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: Runtime Error)

import numpy as np
from queue import Queue
N,M,K=map(int, input().split())
F=np.zeros((N,N),dtype=int)
B=np.zeros((N,N),dtype=int)
for i in range(M):
  a,b=map(int, input().split())
  a-=1
  b-=1
  F[a,b]=1
  F[b,a]=1
for i in range(K):
  c,d=map(int, input().split())
  c-=1
  d-=1
  B[c,d]=1
  B[d,c]=1
  
def Adj(u):
  adj=[]
  for v in range(N):
    if F[u,v]==1 and v!=u:
    	adj.append(v)
  return adj    

def BFS():
  cands=[]
  for s in range(N):
    cand=[]
    visited=[s]
    #main関数でスタートを塗りつぶすのを忘れないように
    Q=Queue()
    Q.put(s)
    while not Q.empty():
      u=Q.get()
      if u!=s and B[s,u]==0 and F[s,u]==0:
        cand.append(u)
      for v in Adj(u):  
        if v not in visited:
          Q.put(v)
          visited.append(v)
    cands.append(str(len(cand)))
  print(' '.join(cands))
BFS()