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)

/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author champon
 */

#include <iostream>
#include <fstream>

#include <bits/stdc++.h>
#define se cout << "test ok" << endl;
#define sp << " " <<
using namespace std;
using ll = long long;
using ld = long double;
const ll mod = ll(1e9)+7;
const ll inf = ll(5e18);
template<typename T1, typename T2> ll ceill(T1 a, T2 b){ return (a+b-1)/b; }
void ans(bool b, ostream& out=cout){ out << (b ? "Yes" : "No") << endl; }
void ans2(bool b, ostream& out=cout){ out << (b ? "YES" : "NO") << endl; }
template<typename T> inline bool chmax(T &a, T b){ if(a<b){a=b; return true;} return false; }
template<typename T> inline bool chmin(T &a, T b){ if(a>b){a=b; return true;} return false; }
template<typename A, size_t N, typename T> void Fill(A (&array)[N], const T &val){ fill((T*)array, (T*)(array+N), val); }
int dx[] = {1, 0, -1, 0, 1, -1, 1, -1};
int dy[] = {0, 1, 0, -1, 1, -1, -1, 1};

#ifndef INCLUDE_DEBUG_HPP
#define INCLUDE_DEBUG_HPP

#include <iostream>
#include <vector>
#include <map>
using namespace std;

namespace dbg {
    using ll = long long;

    class Debug {
    public:
        Debug(){}
        template<typename T>
        void vd(vector<T> vec);
        template<typename T>
        void vd2(vector<vector<T>> vec);
        template<typename T>
        void ad(T *arr, ll n);
        template<typename T, size_t N>
        void ad2(T (&arr)[N], ll n);
        template<typename T>
        void md(T mp);
    };

    template<typename T>
    void Debug::vd(vector<T> vec) {
        for (auto vv : vec) cout << vv << " ";
        cout << endl;
    }

    template<typename T>
    void Debug::vd2(vector<vector<T>> vec) {
        for (auto vv : vec) for (auto vvv : vv) cout << vvv << " ";
        cout << endl;
    }

    template<typename T>
    void Debug::ad(T *arr, ll n) {
        for (int i = 0; i <= n; i++) cout << arr[i] << " ";
        cout << endl;
    }

    template<typename T, size_t N>
    void Debug::ad2(T (&arr)[N], ll n) {
        for (int i = 0; i <= N; i++) for (int j = 0; j <= n; j++) cout << arr[i][j] << " ";
        cout << endl;
    }

    template<typename T>
    void Debug::md(T mp) {
        cout << "key : value" << endl;
        for (auto const &m : mp) cout << m.first << " : " << m.second << endl;
        cout << endl;
    }

}

#endif //INCLUDE_DEBUG_HPP

using dbg::Debug;
Debug debug;

#ifndef DEFINE_UNIONFIND_HPP
#define DEFINE_UNIONFIND_HPP


#include <numeric>

using namespace std;

namespace unionfind {

    using ll = long long;

    class UnionFind {
    public:
        ll n;
        vector<ll> par;
        vector<ll> rank;
        vector<ll> size;

        UnionFind(int n);
        ll find(ll x);
        void unite(ll x, ll y);
        bool same(ll x, ll y);
        ll getsize(ll x);
        int rootCount();
    };

    UnionFind::UnionFind(int n):n(n), par(n, 0), rank(n, 0), size(n, 1) {
        iota(par.begin(), par.end(), 0);
    }

    ll UnionFind::find(ll x) {
        if (par[x] == x) return x;
        else return par[x] = find(par[x]);
    }

    void UnionFind::unite(ll x, ll y) {
        x = find(x);
        y = find(y);
        if (x == y) return;
        if (rank[x] < rank[y]) {
            par[x] = y;
            size[y] += size[x];
        } else {
            par[y] = x;
            size[x] += size[y];
            if (rank[x] == rank[y]) rank[x]++;
        }
    }

    bool UnionFind::same(ll x, ll y) {
        return find(x) == find(y);
    }

// get size of tree
    ll UnionFind::getsize(ll x) {
        return size[find(x)];
    }

// get the number of roots
    int UnionFind::rootCount() {
        int cnt = 0;
        for (int i = 0; i < n; i++) {
            if (i == par[i]) cnt++;
        }
        return cnt;
    }


// verify
// https://atc001.contest.atcoder.jp/tasks/unionfind_a

}

#endif //DEFINE_UNIONFIND_HPP
using unionfind::UnionFind;


class DFriendSuggestions {
public:
	void solve(std::istream& in, std::ostream& out)
	{
	    ll n, m, k;
	    in >> n >> m >> k;
        vector<int> a(m), b(m);
        UnionFind uf(n);
	    for(int i=0; i<m; i++){
            in >> a[i] >> b[i];
            a[i]--; b[i]--;
            uf.unite(a[i], b[i]);
	    }

	    vector<int> c(k), d(k);
	    for(int i=0; i<k; i++){
	        in >> c[i] >> d[i];
	        c[i]--; d[i]--;
	    }

	    vector<int> ab(n, 0), cd(n, 0);
	    for(int i=0; i<m; i++){
	        if(uf.same(a[i], b[i])){
	            ab[a[i]]++;
	            ab[b[i]]++;
	        }
	    }
        for(int i=0; i<k; i++){
            if(uf.same(c[i], d[i])){
                cd[c[i]]++;
                cd[d[i]]++;
            }
        }

	    for(int i=0; i<n; i++){
	        int par = uf.par[i];
	        int sz = uf.getsize(par);
            out << sz - ab[i] - cd[i] - 1 << " ";
	    }
	    out << endl;
	}
};


int main() {
	DFriendSuggestions solver;
	std::istream& in(std::cin);
	std::ostream& out(std::cout);
	solver.solve(in, out);
	return 0;
}