Problem:
Score : 400 points

Problem Statement

An SNS has N users - User 1, User 2, \cdots, User N.

Between these N users, there are some relationships - M friendships and K blockships.

For each i = 1, 2, \cdots, M, there is a bidirectional friendship between User A_i and User B_i.

For each i = 1, 2, \cdots, K, there is a bidirectional blockship between User C_i and User D_i.

We define User a to be a friend candidate for User b when all of the following four conditions are satisfied:

a \neq b.

There is not a friendship between User a and User b.

There is not a blockship between User a and User b.

There exists a sequence c_0, c_1, c_2, \cdots, c_L consisting of integers between 1 and N (inclusive) such that c_0 = a, c_L = b, and there is a friendship between User c_i and c_{i+1} for each i = 0, 1, \cdots, L - 1.

For each user i = 1, 2, ... N, how many friend candidates does it have?

Constraints

All values in input are integers.

2 ≤ N ≤ 10^5

0 \leq M \leq 10^5

0 \leq K \leq 10^5

1 \leq A_i, B_i \leq N

A_i \neq B_i

1 \leq C_i, D_i \leq N

C_i \neq D_i

(A_i, B_i) \neq (A_j, B_j) (i \neq j)

(A_i, B_i) \neq (B_j, A_j)

(C_i, D_i) \neq (C_j, D_j) (i \neq j)

(C_i, D_i) \neq (D_j, C_j)

(A_i, B_i) \neq (C_j, D_j)

(A_i, B_i) \neq (D_j, C_j)

Input

Input is given from Standard Input in the following format:

N M K
A_1 B_1
\vdots
A_M B_M
C_1 D_1
\vdots
C_K D_K

Output

Print the answers in order, with space in between.

Sample Input 1

4 4 1
2 1
1 3
3 2
3 4
4 1

Sample Output 1

0 1 0 1

There is a friendship between User 2 and 3, and between 3 and 4. Also, there is no friendship or blockship between User 2 and 4. Thus, User 4 is a friend candidate for User 2.

However, neither User 1 or 3 is a friend candidate for User 2, so User 2 has one friend candidate.

Sample Input 2

5 10 0
1 2
1 3
1 4
1 5
3 2
2 4
2 5
4 3
5 3
4 5

Sample Output 2

0 0 0 0 0

Everyone is a friend of everyone else and has no friend candidate.

Sample Input 3

10 9 3
10 1
6 7
8 2
2 5
8 4
7 3
10 9
6 4
5 8
2 6
7 5
3 1

Sample Output 3

1 3 5 4 3 3 3 3 1 0

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

require 'pp'
_, m, k = gets.split.map(&:to_i)
persons = []
groups = []
m.times do |i|
  a, b = gets.split.map(&:to_i)
  case [persons[a].nil?, persons[b].nil?]
  when [true, true]
    groups << [a, b]
    persons[a] = [groups.length-1, [b], []]
    persons[b] = [groups.length-1, [a], []]
  when [true, false]
    groups[persons[b][0]] << a
    persons[a] = [persons[b][0], [b], []]
    persons[b][1] << a
  when [false, true]
    groups[persons[a][0]] << b
    persons[b] = [persons[a][0], [a], []]
    persons[a][1] << b
  when [false, false]
    if persons[a][0] != persons[b][0]
      t_gid = persons[b][0]
      t_g = groups[t_gid]
      groups[persons[b][0]].each { |n| persons[n][0] = persons[a][0] }
      groups[persons[a][0]] = groups[persons[a][0]] + t_g
      groups[t_gid] = nil
    end
    persons[b][1] << a
    persons[a][1] << b
  end
end
groups.compact!
k.times do
  c, d = gets.split.map(&:to_i)
  if persons[c].nil?
    persons[c] = [nil, [], [d]]
  else
    persons[c][2] << d
  end
  if persons[d].nil?
    persons[d] = [nil, [], [c]]
  else
    persons[d][2] << c
  end
end

result = persons.compact.map do |gid, friends, blocks|
  if gid.nil?
    0
  else
    (groups[gid] - friends - blocks).count - 1
  end
end
puts result.map(&:to_s).join(' ')