13, 15, 16, 20, 21, 38] [1, 3, 5, 7, 8, 16, 18, 20, 21, 30] [1, 3, 4, 8, 10, 11, 13, 25, 27, 31] [1, 3, 5, 6, 13, 15, 16, 18, 20, 21] [1, 3, 5, 6, 12, 14, 15, 19, 20, 22] [1, 3, 4, 7, 8, 10, 19, 21, 29, 34] [1, 2, 5, 7, 11, 13, 17, 19, 20, 22] [1, 3, 4, 6, 10, 14, 18, 19, 20, 21] [1, 3, 5, 6, 11, 12, 17, 18, 20, 21] [1, 2, 5, 7, 11, 12, 14, 19, 27, 35] [1, 3, 5, 7, 9, 10, 20, 21, 29, 32] [1, 3, 5, 7, 8, 15, 16, 18, 20, 21] [1, 3, 5, 7, 8, 15, 17, 18, 20, 24] [1, 3, 4, 9, 10, 12, 13, 25, 27, 29] [1, 3, 5, 7, 9, 11, 13, 14, 27, 28] [1, 3, 5, 6, 12, 13, 17, 19, 20, 22] [1, 3, 5, 6, 13, 15, 17, 20, 21, 26] [1, 2, 5, 8, 11, 13, 15, 25, 26, 27] [1, 3, 4, 9, 11, 16, 18, 19, 20, 22] [1, 3, 4, 6, 9, 10, 17, 20, 22, 32] [1, 2, 4, 5, 11, 12, 18, 19, 21, 23] [1, 2, 4, 5, 11, 14, 15, 19, 27, 35] [1, 3, 4, 9, 11, 15, 17, 20, 24, 27] [1, 3, 4, 8, 10, 14, 18, 19, 20, 21] [1, 3, 4, 8, 10, 11, 14, 19, 26, 31] [1, 3, 4, 9, 10, 15, 17, 18, 20, 21] [1, 2, 5, 7, 11, 15, 19, 20, 21, 22] [1, 2, 5, 7, 11, 13, 16, 19, 20, 21] [1, 3, 4, 9, 11, 16, 17, 20, 21, 35] [1, 3, 5, 7, 9, 10, 21, 22, 33, 34] [1, 2, 4, 5, 10, 12, 17, 18, 20, 21] [1, 2, 5, 8, 10, 14, 16, 19, 20, 21] [1, 2, 5, 7, 11, 15, 16, 17, 21, 24] [1, 3, 5, 6, 13, 15, 17, 18, 24, 37] [1, 3, 4, 9, 10, 15, 16, 18, 20, 21] [1, 3, 4, 7, 8, 11, 12, 13, 27, 29] [1, 3, 5, 6, 13, 15, 17, 18, 23, 24] [1, 3, 4, 6, 11, 13, 17, 18, 20, 21] [1, 3, 4, 9, 11, 12, 16, 24, 26, 30] [1, 3, 5, 7, 9, 11, 13, 14, 28, 29] [1, 3, 4, 6, 11, 13, 18, 20, 24, 28] [1, 3, 5, 7, 8, 10, 19, 20, 31, 32] [1, 3, 4, 9, 11, 15, 17, 18, 22, 38] [1, 3, 4, 9, 11, 16, 17, 20, 26, 38] [1, 2, 5, 7, 11, 15, 16, 18, 23, 35] [1, 3, 5, 6, 13, 15, 17, 18, 20, 24] [1, 2, 5, 7, 11, 15, 17, 19, 20, 22] [1, 2, 5, 8, 11, 14, 17, 20, 21, 22] [1, 3, 4, 5, 8, 14, 20, 26, 32, 38] [1, 3, 4, 9, 11, 16, 17, 19, 20, 25] [1, 2, 5, 6, 9, 10, 12, 13, 27, 29] [1, 2, 4, 6, 9, 13, 15, 19, 27, 35] [1, 2, 5, 8, 11, 12, 13, 27, 28, 29] [1, 3, 4, 6, 11, 13, 18, 19, 21, 22] [1, 3, 4, 6, 10, 14, 19, 20, 27, 32] [1, 3, 5, 6, 13, 15, 16, 18, 24, 35] [1, 3, 5, 7, 8, 14, 18, 20, 21, 