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 Python (3.4.3) (judge verdict: Accepted)

import collections
n,m = map(int,input().split())
p = list(map(int,input().split()))
base = 0
basemap = []
for i in range(n):
	if (i+1) == p[i]:
		base += 1
		basemap.append(i+1)

branch = dict()
for i in range(1,n+1):
	branch[i] = []

for i in range(m):
	x,y = map(int,input().split())
	branch[x].append(y)
	branch[y].append(x)
compare = [0 for i in range(n+1)]
for i in range(1,n+1):
	if branch[i] != []:
		compare[i] = 1

arrival = [0 for i in range(n+1)]
ans = []
q = []

ind = 1
while arrival != compare:
	counter = base
	while not(arrival[ind] == 0 and compare[ind] == 1):
		ind += 1
	q.append(ind)
	arrival[ind] = 1
	section = [q[0]]
	while len(q) > 0:
		next = branch[q[0]]
		for i in range(len(next)):
			if arrival[next[i]] == 0:
				section.append(next[i])
				arrival[next[i]] = 1
				q.append(next[i])
		q.pop(0)
	psec = []
	for i in range(len(section)):
		psec.append(p[section[i]-1])
	t = section + psec + basemap
	search = collections.Counter(t)
	for i in search:
		if search[i] == 2:
			 counter += 1
	ans.append(counter)
print(max(ans))