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: Runtime Error)

import sys
sys.setrecursionlimit(10**9)

class UnionFind():
	def __init__(self, n):
		self.size = n
		self.root = [-1 for _ in range(n+1)]
		self.rnk = [0 for _ in range(n+1)]

	def findRoot(self, a):
		if self.root[a] < 0:
			return a
		else:
			return self.findRoot(self.root[a])

	def uniteTree(self, a, b):
		a = self.findRoot(a)
		b = self.findRoot(b)

		if a == b:
			return

		elif self.rnk[a] > self.rnk[b]:
			self.root[a] += self.root[b]
			self.root[b] = a

		elif self.rnk[b] > self.rnk[a]:
			self.root[b] += self.root[a]
			self.root[a] = b

		elif self.rnk[a] == self.rnk[b]:
			self.root[b] += self.rnk[a]
			self.root[a] = b
			self.rnk[b] += 1

	def judgeTree(self, a, b):
		return self.findRoot(a) == self.findRoot(b)

	def count(self, a):
		return self.rnk[self.findRoot(a)] * (-1)



N, M = map(int, input().split())
A = list(map(int, input().split()))
O = [list(map(int, input().split())) for _ in range(M)]

ope = UnionFind(N)

for i in range(M):
	ope.uniteTree(O[i][0], O[i][1])

cnt = 0
for i in range(N):
	if ope.judgeTree(A[i], i+1):
		cnt += 1

print(cnt)