Problem Statement

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.

Constraints

• $1 \le T \le 2 \times 10^{5}$
• $0 \le X,Y,Z \le 10^{9}$
• $3 \le X + Y + Z$

Input

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

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