T=int(input())
for t in range(T):
    A,B,C=map(int,input().split())
    def solve(A,B,C):
        if (A+B+C)%2==0:
            retu=B+2*C
            if A<C:
                retu-=(C-A+1)//2*3
        else:
            retu=0
            if A:
                retu=max(retu,solve(A-1,B,C))
            if B:
                retu=max(retu,solve(A,B-1,C))
            if C:
                retu=max(retu,solve(A,B,C-1))
        return retu
    ans=solve(A,B,C)
    print(ans)