import sympy
import itertools
def solve(input):
    part2 = 0
    for line in open(input):
        parts = line.split()[1:]
        idxs = [delist(p) for p in parts[:-1]]
        target = delist(parts[-1])

        BTNS = len(idxs)
        N = len(target)
        matrix = [[int(i in row) for i in range(N)] for row in idxs]

        #print(matrix, target)
        M = sympy.Matrix(matrix + [target]).T
        #print(repr(M))
        S, pivots = M.rref()
        if len(pivots) == BTNS:
            # solved
            presses = S.col(-1)
            print("*", target, presses.T, sum(presses))
            part2 += sum(presses)
        else:
            # not solved
            # the system of equations is underdetermined, either because
            # we started with too few equations or because some of them were
            # not linearly independent.
            # the upshot is that we have one or more free variables
            # (in practice 1-3 free variables) so if we just iterate
            # through all legal values for those variables we should
            # be able to find a solution?
            # unfortunately i am still running into some unsolveable cases
            # and i'm not sure why.

            #if BTNS - len(pivots) >= 3:
            #    print(repr(S))
            #continue

            coords = []
            limits = []
            extra_rows = []
            for p in range(BTNS):
                if p not in pivots:
                    print(p, M.col(p))
                    row = [0]*(BTNS+1)
                    row[p] = 1
                    coords.append((M.rows, M.cols-1))
                    extra_rows.append(row)
                    limit = min(target[i] for i,x in enumerate(M.col(p)) if x)
                    limits.append(limit)
            M = M.col_join(sympy.Matrix(extra_rows))
            print(repr(M), limits)
            totals = []
            for values in itertools.product(*[range(l+1) for l in limits]):
                for c,v in zip(coords,values):
                    M[c] = v
                S, newpivot = M.rref()
                presses = S.col(-1)
                if all(int(x) >= 0 for x in presses):
                    print(presses.T, flush=True)
                    totals.append(sum(S.col(-1)))
            if totals:
                print("*", target, totals, min(totals))
                part2 += min(totals)
            else:
                print("uhoh", target)
    print(part2)
    #print(less, greater)

def delist(s):
    return [int(x) for x in s.strip("{}()").split(',')]

#solve("sample")
solve("input")