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Permutation Swaps!


Problem Description

Rishabh has a permutation A of N integers 1, 2, ... N but he doesn't like it. Rishabh wants to get a permutation B.

Also, Rishabh has some M good pairs given in a form of 2D matrix C of size M x 2 where (C[i][0], C[i][1]) denotes that two indexes of the permutation A.

In one operation he can swap Ax and Ay only if (x, y) is a good pair.

You have to tell whether Rishabh can obtain permutation B by performing the above operation any number of times on permutation A.

If the permutation B can be obtained return 1 else return 0.



Problem Constraints
  • 2 <= N <= 105
  • 1 <= M <= 105
  • 1 <= A[i], B[i] <= N
  • A[i] and B[i] are all distinct.
  • 1 <= C[i][0] < C[i][1] <= N


Input Format

First arguement is an integer array A of size N denoting the permutation A.

Second arguement is an integer array B of size N denoting the permutation B.

Third argument is an 2D integer array C of size M x 2 denoting the M good pairs.



Output Format

If the permutation B can be obtained return 1 else return 0.



Example Input

Input 1:

 A = [1, 3, 2, 4]
 B = [1, 4, 2, 3]
 C = [ 
        [3, 4]
     ]

Input 2:

 A = [1, 3, 2, 4]
 B = [1, 4, 2, 3]
 C = [
        [2, 4]
     ] 



Example Output

Output 1:

 0

Output 2:

 1



Example Explanation

Explanation 1:

 As A != B you have to perform operations on A but there is only good pair available i,e (3, 4) so if you swap
 A3 with A4 you get A = [1, 3, 4, 2] which is not equal to B so we will return 0.

Explanation 2:

 As A != B you have to perform operations on A but there is only good pair available i,e (2, 4) so if you swap
 A2 with A4 you get A = [1, 4, 2, 3] which is equal to B so we will return 1.



NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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