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: Time Limit Exceeded)

#![allow(non_snake_case)]
#![allow(unused_imports)]

use proconio::{input, fastout};
use proconio::marker::*;
use whiteread::parse_line;
use std::collections::*;
use num::*;
use num_traits::*;
use superslice::*;
use std::ops::*;

use itertools::Itertools;
use itertools_num::ItertoolsNum;

#[derive(Debug, Clone)]
pub struct UnionFind<K> {
    // For element at index *i*, store the index of its parent; the representative itself
    // stores its own index. This forms equivalence classes which are the disjoint sets, each
    // with a unique representative.
    parent: Vec<K>,

    // size vector
    size: Vec<usize>,
    // group_num
    group_num: usize,
}

#[inline]
unsafe fn get_unchecked<K>(xs: &[K], index: usize) -> &K {
    debug_assert!(index < xs.len());
    xs.get_unchecked(index)
}

#[inline]
unsafe fn get_unchecked_mut<K>(xs: &mut [K], index: usize) -> &mut K {
    debug_assert!(index < xs.len());
    xs.get_unchecked_mut(index)
}

impl<K> UnionFind<K>
where
    K: PrimInt + std::hash::Hash,
{
    /// Create a new `UnionFind` of `n` disjoint sets.
    pub fn new(n: usize) -> Self {
        let size = vec![1; n];
        let parent = (0..n).map(|x| K::from(x).unwrap()).collect::<Vec<K>>();
        let group_num = n;
        Self { parent, size, group_num }
    }

    /// Return the representative for `x`.
    ///
    /// **Panics** if `x` is out of bounds.
    pub fn find(&self, x: K) -> K {
        assert!(x.to_usize().unwrap() < self.parent.len());
        unsafe {
            let mut x = x;
            loop {
                // Use unchecked indexing because we can trust the internal set ids.
                let xparent = *get_unchecked(&self.parent, x.to_usize().unwrap());
                if xparent == x {
                    break;
                }
                x = xparent;
            }
            x
        }
    }

    /// Return the representative for `x`.
    ///
    /// Write back the found representative, flattening the internal
    /// datastructure in the process and quicken future lookups.
    ///
    /// **Panics** if `x` is out of bounds.
    pub fn find_mut(&mut self, x: K) -> K {
        assert!(x.to_usize().unwrap() < self.parent.len());
        unsafe { self.find_mut_recursive(x) }
    }

    unsafe fn find_mut_recursive(&mut self, mut x: K) -> K {
        let mut parent = *get_unchecked(&self.parent, x.to_usize().unwrap());
        while parent != x {
            let grandparent = *get_unchecked(&self.parent, parent.to_usize().unwrap());
            *get_unchecked_mut(&mut self.parent, x.to_usize().unwrap()) = grandparent;
            x = parent;
            parent = grandparent;
        }
        x
    }

    /// Returns `true` if the given elements belong to the same set, and returns
    /// `false` otherwise.
    pub fn equiv(&self, x: K, y: K) -> bool {
        self.find(x) == self.find(y)
    }

    /// Unify the two sets containing `x` and `y`.
    ///
    /// Return `false` if the sets were already the same, `true` if they were unified.
    ///
    /// **Panics** if `x` or `y` is out of bounds.
    pub fn union(&mut self, x: K, y: K) -> bool {
        if x == y {
            return false;
        }
        let xrep = self.find_mut(x);
        let yrep = self.find_mut(y);

        if xrep == yrep {
            return false;
        }

        let xrepu = xrep.to_usize().unwrap();
        let yrepu = yrep.to_usize().unwrap();
        let xsize = self.size[xrepu];
        let ysize = self.size[yrepu];

        // The rank corresponds roughly to the depth of the treeset, so put the
        // smaller set below the larger
        if xsize > ysize {
            self.parent[yrepu] = xrep;
            self.size[xrepu] += ysize;
        } else {
            self.parent[xrepu] = yrep;
            self.size[yrepu] += xsize;
        }
        self.group_num -= 1;
        true
    }

    /// Return a vector mapping each element to its representative.
    pub fn into_labeling(mut self) -> Vec<K> {
        // write in the labeling of each element
        unsafe {
            for ix in 0..self.parent.len() {
                let k = *get_unchecked(&self.parent, ix);
                let xrep = self.find_mut_recursive(k);
                *self.parent.get_unchecked_mut(ix) = xrep;
            }
        }
        self.parent
    }

    pub fn size(&self, x: K) -> usize {
        let xrep = self.find(x);
        let xrepu = xrep.to_usize().unwrap();

        self.size[xrepu]
    }

    pub fn member(&self, x: K) -> HashSet<K> {
        let xrep = self.find(x);
        let mut set: HashSet<K> = HashSet::new();

        for i in 0..self.parent.len() {
            let i_k = K::from(i).unwrap();
            if self.find(i_k) == xrep {
                set.insert(i_k);
            }
        }

        set
    }

    pub fn member_map(&self) -> HashMap<K, HashSet<K>> {
        let mut map: HashMap<K, HashSet<K>> = HashMap::new();
        for i in 0..self.parent.len() {
            map.entry(K::from(i).unwrap()).or_insert(self.member(K::from(i).unwrap()));
        }
        map
    }
}


#[fastout]
fn solve() {
    input!{
        n: usize, m: usize,
        p_vec: [usize; n],
        xy_vec: [(usize, usize); m]
    }

    let mut un: UnionFind<usize> = UnionFind::new(n);

    for &(x, y) in xy_vec.iter() {
        un.union(x-1, y-1);
    }

    let mut ans = 0;
    let member_map = un.member_map();
    for (i, p) in p_vec.iter().enumerate() {
        if i == *p-1 { 
            ans += 1;
            continue;
        }

        // let member = un.member(p-1);
        // dbg!(&member);
        if member_map.get(&(p-1)).unwrap().contains(&(p_vec[p-1]-1)) {
            ans += 1;
        }
    }

    println!("{}", ans);
}

fn main() {
    solve()
}

#[cfg(test)]
mod test {
    use super::solve;
}