30] [1, 3, 5, 6, 8, 12, 19, 20, 29, 30] [1, 3, 4, 9, 11, 16, 17, 18, 20, 21] [1, 3, 4, 6, 10, 14, 16, 19, 20, 21] [1, 3, 5, 6, 8, 15, 16, 18, 20, 21] [1, 2, 5, 8, 11, 14, 17, 19, 20, 21] [1, 3, 5, 7, 9, 10, 20, 21, 29, 30] [1, 3, 5, 6, 13, 15, 16, 20, 21, 23] [1, 3, 4, 7, 9, 15, 17, 18, 20, 24] [1, 3, 5, 6, 13, 15, 17, 24, 25, 30] [1, 2, 5, 6, 8, 15, 16, 18, 20, 21] [1, 3, 4, 9, 10, 12, 13, 25, 27, 32] [1, 3, 4, 9, 11, 13, 17, 18, 20, 21] [1, 3, 4, 9, 11, 16, 18, 19, 22, 23] [1, 3, 4, 9, 11, 12, 16, 20, 26, 30] [1, 3, 4, 7, 9, 15, 17, 20, 24, 35] CPU times: user 20 ms, sys: 0 ns, total: 20 ms Wall time: 20.5 ms
n = 42
print(n+1)
%time upgrade(cmap, n, n+1)
43 new smallest = 10 [1, 3, 4, 9, 11, 16, 18, 19, 21, 22] [1, 3, 4, 9, 11, 13, 18, 19, 21, 32] [1, 3, 5, 7, 9, 10, 20, 21, 32, 33] [1, 3, 4, 6, 10, 13, 15, 21, 29, 37] [1, 3, 4, 9, 11, 13, 18, 19, 21, 22] [1, 3, 4, 5, 6, 9, 16, 23, 30, 37] [1, 3, 5, 6, 13, 15, 17, 20, 21, 26] [1, 3, 4, 9, 10, 12, 13, 24, 29, 31] [1, 3, 5, 6, 13, 15, 17, 18, 24, 25] [1, 3, 4, 9, 10, 13, 14, 21, 27, 29] [1, 3, 4, 9, 10, 12, 13, 26, 28, 33] [1, 2, 5, 7, 11, 15, 19, 20, 21, 22] [1, 3, 5, 7, 9, 10, 21, 22, 33, 34] [1, 2, 5, 8, 11, 12, 13, 27, 29, 31] [1, 2, 5, 7, 11, 15, 17, 20, 22, 36] [1, 3, 5, 7, 9, 10, 21, 22, 31, 32] [1, 3, 5, 6, 10, 14, 18, 20, 21, 23] [1, 3, 5, 6, 13, 15, 17, 18, 24, 37] [1, 3, 4, 9, 10, 12, 13, 26, 28, 30] [1, 3, 5, 7, 9, 10, 21, 22, 30, 31] [1, 3, 4, 9, 10, 12, 13, 23, 28, 30] [1, 3, 4, 8, 9, 10, 14, 17, 29, 32] [1, 3, 5, 7, 9, 11, 13, 14, 28, 29] [1, 2, 5, 8, 11, 12, 13, 26, 28, 30] [1, 2, 5, 7, 11, 15, 19, 21, 24, 26] [1, 3, 4, 9, 11, 16, 19, 20, 22, 34] [1, 2, 5, 7, 11, 15, 19, 21, 22, 24] [1, 3, 4, 9, 11, 16, 17, 20, 26, 38] [1, 3, 4, 6, 10, 14, 18, 20, 21, 23] [1, 2, 5, 7, 11, 15, 17, 20, 21, 22] [1, 3, 4, 9, 10, 12, 13, 27, 29, 34] [1, 2, 5, 8, 11, 14, 17, 20, 21, 22] [1, 3, 4, 5, 8, 14, 20, 26, 32, 38] [1, 2, 5, 7, 11, 12, 14, 20, 28, 36] [1, 3, 4, 6, 11, 13, 18, 19, 21, 22] [1, 3, 5, 6, 12, 13, 19, 20, 22, 24] [1, 3, 5, 7, 9, 10, 21, 22, 32, 33] [1, 3, 4, 9, 11, 16, 20, 26, 27, 