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 PyPy3 (2.4.0) (judge verdict: Accepted)

def main():
    N, M, K=map(int, input().split())
    friend_or_block = [0] * N
    friends_chain = UnionFindTree(N)

    for _ in range(M):
        a, b = map(int, input().split())
        a, b = a-1, b-1
        friends_chain.unite(a, b)
        friend_or_block[a] += 1
        friend_or_block[b] += 1

    for _ in range(K):
        c, d = map(int, input().split())
        c, d = c-1, d-1
        if friends_chain.same(c, d):
            friend_or_block[c] += 1
            friend_or_block[d] += 1

    print(*[friends_chain.count(i) - friend_or_block[i] - 1 for i in range(N)])

class UnionFindTree:
    def __init__(self, n):
        self.parent = [-1] * n

    def root(self, x):
        p, s = self.parent[x], list()
        while p >= 0:
            s.append(x)
            x, p = p, self.parent[p]
        for c in s: self.parent[c] = x
        return x

    def same(self, x, y): return self.root(x) == self.root(y)

    def count(self, x): return -self.parent[self.root(x)]

    def unite(self, x, y):
        xr, yr = self.root(x), self.root(y)
        if xr == yr: return
        if self.parent[xr] > self.parent[yr]: xr, yr = yr, xr
        self.parent[xr] += self.parent[yr]
        self.parent[yr] = xr

if __name__ == '__main__':
    main()