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 Ruby (2.3.3) (judge verdict: Accepted)

require "optparse"
require "pp"

params = ARGV.getopts("")

def root_of x, parent
  ret = parent[x]
  unless ret == parent[ret]
    ret = root_of(ret, parent)
    parent[x] = ret
  end
  return ret
end


N, M = gets.split.map(&:to_i)
ps = [0] + gets.split.map(&:to_i)
parent = Array.new(N+1){ |i| i }
rank = Array.new(N+1,0)

M.times do |i|
  x, y = gets.split.map(&:to_i)
  # unless parent.has_key? x
  #   parent[x] = x
  #   rank[x] = 0
  # end
  # unless parent.has_key? y
  #   parent[y] = y
  #   rank[y] = 0
  # end
  xrt = root_of(x, parent)
  yrt = root_of(y, parent)
  rt, lf = xrt, yrt
  rt, lf = lf, rt if rank[xrt] < rank[yrt]
  parent[lf] = rt
  rank[rt] += rank[lf]
  
#   nx = ps[x-1]
#   ny = ps[y-1]
#   gx = gp[nx]
#   gx = gp[gx] while gx != gp[gx]
#   gy = gp[ny]
#   gy = gp[gy] while gy != gp[gy]
#   if gx != gy
#     marged = [gx,gy].min
#     ue = gp[nx]
#     gp[nx] = marged
#     ue, gp[ue] = gp[ue], marged while ue != marged
#     ue = gp[ny]
#     gp[ny] = marged
#     ue, gp[ue] = gp[ue], marged while ue != marged
#     # if gx < gy
#     #   gp[gy] = gx
#     #   gp[ny] = gx
#     # else
#     #   gp[gx] = gy
#     #   gp[nx] = gy
#     # end
#   end
# #  pp [x,y].join(" ")
# #  x, y = y, x if  gp[ps[x-1]] > gp[ps[y-1]]
# #  gp[ps[y-1]] = gp[ps[x-1]]
# #  pp gp
end

ret = 0
N.times do |i|
  n = i+1
  m = ps[n]
  if root_of(n, parent) == root_of(m, parent)
    ret += 1
  end
  # n_ue = gp[n]
  # while n_ue != gp[n_ue]
  #   n_ue = gp[n_ue]
  # end
  # m_ue = gp[m]
  # while m_ue != gp[m_ue]
  #   m_ue = gp[m_ue]
  # end
  # if n_ue == m_ue
  #   ret += 1
  # end
end

# N.times do |i|
#   ue = gp[i+1]
#   while gp[ue] != ue
#     gp[i+1] = gp[ue]
#     ue = gp[i+1]
#   end
# end



#pp gp
# ps.each_with_index do |p,i|
#   ret += 1 if gp[ps[p-1]] == gp[p]
# end
# pp parent
# pp rank
puts ret