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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

import sys
import itertools
input = sys.stdin.readline
sys.setrecursionlimit(100000)


def read_values():
    return map(int, input().split())


def read_index():
    return map(lambda x: x - 1, map(int, input().split()))


def read_list():
    return list(read_values())


def read_lists(N):
    return [read_list() for n in range(N)]


def functional(N, mod):
    F = [1] * (N + 1)
    for i in range(N):
        F[i + 1] = (i + 1) * F[i] % mod
    return F



def make_cluster(N, friend):
    import queue
    C = []
    already = [False] * N
    for i in range(N):
        if already[i]:
            continue
        already[i] = True
        s = {i}
        q = queue.Queue()
        q.put(i)
        while not q.empty():
            k = q.get()
            out = friend[k]
            for l in out:
                if already[l]:
                    continue
                s.add(l)
                q.put(l)
                already[l] = True
        C.append(s)

    return C


def main():
    import queue
    N, M, K = read_values()

    friend = [set() for _ in range(N)]
    for _ in range(M):
        a, b = read_index()
        friend[a].add(b)
        friend[b].add(a)
    
    block = [set() for _ in range(N)]
    for _ in range(K):
        a, b = read_index()
        block[a].add(b)
        block[b].add(a)

    already = [False] * N
    C = [0] * N
    for i in range(N):
        if already[i]:
            continue
        s = {i}
        q = queue.Queue()
        already[i] = True
        q.put(i)
        while not q.empty():
            k = q.get()
            out = friend[k]
            for l in out:
                if already[l]:
                    continue
                s.add(l)
                q.put(l)
                already[l] = True
        for j in s:
            C[j] = len(s.difference(block[j]))
    res = [str(C[i] - len(friend[i]) - 1) for i in range(N)]
    print(" ".join(res))


if __name__ == "__main__":
    main()