Description

Little S has a tree with $n$ vertices, rooted at vertex $1$. On vertex $i$ $(1\le i\le n)$, there is a water cup with an initial temperature of $a_i$.

Little S, who picked up a water cup and drank water without knowing the temperature and was scalded many times, decided to change all the temperatures of the water in the cups to $0$.

Now, Little S can do the following two types of operations an arbitrary number of times (possibly zero):

• Use a heater at vertex $i$. This will make the temperature of the water cups on all vertices in subtree $i$ increase by $1$;
• Or, blow a gust of wind from a leaf $i$. This will make the temperature of the water cups on the route between $1$ and $i$ decrease by $1$.

Help Little S determine whether he can make the temperature of all the water cups become $0$.

Input Format

Each test contains multiple test cases.

The first line of the input contains a single integer $c$ — the id of the test. $c=0$ represents that this is a sample test.

The second line contains a single integer $t$ — the number of test cases.

For each test case:

• The first line contains a single integer $n$ — the number of vertices.
• The second line contains $n-1$ integers $f_2,f_3,\dots,f_n$, in which $f_i$ is the parent vertex of vertex $i$. It is guaranteed that $f_i<i$.
• The third line contains $n$ integers $a_i$ — the initial temperature of the water cup on vertex $i$.

Output Format

For each test case:

• If it is possible to make the temperature of all the water cups $0$, print one line, a string Huoyu;
• If it is impossible to do so, print one line, a string Shuiniao.

0
5
5
1 1 2 3
6 5 2 2 1
5
1 1 2 2
6 5 1 2 1
5
1 1 2 2
4 -1 5 -2 -2
5
1 1 2 2
6 -4 8 -3 -3
5
1 1 2 2
-1 -1 -1 -4 -1

Shuiniao
Huoyu
Shuiniao
Shuiniao
Huoyu

Hint

Sample 1 Explanation

Let $A_u$ be a heating operation on vertex $u$, $B_u$ be a wind operation from vertex $u$ and $(S)^k$ be repeating the operations in $S$ for $k$ times.

• In the first, third and fourth test case, it can be proven that Little S can't make the temperature of all the water cups $0$;
• In the second test case, a possible operation sequence is $B_3(A_4)^3(B_4)^5B_5$;
• For the fifth test case, a possible operation sequence is $(A_4)^3A_1$.

Sample 2

See water/water2.in and water/water2.ans in the attachments.

This sample satisfies the constraints of test $3$.

Sample 3

See water/water3.in and water/water3.ans in the attachments.

This sample satisfies the constraints of test $7,8$.

Sample 4

See water/water4.in and water/water4.ans in the attachments.

This sample satisfies the constraints of test $12$.

Sample 5

See water/water5.in and water/water5.ans in the attachments.

This sample satisfies the constraints of test $13,14$.

Sample 6

See water/water6.in and water/water6.ans in the attachments.

This sample satisfies the constraints of test $15\sim 17$.

Sample 7

See water/water7.in and water/water7.ans in the attachments.

This sample satisfies the constraints of test $18\sim 21$.

Constraints

Let $\sum n$ be the sum of $n$ over all test cases in a single test.

For all the tests, it is guaranteed that:

• $1\leq t\leq 1\,000$;
• $2\leq n\leq 10^5$, $\sum n\le 10^6$;
• For each $2\le i\le n$, $1\le f_i<i$;
• For each $1\le i\le n$, $-10^{12}\leq a_i\leq10^{12}$.

• Property A: For each $2\le i\le n$, $f_i=i-1$;
• Property B: For each $1\le i\le n$, $a_i\le \left(\sum_{f_j=i}a_j\right)+5$, where $f_1=0$;
• Property C: The depth of the tree does not exceed $2$, where the depth of the tree denotes the maximum number of edges in the simple path from a node to the root.

Hints

The input and output files are huge in this problem, please use fast I/O methods.