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: Wrong Answer)

import numpy as np

n, f, b = map(int, input().split())
F = [list(map(int, input().split())) for i in range(f)]
B = [list(map(int, input().split())) for i in range(b)]

R=[]

for i in range(1,n+1):
    R.append(set([i]))

f_sets=[]

for friend in F:
    R[friend[0]-1].add(friend[1])
    R[friend[1]-1].add(friend[0])

    set0 = -1
    set1 = -1

    for i, f_set in enumerate(f_sets):
        if friend[0] in f_set:
            set0 = i
        if friend[1] in f_set:
            set1 = i

    if set0==-1 and set1==-1:
        f_sets.append(set(friend))

    if set0==-1 and set1!=-1:
        f_sets[set1].add(friend[0])

    if set0!=-1 and set1==-1:
        f_sets[set0].add(friend[1])

    if set0!=-1 and set1!=-1 and set0!=set1:
        f_sets[set0]=f_sets[set0]|f_sets[set1]
        f_sets.pop(set1)

for block in B:
    R[block[0]-1].add(block[1])
    R[block[1]-1].add(block[0])

ans=[]
for i in range(1,n+1):
    for f_set in f_sets:
        if i in f_set:
             ans.append(len(f_set-R[i-1]))
             break

print(' '.join(map(str, ans)))