equals

Problem Statement

We have a permutation of the integers from 1 through N, p1, p2, .., pN. We also have M pairs of two integers between 1 and N (inclusive), represented as (x1,y1), (x2,y2), .., (xM,yM). AtCoDeer the deer is going to perform the following operation on p as many times as desired so that the number of i (1 i N) such that pi = i is maximized:

  • Choose j such that 1 j M, and swap pxj and pyj.

Find the maximum possible number of i such that pi = i after operations.

Constraints

  • 2 N 105
  • 1 M 105
  • p is a permutation of integers from 1 through N.
  • 1 xj,yj N
  • xj yj
  • If i j, {xi,yi} {xj,yj}.
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
p1 p2 .. pN
x1 y1
x2 y2
:
xM yM

Output

Print the maximum possible number of i such that pi = i after operations.

Sample Input 1

5 2
5 3 1 4 2
1 3
5 4

Sample Output 1

2

If we perform the operation by choosing j=1, p becomes 1 3 5 4 2, which is optimal, so the answer is 2.

Sample Input 2

3 2
3 2 1
1 2
2 3

Sample Output 2

3

If we perform the operation by, for example, choosing j=1, j=2, j=1 in this order, p becomes 1 2 3, which is obviously optimal. Note that we may choose the same j any number of times.

Sample Input 3

10 8
5 3 6 8 7 10 9 1 2 4
3 1
4 1
5 9
2 5
6 5
3 5
8 9
7 9

Sample Output 3

8

Sample Input 4

5 1
1 2 3 4 5
1 5

Sample Output 4

5

We do not have to perform the operation.


Compile Errors


							
Time Limit: 2 Seconds
Memory Limit: 256MB
No. of ACs: 12
Your best score: 0
Source: ARC 097

Subtask Score
1 100
2 0