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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.*;
import java.util.stream.Collectors;

public class Main {

    public static void main(final String[] args) throws Exception {
        final Scanner sc = new Scanner(System.in);
        long N;
        N = sc.nextLong();
        long M;
        M = sc.nextLong();
        long K;
        K = sc.nextLong();

        Set<Point> friends = new HashSet<>();
        for(int i = 0 ; i < M ; i++){
            int a = sc.nextInt() - 1;
            int b = sc.nextInt() - 1;
            int smaller = Math.min(a, b);
            int larger = Math.max(a, b);
            Point p = new Point(smaller, larger);
            friends.add(p);
        }
        Set<Point> blocks = new HashSet<>();
        for(int i = 0 ; i < K ; i++){
            int c = sc.nextInt() - 1;
            int d = sc.nextInt() - 1;
            int smaller = Math.min(c, d);
            int larger = Math.max(c, d);
            Point p = new Point(smaller, larger);
            blocks.add(p);
        }

        final Solver solver = new Solver();
        solver.solve(N, M, K, friends, blocks);
    }
}

class Point {
    final int x;
    final int y;

    Point(int x, int y) {
        this.x = x;
        this.y = y;
    }

    @Override
    public int hashCode() {
        return Objects.hash(x, y);
    }

    @Override
    public boolean equals(Object obj) {
        if (!(obj instanceof Point)) {
            return false;
        }
        final Point other = (Point) obj;
        return this.x == other.x && this.y == other.y;
    }
}

class Solver {
    public void solve(long N, long M, long K, Set<Point> friends, Set<Point> blocks) {
        int INF = (int) 10e5;

        List<List<Integer>> d = new ArrayList<>();
        for (int i = 0; i < N; i++) {
            d.add(new ArrayList<>());
        }
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                int smaller = Math.min(i, j);
                int larger = Math.max(i, j);
                Point p = new Point(smaller, larger);
                if (friends.contains(p)) {
                    d.get(i).set(j, 1);
                    continue;
                }
                d.get(i).set(j, INF);
            }
        }

        for (int k = 0; k < N; k++) {
            for (int i = 0; i < N; i++) {
                for (int j = 0; j < N; j++) {
                    d.get(i).set(j, Math.min(d.get(i).get(j), d.get(i).get(k) + d.get(k).get(j)));
                }
            }
        }

        List<Long> candidates = new ArrayList<>();
        for (int i = 0; i < N; i++) {
            long candidate = 0;
            for (int j = 0; j < N; j++) {
                if (i == j) {
                    continue;
                }

                int smaller = Math.min(i, j);
                int larger = Math.max(i, j);
                Point p = new Point(smaller, larger);
                if (blocks.contains(p) || friends.contains(p)) {
                    continue;
                }

                if (d.get(i).get(j) < INF) {
                    candidate++;
                }
            }
            candidates.add(candidate);
        }
        System.out.println(candidates.stream().map(String::valueOf).collect(Collectors.joining(" ")));
    }
}