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: Time Limit Exceeded)

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

namespace CsAtCoderSubmitExam
{
    class BeginnerContest157
    {
        // D - Friend Suggestions
        class Friend
        {
            public int A;
            public int B;
            public Friend(int a, int b)
            {
                A = a;
                B = b;
            }

            public override string ToString()
            {
                return $"A:{A}, B:{B}";
            }
        }

        class Block
        {
            public int C;
            public int D;
            public Block(int c, int d)
            {
                C = c;
                D = d;
            }

            public override string ToString()
            {
                return $"C:{C}, D:{D}";
            }
        }

        static void readInput(ref int N, ref int M, ref int K, List<Friend> friends, List<Block> blocks)
        {
            var f = true;
            if (f)
            {
                var nm = Console.ReadLine().Split(' ');
                N = int.Parse(nm[0]);
                M = int.Parse(nm[1]);
                K = int.Parse(nm[2]);
                for (var i = 0; i < M; i++)
                {
                    var ab = Console.ReadLine().Split(' ');
                    friends.Add(new Friend(int.Parse(ab[0]), int.Parse(ab[1])));
                }

                for (var i = 0; i < K; i++)
                {
                    var cd = Console.ReadLine().Split(' ');
                    blocks.Add(new Block(int.Parse(cd[0]), int.Parse(cd[1])));
                }
            }
            else
            {
                N = 4;
                M = 4;
                K = 1;
                friends.Add(new Friend(2, 1));
                friends.Add(new Friend(1, 3));
                friends.Add(new Friend(3, 2));
                friends.Add(new Friend(3, 4));
                blocks.Add(new Block(4, 1));
            }
        }

        static void Main(string[] args)
        {
            var N = 0;
            var M = 0;
            var K = 0;
            var Friends = new List<Friend>();
            var Blocks = new List<Block>();
            readInput(ref N, ref M, ref K, Friends, Blocks);

            var friendsHash = new HashSet<int>();
            foreach (var f in Friends)
            {
                friendsHash.Add(f.A * 100 + f.B);
                friendsHash.Add(f.B * 100 + f.A);
            }

            var ans = new List<int>();

            for (var i = 1; i <= N; i++)
            {
                var n = 0;
                for (var j = 1; j <= N; j++)
                {
                    if (j != i)
                    {
                        if (Blocks.Any(b => (b.C == i && b.D == j) || (b.C == j && b.D == i)) == false)
                        {
                            if (Friends.Any(f => (f.A == i && f.B == j) || (f.A == j && f.B == i)) == false)
                            {
                                //if (IsChained(i, j, Friends))
                                if (IsChained2(i, j, Friends, friendsHash))
                                {
                                    n++;
                                }
                            }
                        }
                    }
                }
                ans.Add(n);
            }

            Console.WriteLine(string.Join(" ", ans.Select(a => a.ToString()).ToArray()));
        }

        private static bool IsChained2(int c1, int c2, IEnumerable<Friend> friends, HashSet<int> friendsHash)
        {
            foreach (var f in friends)
            {
                if (f.A == c1)
                {
                    if (friendsHash.Contains(f.A * 100 + c2))
                    {
                        return true;
                    }
                    else
                    {
                        var restFriends = friends.Where(ff => ff != f);
                        if (IsChained2(f.B, c2, restFriends, friendsHash))
                        {
                            return true;
                        }
                    }
                }
                else if (f.B == c1)
                {
                    if (friendsHash.Contains(f.B * 100 + c2))
                    {
                        return true;
                    }
                    else
                    {
                        var restFriends = friends.Where(ff => ff != f);
                        if (IsChained2(f.A, c2, restFriends, friendsHash))
                        {
                            return true;
                        }
                    }
                }
            }

            return false;
        }
    }
}