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 C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <iostream>
#include <vector>

using namespace std;

const int inf = 10000000;

int main() {
  int n, m, k;
  cin >> n >> m >> k;

  vector<vector<int>> vec1(n, vector<int>(n, 0));
  for (int i = 0; i < m; ++i) {
    int a, b;
    cin >> a >> b;
    vec1[a - 1][b - 1] = vec1[b - 1][a - 1] = 1;
  }
  for (int i = 0; i < k; ++i) {
    int c, d;
    cin >> c >> d;
    vec1[c - 1][d - 1] = vec1[d - 1][c - 1] = -1;
  }

  vector<vector<int>> vec2 = vec1;
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < n; ++j)
      if (vec2[i][j] != 1)
        vec2[i][j] = inf;

  for (int h = 0; h < n; ++h)
    for (int i = 0; i < n; ++i)
      for (int j = 0; j < n; ++j)
        if (vec2[i][h] + vec2[h][j] < vec2[i][j])
          vec2[i][j] = vec2[j][i] = vec2[i][h] + vec2[h][j];

  vector<int> ans;
  for (int i = 0; i < n; ++i) {
    int sum = 0;
    for (int j = 0; j < n; ++j) {
      if (i == j || vec1[i][j] != 0 || vec2[i][j] == inf)
        continue;
      ++sum;
    }
    ans.push_back(sum);
  }

  cout << ans[0];
  for (int i = 1; i < n; ++i)
    cout << " " << ans[i];
  cout << endl;
}