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(unused_macros)]
macro_rules! get {
    ([$t:ty] ; $n:expr) => {
        (0..$n)
        .map(|_| get!([$t])).collect::<Vec<_>>()
    };
    ($($t:ty),+ ; $n:expr) => {
        (0..$n).map(|_| get!($($t),+)).collect::<Vec<_>>()
    };
    ([$t:ty]) => {
        rl().split_whitespace()
        .map(|x| x.parse().unwrap())
        .collect::<Vec<$t>>()
    };
    ($t:ty) => {
        rl().parse::<$t>().unwrap()
    };
    ($($t:ty),*) => {
        {
            let line =rl();
            let mut iter = line.split_whitespace();
            ($(iter.next().unwrap().parse::<$t>().unwrap()),*)
        }
    };
}
fn rl() -> String {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    line.trim().to_string()
}

struct UnionFind {
    par: Vec<usize>,
    rank: Vec<usize>,
}
impl UnionFind {
    fn new(size: usize) -> UnionFind {
        let mut par = Vec::with_capacity(size);
        let mut rank = Vec::with_capacity(size);
        for i in 0..size {
            par.push(i);
            rank.push(0);
        }
        UnionFind {
            par: par,
            rank: rank,
        }
    }
    fn root(&mut self, x: usize) -> usize {
        if self.par[x] == x {
            x
        } else {
            let par = self.par[x];
            let ppar = self.root(par);
            self.par[x] = ppar;
            ppar
        }
    }
    fn same(&mut self, x: usize, y: usize) -> bool {
        return self.root(x) == self.root(y);
    }
    fn unite(&mut self, x: usize, y: usize) {
        let px = self.root(x);
        let py = self.root(y);
        if px == py {
            return;
        }
        if self.rank[px] < self.rank[py] {
            self.par[px] = py;
        } else {
            self.par[py] = px;
            if self.rank[px] == self.rank[py] {
                self.rank[px] += 1;
            }
        }
    }
}

fn main() {
    let (n, m) = get!(usize, usize);
    let mut nv = get!([usize]);
    for i in nv.iter_mut() {
        *i -= 1;
    }
    let mut uf = UnionFind::new(n);
    for _ in 0..m {
        let (x, y) = get!(usize, usize);
        uf.unite(x - 1, y - 1);
    }
    let mut count = 0;
    for (i, x) in nv.iter().enumerate() {
        if uf.same(i, *x) {
            count += 1;
        }
    }
    println!("{}", count);
}