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 Lua (5.3.2) (judge verdict: Time Limit Exceeded)

local n, m = io.read("*n", "*n","*l")
local str = io.read()
local posval = {}
for strnum in string.gmatch(str, "%d+") do
  table.insert(posval, tonumber(strnum))
end

local parent = {}
for i = 1, n do parent[i] = 0 end
function findroot(x)
  local cand = x
  while(parent[cand] ~= 0) do
    cand = parent[cand]
  end
  return cand
end

for i = 1, m do
  local a, b = io.read("*n", "*n")
  local aroot, broot = findroot(a), findroot(b)
  if(aroot ~= broot) then
    parent[broot] = aroot
  end
end
local ret = 0
for i = 1, n do
  local gsrc, gdst = findroot(i), findroot(posval[i])
  if(gsrc ~= 0 and gsrc == gdst) then ret = ret + 1 end
end
print(ret)