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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <cstring>
#include <string>
#include <cmath>
#include <vector>
#include <queue>
#define ll long long
#define mp(a,b) make_pair(a,b)
#define si(n) scanf("%d",&n)
#define sl(n) scanf("%lld",&n)
using namespace std;

std::vector<ll> v[1000000];
ll arr[1000000];
ll ans = 0;

ll binarySearch(vector<ll> blah1, ll l, ll r, ll x)
{
    while (l <= r)
    {
        ll m = l + (r-l)/2;
        if (blah1[m] == x)
            return m;
        if (blah1[m] < x)
            l = m + 1;
        else
            r = m - 1;
    }
    return -1;
}

void solve1(vector<ll> v1,vector<ll> v2){
  sort(v1.begin(),v1.end());
  sort(v2.begin(),v2.end());
  for(ll i=0;i<v1.size();i++){
    if(binarySearch(v2,0,v2.size()-1,v1[i])!=-1)
      ans+=1;
  }
}

void solve(ll n){
  bool visited[1000000];
  memset(visited,false,sizeof(visited));
  for(ll i=1;i<=n;i++){
    if(visited[i]==false){
      std::vector<ll> v1;
      std::vector<ll> v2;
      queue<ll> q;
      q.push(i);
      if(i==arr[i]){
        ans+=1;
      }
      else{
        v1.push_back(i);
        v2.push_back(arr[i]);
      }
      visited[i]=true;
      while(!q.empty()){
        i = q.front();
        q.pop();
        for(ll j=0;j<v[i].size();j++){
          if(visited[v[i][j]]==false){
            q.push(v[i][j]);
            visited[v[i][j]]=true;
            if(v[i][j]==arr[v[i][j]]){
              ans+=1;
            }
            else{
              v1.push_back(v[i][j]);
              v2.push_back(arr[v[i][j]]);
            }
          }
        }
      }
      if(v1.size()>0){
        solve1(v1,v2);
      }
    }
  }
}

int main(){
  ll n,m;
  sl(n);
  sl(m);
  for(ll i=1;i<=n;i++){
    sl(arr[i]);
  }
  bool check1[1000000];
  memset(check1,false,sizeof(check1));
  for(ll i=0;i<m;i++){
    ll a,b;
    sl(a);
    sl(b);
    check1[a]=true;
    check1[b]=true;
    v[a].push_back(b);
    v[b].push_back(a);
  }
  solve(n);
  for(ll i=1;i<=n;i++){
    if(check1[i]==false && arr[i]==i)
      ans+=1;
  }
  printf("%lld\n",ans);
}