Problem:
Score : 400 points

Problem Statement

We have a permutation of the integers from 1 through N, p_1, p_2, .., p_N.
We also have M pairs of two integers between 1 and N (inclusive), represented as (x_1,y_1), (x_2,y_2), .., (x_M,y_M).
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 p_i = i is maximized:

Choose j such that 1 ≤ j ≤ M, and swap p_{x_j} and p_{y_j}.

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

Constraints

2 ≤ N ≤ 10^5

1 ≤ M ≤ 10^5

p is a permutation of integers from 1 through N.

1 ≤ x_j,y_j ≤ N

x_j ≠ y_j

If i ≠ j, \{x_i,y_i\} ≠ \{x_j,y_j\}.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
p_1 p_2 .. p_N
x_1 y_1
x_2 y_2
:
x_M y_M

Output

Print the maximum possible number of i such that p_i = 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.

Solution in C (GCC 9.2.1) (judge verdict: Accepted)

#include<stdio.h>
#define SIZE 100001
int PAR[SIZE],RANK[SIZE];
void init_uf(int n){for(int i=0;i<n;i++){PAR[i]=i;RANK[i]=0;}}//initialize
int root(int i){return PAR[i]==i?i:(PAR[i]=root(PAR[i]));}//search group
int same(int x,int y){return root(x)==root(y);}//judge same group
void unite(int x,int y){//add edge
  x=root(x);y=root(y);
  if(x==y)return;
  if(RANK[x]<RANK[y])PAR[x]=y;
  else{PAR[y]=x;if(RANK[x]==RANK[y])RANK[x]++;}
}
int main(){
  int i,n,m,p[SIZE],x,y;
  scanf("%d%d",&n,&m);
  init_uf(n);
  for(i=1;i<=n;i++)scanf("%d",&p[i]);
  for(i=0;i<m;i++){scanf("%d%d",&x,&y);unite(x,y);}
  x=0;for(i=1;i<=n;i++)x+=same(i,p[i]);
  printf("%d",x);
}