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: Accepted)

import sys
sys.setrecursionlimit(10 ** 7)

class UnionFind():
    def __init__(self, n):
        self.n = n #要素数
        self.parents = [-1] * n #親格納配列(親のときは下流の要素数のマイナスを返す)

    def find(self,x):
        if self.parents[x] < 0: #親のとき
            return x
        else:
            self.parents[x] = self.find(self.parents[x]) #再帰で親に繋ぎ変える
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y: #親が同じときスキップ
            return

        if self.parents[x] > self.parents[y]: #要素数が多いほうをxにする
            x, y = y, x

        self.parents[x] += self.parents[y] #xの要素数はyの要素数ぶん増える
        self.parents[y] = x #yをxの子にする

    def size(self, x): #xの属するグループの要素数
        return -self.parents[self.find(x)]

    def same(self, x, y): #同じグループか判定
        return self.find(x) == self.find(y)

    def members(self, x): #xの属するグループの要素一覧
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self): #根の一覧
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self): #グループ個数
        return len(self.roots())

    def all_group_members(self): #根とその要素の辞書配列
        return {r: self.members(r) for r in self.roots()}

    def __str__(self): #print用
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

        
n,m,k=map(int,input().split())

U=UnionFind(n)
M=[[] for i in range(n)]
K=[[] for i in range(n)]

for i in range(m):
    a,b=map(int,input().split())
    a-=1
    b-=1
    U.union(a,b)
    M[a].append(b)
    M[b].append(a)
    
for i in range(k):
    a,b=map(int,input().split())
    a-=1
    b-=1
    if U.same(a,b):
        K[a].append(b)
        K[b].append(a)

ans=[]
for i in range(n):
    m=M[i]
    k=K[i]
    ans.append(U.size(i)-len(m)-len(k)-1)
print(*ans)