30] [1, 3, 5, 6, 13, 15, 17, 24, 30, 37] [1, 3, 4, 8, 10, 14, 18, 20, 21, 23] [1, 3, 5, 7, 8, 10, 18, 21, 27, 33] [1, 3, 5, 6, 13, 15, 16, 20, 21, 38] [1, 3, 5, 6, 13, 15, 16, 20, 21, 23] [1, 3, 5, 6, 7, 10, 12, 20, 28, 36] [1, 2, 5, 7, 11, 15, 17, 20, 21, 28] [1, 3, 5, 6, 13, 15, 17, 24, 25, 30] [1, 3, 5, 7, 9, 11, 13, 14, 29, 30] [1, 3, 4, 9, 10, 12, 13, 27, 29, 31] CPU times: user 16 ms, sys: 0 ns, total: 16 ms Wall time: 13.6 ms
n = 43
print(n+1)
%time upgrade(cmap, n, n+1)
44 new smallest = 10 [1, 3, 4, 9, 11, 16, 18, 19, 21, 22] [1, 3, 4, 6, 10, 13, 15, 21, 29, 37] [1, 3, 4, 9, 11, 13, 18, 19, 21, 22] [1, 3, 4, 9, 10, 12, 13, 24, 29, 31] [1, 2, 5, 7, 11, 15, 19, 20, 21, 22] [1, 3, 5, 7, 9, 10, 21, 22, 33, 34] [1, 2, 5, 8, 11, 12, 13, 27, 29, 31] [1, 2, 5, 7, 11, 15, 17, 20, 22, 36] [1, 3, 5, 7, 9, 10, 21, 22, 31, 32] [1, 3, 5, 6, 10, 14, 18, 20, 21, 23] [1, 3, 5, 7, 9, 10, 21, 22, 30, 31] [1, 3, 4, 9, 11, 16, 19, 20, 22, 34] [1, 2, 5, 7, 11, 15, 19, 21, 22, 24] [1, 3, 4, 6, 10, 14, 18, 20, 21, 23] [1, 2, 5, 7, 11, 15, 17, 20, 21, 22] [1, 3, 4, 9, 10, 12, 13, 27, 29, 34] [1, 2, 5, 8, 11, 14, 17, 20, 21, 22] [1, 3, 4, 6, 11, 13, 18, 19, 21, 22] [1, 3, 5, 7, 9, 10, 21, 22, 32, 33] [1, 3, 5, 6, 12, 13, 19, 20, 22, 24] [1, 3, 4, 8, 10, 14, 18, 20, 21, 23] [1, 3, 5, 6, 13, 15, 16, 20, 21, 38] [1, 3, 5, 6, 13, 15, 16, 20, 21, 23] [1, 3, 5, 7, 9, 11, 13, 14, 29, 30] [1, 3, 4, 9, 10, 12, 13, 27, 29, 31] CPU times: user 8 ms, sys: 0 ns, total: 8 ms Wall time: 5.12 ms
n = 44
print(n+1)
%time upgrade(cmap, n, n+1)
45 new smallest = 11 new smallest = 10 [1, 3, 4, 9, 11, 16, 19, 20, 22, 34] [1, 2, 5, 7, 11, 15, 19, 21, 22, 24] CPU times: user 4 ms, sys: 0 ns, total: 4 ms Wall time: 6.3 ms
n = 45
print(n+1)
%time upgrade(cmap, n, n+1)
46 new smallest = 11 new smallest = 10 [1, 2, 5, 7, 11, 15, 19, 21, 22, 24] CPU times: user 4 ms, sys: 0 ns, total: 4 ms Wall time: 726 µs
n = 46
print(n+1)
%time upgrade(cmap, n, n+1)
pickle.dump(cmap, open( "coins.p", "wb" ) )
pickle.load( open( "coins.p", "rb" ) )
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