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 Rust (1.15.1) (judge verdict: Accepted)

#![allow(non_snake_case,unused_imports)]
use std::io::Read;
use std::cmp::max;
use std::cmp::min;
use std::str::FromStr;
use std::collections::HashMap;
use std::collections::HashSet;
use std::collections::BinaryHeap;

struct UnionFind{
    P: Vec<usize>,
}

impl UnionFind {
    fn new(n:usize) -> UnionFind{
        UnionFind {P:(0..n).collect()}
    }
    fn get_parent(&mut self,n:usize) -> usize{
        if self.P[n] == n{ return n;}
        let p = self.P[n];
        self.P[n] = self.get_parent(p);
        self.P[n]
    }
    fn is_unite(&mut self,x:usize,y:usize) -> bool{
        self.get_parent(x)==self.get_parent(y)
    }
    fn merge(&mut self,x:usize,y:usize){
        if self.is_unite(x,y) {return;}
        let i = self.get_parent(x);
        let j = self.get_parent(y);
        self.P[j] = i;
    }
}

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    let N:usize = iter.next().unwrap().parse().unwrap();
    let M:usize = iter.next().unwrap().parse().unwrap();
    let P = (0..N).map(|_| iter.next().unwrap().parse::<usize>().unwrap()-1).collect::<Vec<_>>();
    let mut T = UnionFind::new(N);
    for _ in 0..M{
        let x:usize = iter.next().unwrap().parse::<usize>().unwrap() -1;
        let y:usize = iter.next().unwrap().parse::<usize>().unwrap() -1;
        T.merge(x,y);
    }
    let ans = (0..N).filter(|&i| T.is_unite(i,P[i])).collect::<Vec<_>>().len();
    println!("{}",ans);
}