def even_solve(A,B,C):
    ans = B+2*C
    C -= min(A,C)
    ans -= 3*(C//2)
    ans -= 3*(C%2)
    return ans

def solve():
    A,B,C = map(int,input().split())
    if (A+B+C)%2:
        ans = 0
        if A > 0:
            ans = max(ans,even_solve(A-1,B,C))
        if B > 0:
            ans = max(ans,even_solve(A,B-1,C))
        if C > 0:
            ans = max(ans,even_solve(A,B,C-1))
        print(ans)
    else:
        print(even_solve(A,B,C))
        
T = int(input())
for i in range(T):
    solve()