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 (1.42.0) (judge verdict: Accepted)

#[allow(unused_imports)]
use {
   proconio::{fastout, input, marker::*},
   std::cmp::*,
   std::collections::*,
};

#[fastout]
fn main() {
   input! {
      n: usize,
      m: usize,
      p: [Usize1; n],
      xy: [(Usize1, Usize1); m]
   }

   let mut uf = (0..n).collect::<Vec<_>>();
   for &(x, y) in xy.iter() {
      uf.unite(x, y);
   }

   let mut nums = vec![BTreeSet::<usize>::new(); n];
   for i in 0..n {
      let r = uf.root(i);
      nums[r].insert(p[i]);
   }

   let mut ans = 0;
   for (i, r) in (0..n).map(|i| (i, uf.root(i))) {
      if nums[r].contains(&i) {
         ans += 1;
      }
   }
   println!("{}", ans);
}

trait UnionFind {
   fn unite(&mut self, x: usize, y: usize);
   fn same(&mut self, x: usize, y: usize) -> bool;
   fn root(&mut self, x: usize) -> usize;
}
impl UnionFind for [usize] {
   fn unite(&mut self, x: usize, y: usize) {
      let rx = self.root(x);
      let ry = self.root(y);
      if rx == ry {
         return;
      }
      self[ry] = rx;
   }
   fn same(&mut self, x: usize, y: usize) -> bool { self.root(x) == self.root(y) }
   fn root(&mut self, x: usize) -> usize {
      if self[x] == x {
         x
      } else {
         self[x] = self.root(self[x]);
         self[x]
      }
   }
}