AT_arc198_b [ARC198B] Rivalry

Determine whether there exists a sequence $ A=(A_1,A_2,\dots,A_{X+Y+Z}) $ of length $ X+Y+Z $ that contains exactly $ X $ zeros, $ Y $ ones, and $ Z $ twos, and satisfies the following condition: - For every $ i(1 \le i \le X+Y+Z) $ , exactly $ A_i $ numbers among $ A_{i-1} $ and $ A_{i+1} $ are less than $ A_i $ . Here, assume $ A_0 = A_{X+Y+Z} $ and $ A_{X+Y+Z+1} = A_1 $ . You are given $ T $ test cases. Solve each of them.

The input is given from Standard Input in the following format: > $ T $ $ \mathrm{case}_1 $ $ \mathrm{case}_2 $ $ \vdots $ $ \mathrm{case}_T $ Each test case is given in the following format: > $ X\ Y\ Z $

Output $ T $ lines. The $ i $ -th $ (1 \le i \le T) $ line should contain `Yes` if such a sequence exists, and `No` otherwise.

### Sample Explanation 1 For the first test case, the sequence $ A = (2,0,0,1) $ satisfies the condition. For the second test case, no sequence satisfies the condition. ### Constraints - $ 1 \le T \le 2 \times 10^{5} $ - $ 0 \le X,Y,Z \le 10^{9} $ - $ 3 \le X + Y + Z $