Problem Statement

You are given a rooted tree with $N$ vertices. The vertices are numbered $1$ to $N$, and the root is vertex $1$. The parent of each vertex $i$ except the root is vertex $P_i$. Each vertex, including the root, has ** no child or exactly two children**.

Determine whether it is possible to write one of the characters X and Y on each vertex of the given tree to satisfy the following condition.

Condition: For each edge of the tree, consider the string of length $2$ obtained by concatenating the characters written on the endpoints in the order from the parent $P_i$ to the child $i$. Among the $(N - 1)$ strings obtained in this way,

• exactly $A$ are XX,
• exactly $B$ are XY,
• exactly $C$ are YX, and
• none is YY.

You have $T$ test cases to solve.

Constraints

• $T \geq 1$
• $N \geq 1$
• For each input, the sum of $N$ over the test cases is at most $10^4$.
• $A \geq 0$
• $B \geq 0$
• $C \geq 0$
• $A + B + C = N - 1$
• $1 \leq P_i < i \ \ (2 \leq i \leq N)$
• Each vertex $k \ (1 \leq k \leq N)$ occurs as a parent $P_i \ (2 \leq i \leq N)$ zero times or twice in total.

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 $\mathrm{case}_i \ (1 \leq i \leq T)$ is in the following format:

N A B C
P_2 P_3 \cdots P_N

Output

Print $T$ lines. The $i$-th line should contain Yes if there is a way to write characters to satisfy the condition, and No otherwise.