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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
#[allow(unused_imports)]
use itertools::Itertools;
#[allow(unused_imports)]
use num::*;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::collections::*;

pub struct UnionFind {
  n: usize,
  root: Vec<usize>,
  rank: Vec<usize>,
  size: Vec<usize>,
}
impl UnionFind {
  pub fn new(n: usize) -> Self {
    let root = (0..n).collect();
    let rank = vec![0; n];
    let size = vec![1; n];
    Self {
      n,
      root,
      rank,
      size,
    }
  }

  pub fn find(&mut self, x: usize) -> usize {
    if x >= self.n {
      panic!();
    }
    if self.root[x] == x {
      x
    } else {
      let root = self.find(self.root[x]);
      self.root[x] = root;
      root
    }
  }

  pub fn unite(&mut self, x: usize, y: usize) {
    if x >= self.n || y >= self.n {
      panic!();
    }
    let x_root = self.find(x);
    let y_root = self.find(y);
    if x_root == y_root {
      return;
    }
    if self.rank[x_root] < self.rank[y_root] {
      self.root[x_root] = y_root;
      self.size[y_root] += self.size[x_root];
    } else {
      self.root[y_root] = x_root;
      self.size[x_root] += self.size[y_root];
      if self.rank[x_root] == self.rank[y_root] {
        self.rank[x_root] += 1;
      }
    }
  }

  pub fn size(&mut self, x: usize) -> usize {
    if x >= self.n {
      panic!();
    }
    let x_root = self.find(x);
    self.size[x_root]
  }

  pub fn is_same(&mut self, x: usize, y: usize) -> bool {
    if x >= self.n || y >= self.n {
      panic!();
    }
    self.find(x) == self.find(y)
  }
}

fn main() {
  input! {
    n: usize, m: usize,
    pv: [Usize1; n],
    xyv: [(Usize1, Usize1); m]
  };

  let mut uf = UnionFind::new(n);
  for (x, y) in xyv {
    uf.unite(x, y);
  }
  let mut res = 0;
  for i in 0..n {
    let x = pv[i];
    if uf.is_same(x, i) {
      res += 1;
    }
  }
  println!("{}", res);
}
*/

fn main() {
    let exe = "/tmp/bin2D4C07B7";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";