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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace Tasks
{
    public class D
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var (N, M, K) = Scanner.Scan<int, int, int>();
            var friends = new List<int>[N].Select(x => new List<int>()).ToArray();
            var blocks = new List<int>[N].Select(x => new List<int>()).ToArray();
            var dsu = new DSU(N);
            for (var i = 0; i < M; i++)
            {
                var (A, B) = Scanner.Scan<int, int>();
                dsu.Merge(--A, --B);
                friends[A].Add(B);
                friends[B].Add(A);
            }

            for (var i = 0; i < K; i++)
            {
                var (C, D) = Scanner.Scan<int, int>();
                blocks[--C].Add(--D);
                blocks[D].Add(C);
            }

            var answer = new int[N];
            for (var i = 0; i < N; i++)
            {
                answer[i] = dsu.SizeOf(i) - friends[i].Count - 1;
                foreach (var block in blocks[i])
                    if (dsu.IsSame(i, block)) answer[i]--;
            }
            Console.WriteLine(string.Join(" ", answer));
        }

        public class DSU
        {
            private readonly int _n;
            private readonly int[] _parentOrSize;

            public DSU(int n = 0)
            {
                _n = n;
                _parentOrSize = Enumerable.Repeat(-1, n).ToArray();
            }

            public int Merge(int a, int b)
            {
                if (a < 0 || _n <= a) throw new IndexOutOfRangeException(nameof(a));
                if (b < 0 || _n <= b) throw new IndexOutOfRangeException(nameof(b));
                var (x, y) = (LeaderOf(a), LeaderOf(b));
                if (x == y) return x;
                if (-_parentOrSize[x] < -_parentOrSize[y]) (x, y) = (y, x);
                _parentOrSize[x] += _parentOrSize[y];
                _parentOrSize[y] = x;
                return x;
            }

            public bool IsSame(int a, int b)
            {
                if (a < 0 || _n <= a) throw new IndexOutOfRangeException(nameof(a));
                if (b < 0 || _n <= b) throw new IndexOutOfRangeException(nameof(b));
                return LeaderOf(a) == LeaderOf(b);
            }

            public int LeaderOf(int a)
            {
                if (a < 0 || _n <= a) throw new IndexOutOfRangeException(nameof(a));
                if (_parentOrSize[a] < 0) return a;
                return _parentOrSize[a] = LeaderOf(_parentOrSize[a]);
            }

            public int SizeOf(int a)
            {
                if (a < 0 || _n <= a) throw new IndexOutOfRangeException(nameof(a));
                return -_parentOrSize[LeaderOf(a)];
            }

            public IEnumerable<IEnumerable<int>> Groups()
            {
                var leaders = new int[_n];
                var groupSize = new int[_n];
                for (var i = 0; i < _n; i++)
                {
                    leaders[i] = LeaderOf(i);
                    groupSize[leaders[i]]++;
                }

                var ret = new List<int>[_n].Select(x => new List<int>()).ToArray();
                for (var i = 0; i < _n; i++) ret[leaders[i]].Add(i);
                return ret.Where(x => x.Any());
            }
        }

        public static class Scanner
        {
            private static Queue<string> queue = new Queue<string>();
            public static T Next<T>()
            {
                if (!queue.Any()) foreach (var item in Console.ReadLine().Trim().Split(" ")) queue.Enqueue(item);
                return (T)Convert.ChangeType(queue.Dequeue(), typeof(T));
            }
            public static T Scan<T>() => Next<T>();
            public static (T1, T2) Scan<T1, T2>() => (Next<T1>(), Next<T2>());
            public static (T1, T2, T3) Scan<T1, T2, T3>() => (Next<T1>(), Next<T2>(), Next<T3>());
            public static (T1, T2, T3, T4) Scan<T1, T2, T3, T4>() => (Next<T1>(), Next<T2>(), Next<T3>(), Next<T4>());
            public static (T1, T2, T3, T4, T5) Scan<T1, T2, T3, T4, T5>() => (Next<T1>(), Next<T2>(), Next<T3>(), Next<T4>(), Next<T5>());
            public static IEnumerable<T> ScanEnumerable<T>() => Console.ReadLine().Trim().Split(" ").Select(x => (T)Convert.ChangeType(x, typeof(T)));
        }
    }
}