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.