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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

static class Program
{
    class Node<T>
    {
        private int m_height;
        private Node<T> m_parent;
        public T Item { get; private set; }
        public Node(T item)
        {
            m_height = 0;
            m_parent = this;
            Item = item;
        }
        public Node<T> Find()
        {
            if (m_parent == this) { return this; }

            Node<T> parent = m_parent.Find();
            m_parent = parent;
            return parent;
        }
        public static void Unite(Node<T> a, Node<T> b)
        {
            Node<T> p = a.Find();
            Node<T> q = b.Find();
            if (p.m_height < q.m_height)
            {
                p.m_parent = q;
                q.m_height = Math.Max(p.m_height + 1, q.m_height);
            }
            else
            {
                q.m_parent = p;
                p.m_height = Math.Max(q.m_height + 1, p.m_height);
            }
        }
    }

    static IEnumerable<int> Solve(int N, int M, int K, int[][] p1, int[][] p2)
    {
        var nodes = new Node<int>[N];
        for (int i = 0; i < N; ++i) { nodes[i] = new Node<int>(i); }
        var answers = new int[N];
        foreach (int[] p in p1)
        {
            int a = p[0] - 1;
            int b = p[1] - 1;
            Node<int>.Unite(nodes[a], nodes[b]);
            --answers[a];
            --answers[b];
        }
        var counts = new int[N];
        foreach (var node in nodes) { ++counts[node.Find().Item]; }
        for (int i = 0; i < N; ++i)
        {
            answers[i] += counts[nodes[i].Find().Item] - 1;
        }
        foreach (int[] p in p2)
        {
            int a = p[0] - 1;
            int b = p[1] - 1;
            if (nodes[a].Find() == nodes[b].Find())
            {
                --answers[a];
                --answers[b];
            }
        }
        return answers;
    }

    static void Main(string[] args)
    {
        var V1 = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        int N = V1[0], M = V1[1], K = V1[2];
        var p1 = new int[M][];
        for (int i = 0; i < M; ++i) { p1[i] = Array.ConvertAll(Console.ReadLine().Split(), int.Parse); }
        var p2 = new int[K][];
        for (int i = 0; i < K; ++i) { p2[i] = Array.ConvertAll(Console.ReadLine().Split(), int.Parse); }
        Console.WriteLine(string.Join(" ", Solve(N, M, K, p1, p2)));
    }
}