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 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <sstream>
#include <queue>
#include <deque>
#include <bitset>
#include <iterator>
#include <list>
#include <stack>
#include <map>
#include <set>
#include <functional>
#include <numeric>
#include <utility>
#include <limits>
#include <time.h>
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <assert.h>

using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef vector<ll> vec;
typedef vector<vec> vec2;
typedef map<ll,ll> MPll;
typedef set<ll> setl;

template <typename T>
struct UnionFindTree{

    vector<T> par;

    UnionFindTree(T n) : par(n+1){
        for (int i = 1; i <= n; ++i) {
            par[i] = i;
        }
    }

    T root(T x){
        if(par[x] == x) return x;
        else  return par[x] = root(par[x]);
    }

    void unite(T x,T y){
        if(!same(x,y)) par[root(x)] = root(par[y]);
    }

    T same(T x,T y){
        return root(x) == root(y);
    }

};

signed main(){
    ll N,M;
    cin >>N>>M;
    ll p[N+1];

    UnionFindTree<ll> t(N);

    for (int i = 1; i <= N; ++i) {
        cin >> p[i];
    }

    for (int j = 0; j < M; ++j) {
        ll x,y;
        cin >>x>>y;
        t.unite(x,y);
    }

    ll ans = 0;

    for (int k = 1; k <= N; ++k) {
        if(t.same(p[k],k)) ans++;
    }

    cout << ans << endl;
}