def even_case(a, b, c):
    res = b + 2 * c  # max
    c = max(c - a, 0)  # Cは極力Aとペアにする
    res -= 3 * (c // 2)  # C+Cを食べると1点。(A+C)*2と比べて3点損
    res -= 3 * (c % 2)  # Cが余るときBも余る。B+Cは0点。これも3点損
    return res


def main():
    t = int(input())
    for _ in range(t):
        a, b, c = map(int, input().split())
        if (a + b + c) % 2 == 1:
            ans = 0
            try:
                ans = max(ans, even_case(a - 1, b, c))
                ans = max(ans, even_case(a, b - 1, c))
                ans = max(ans, even_case(a, b, c - 1))
                print(ans)
            except IndexError:
                pass
        else:
            print(even_case(a, b, c))


if __name__ == "__main__":
    main()