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)

fn main() {
	let mut s = String::new();
	use std::io::Read;
	std::io::stdin().read_to_string(&mut s).unwrap();
	let mut s = s.split_whitespace();
	let n: usize = s.next().unwrap().parse().unwrap();
	let m: usize = s.next().unwrap().parse().unwrap();
	let p: Vec<usize> = s
		.by_ref()
		.take(n)
		.map(|a| a.parse::<usize>().unwrap() - 1)
		.collect();
	let mut uf = UnionFind::new(n);
	for _ in 0..m {
		let x: usize = s.next().unwrap().parse().unwrap();
		let y: usize = s.next().unwrap().parse().unwrap();
		uf.unite(x - 1, y - 1);
	}
	let ans = (0..n).fold(0, |r, i| {
		r + if uf.find(i) == uf.find(p[i]) { 1 } else { 0 }
	});
	println!("{}", ans);
}

pub struct UnionFind {
	data: Vec<i32>,
}

impl UnionFind {
	pub fn new(n: usize) -> UnionFind {
		UnionFind { data: vec![-1; n] }
	}

	pub fn unite(&mut self, x: usize, y: usize) -> bool {
		let x = self.find(x);
		let y = self.find(y);
		if x == y {
			false
		} else {
			let (x, y) = if self.data[x] > self.data[y] {
				(y, x)
			} else {
				(x, y)
			};
			self.data[x] += self.data[y];
			self.data[y] = x as i32;
			true
		}
	}

	pub fn find(&mut self, i: usize) -> usize {
		if self.data[i] < 0 {
			i
		} else {
			let p = self.data[i] as usize;
			self.data[i] = self.find(p) as i32;
			self.data[i] as usize
		}
	}

	pub fn size(&mut self, i: usize) -> usize {
		let i = self.find(i);
		(-self.data[i]) as usize
	}
}