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: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,o,n) for(long long i = o;i<n;i++)
#define oneforall ios::sync_with_stdio(false);cin.tie(0);
#define all(v) (v).begin(),(v).end()
#define ini(...) int __VA_ARGS__; in(__VA_ARGS__)
#define inl(...) long long __VA_ARGS__; in(__VA_ARGS__)
#define ins(...) string __VA_ARGS__; in(__VA_ARGS__)
const long long INF=1e18;
void in(){} template <typename T,class... U> void in(T &t,U &...u){ cin >> t; in(u...);}
void out(){cout << "\n";} template <typename T,class... U> void out(const T &t,const U &...u){ cout << t; if(sizeof...(u)) cout << " "; out(u...);}
typedef vector<int> vi;
typedef vector<long long> vl;
typedef long long ll;
typedef vector<pair<long,long>> vpll;
typedef vector<pair<int,int>> vpii;

struct union_find
{
	typedef vector<int> vi;
	vi par,cnt,rank;
	union_find(int x):par(x),cnt(x,1),rank(x,0){
		for (int i = 0;i < x; i++) {
			par[i] = i;
		}
	}

	int find(int x){
		if(par[x] == x)return x;
		return par[x] = find(par[x]);
	}

	void unite(int x_,int _x){
		x_ = find(x_);
		_x = find(_x);
		if(x_!=_x){
			if(rank[x_] >= rank[_x]){
				if(rank[x_] == rank[_x]){rank[x_]++;}
				par[_x] = x_;
				cnt[x_] += cnt[_x];
			}
			else{
				par[x_] = _x;
				cnt[_x] += cnt[x_];
			}
		}
	}

	int count(int x){
		return cnt[find(x)];
	}

	bool same(int x_,int _x){
		return find(x_) == find(_x);
	}

};
int main() {
	oneforall
	oneforall
	oneforall
	oneforall
	oneforall
	oneforall
	oneforall
	oneforall
	oneforall
	oneforall
	oneforall
	oneforall
	oneforall
	oneforall
	ini(n);
	ini(n1);
	ini(n_);
	vector<vi> fr(n);
	vector<vi> bl(n);
	union_find uf(n);
	FOR(i,0,n1){
		ini(x);
		x--;
		ini(x1);
		x1--;
		fr[x].push_back(x1);
		fr[x1].push_back(x);
		uf.unite(x,x1);
	}
	FOR(i,0,n_){
		ini(x);
		x--;
		ini(x1);
		x1--;
		bl[x].push_back(x1);
		bl[x1].push_back(x);
	}
	FOR(i,0,n){
		int total = uf.count(i)-fr[i].size()-1;
		for(auto x:bl[i]){
			if(uf.same(i,x)){
				total--;
			}
		}
		cout<<total<<" ";
	}
	return 0;
}