def mult(chain):
    n = len(chain)
    
    # single matrix chain has zero cost
    aux = {(i, i): (0,) + chain[i] for i in range(n)}

    # i: length of subchain
    for i in range(1, n):
        # j: starting index of subchain
        for j in range(0, n - i):
            best = float('inf')

            # k: splitting point of subchain
            for k in range(j, j + i):
                # multiply subchains at splitting point
                lcost, lname, lrow, lcol = aux[j, k]
                rcost, rname, rrow, rcol = aux[k + 1, j + i]
                cost = lcost + rcost + lrow * lcol * rcol
                var = '(%s%s)' % (lname, rname)

                # pick the best one
                if cost < best:
                    best = cost
                    aux[j, j + i] = cost, var, lrow, rcol

    return dict(zip(['cost', 'order', 'rows', 'cols'], aux[0, n - 1]))