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 JavaScript (node.js v5.12) (judge verdict: Accepted)

function Main(s){
  s = s.split("\n");
  s[0] = s[0].split(" ").map(a=>+a);
  var n = s[0][0];
  var m = s[0][1];
  var p = s[1].split(" ").map(a=>+a);
  var x = [], y = [];
  for(i = 0; i < m; i++){
    x[i] = s[i+2].split(" ").map(a=>+a);
    y[i] = x[i][1];
    x[i] = x[i][0];
  }
  var g = group(x,y,n);
  var ans = 0;
  for(i = 0; i < n; i++){
    if(g[i+1] === g[p[i]])ans++;
  }
  console.log(ans);
}
function group(a,b,n){
  var p = Array(n+1).fill(0).map(a=>[]);
  var q = Array(n+1);
  var al = a.length;
  for(var i = 0; i < al; i++){
    p[a[i]].push(b[i]);
    p[b[i]].push(a[i]);
  }
  var k = 1;
  for(i = 0; i <= n; i++){
    if(q[i])continue;
    q[i] = k;
    a = p[i];
    while(a.length){
      b = a.pop();
      if(q[b])continue;
      q[b] = k;
      for(var j = 0; j < p[b].length; j++){
        a.push(p[b][j]);
      }
    }
    k++;
  }
  return q;
}
Main(require("fs").readFileSync("/dev/stdin","utf8"));