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 <bits/stdc++.h>
#include <map> // pair
using namespace std;

typedef long long ll;
#define vec vector<int>
#define vecll vector<ll>
#define vpair vector<pair<int, int>>
#define vpairll vector<pair<ll, ll>>
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define rep(i,n)   for(int i=(int)0; i<(int)n; i++)
#define llrep(i,n)   for(ll i=(ll)0; i<(ll)n; i++)
#define REP(i,m,n) for(int i=(int)m; i<(int)n; i++)
#define all(var)     (var).begin(), (var).end()
#define prt(var)     cout << var << endl
#define prt_dbl(i,var) cout<<fixed<<setprecision(i)<<var<<endl;

int main(){

  int N,M,K;
  cin>>N>>M>>K;
  vector<vector<int>> A(N,vector<int>(N,0));
  rep(i,M){
    int a,b;
    cin>>a>>b;
    A.at(a-1).at(b-1)=1;
    A.at(b-1).at(a-1)=1;
  }
  rep(i,K){
    int a,b;
    cin>>a>>b;
    A.at(a-1).at(b-1)=-1;
    A.at(b-1).at(a-1)=-1;
  }
  rep(i,N){
    int count = -1;
    rep(j,N){
      if(A.at(i).at(j)==0)count++;
      if(A.at(i).at(j)==-1)break;
    }
    cout<<count<<" ";
  }
  cout<<endl;
}