Problem Description

You are given a rooted tree with $ N $ vertices. Each vertex is numbered from $ 1 $ to $ N $, and vertex $ 1 $ is the root of the tree. All edges are undirected, and the parent of the $ i $th vertex ( $ 2 ≦ i ≦ N $ ) is $ p_i $.

Initially, each vertex is painted either white or black. The initial color of the $ i $th vertex ( $ 1 ≦ i ≦ N $ ) is white if $ C_i = 0 $ and black if $ C_i = 1 $.

You will be given $ Q $ queries to process in order. There are two types of queries, with the following input format and content:

• 1 u: Invert the color of all vertices in the subtree rooted at vertex $ u $.
• 2 u v: Output YES if it is possible to travel from vertex $ u $ to vertex $ v $ by alternating between white and black vertices, otherwise output NO. The initial color does not matter.

Input Format

The input is provided from standard input in the following format:

$ N $ $ p_2 $ $ p_3 $ $ : $ $ p_N $ $ C_1 $ $ C_2 $ $ : $ $ C_N $ $ Q $ $ query_1 $ $ query_2 $ $ : $ $ query_Q $

Output Format

For each query with the format 2 u v, output the answer in a single line in the order the queries are given.

Sample Input and Output

Sample Input #1

6
1
1
2
2
3
0
1
0
0
1
1
10
2 4 1
2 4 3
2 1 2
1 2
2 4 1
1 3
1 5
2 1 6
1 1
2 5 4

Sample Output #1

YES
NO
YES
NO
YES
YES

Sample Input #2

7
1
2
3
3
5
6
0
0
1
0
0
1
1
7
2 1 4
2 4 2
2 4 5
2 4 6
2 6 1
2 7 1
2 2 6

Sample Output #2

NO
YES
YES
YES
NO
NO
YES

Sample Input #3

2
1
0
1
11
2 1 2
2 2 1
1 2
2 1 2
2 2 1
1 1
2 1 2
2 2 1
1 2
2 1 2
2 2 1

Sample Output #3

YES
YES
NO
NO
NO
NO
YES
YES

Sample Input #4

5
1
2
3
4
0
1
0
1
0
11
2 1 2
2 1 4
2 3 1
2 5 1
2 4 5
1 3
2 1 2
2 1 4
2 3 1
2 5 1
2 4 5

Sample Output #4

YES
YES
YES
YES
YES
YES
NO
NO
NO
YES

Sample Input #5

9
4
2
6
8
1
4
1
8
0
0
1
0
0
1
1
1
0
2
2 9 8
2 9 4

Sample Output #5

YES
YES

Notes/Hints

Constraints

• All input values are integers.
• $ 2 ≦ N ≦ 10^5 $
• $ 1 ≦ p_i ≦ N $
• $ C_i = 0 $ or $ 1 $
• $ 1 ≦ Q ≦ 10^5 $
• The input rooted tree is always connected.
• For query 1 u, $ 1 ≦ u ≦ N $.
• For query 2 u v, $ 1 ≦ u, v ≦ N $ and $ u ≠ v $.
• At least one query with the format 2 u v is guaranteed to exist.

见题面 Input 部分

见题面 Output 部分