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 Rust (1.15.1) (judge verdict: Accepted)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use std::ops::{Add, Sub, Neg};
use competitive::prelude::*;

struct UnionFind<T> {
    parents: Vec<usize>,
    ranks: Vec<usize>,
    weights: Vec<T>,
}

impl<T> UnionFind<T>
    where T: Add<Output=T> + Clone + Copy + From<u8> + Neg<Output=T> + Sub<Output=T>
{
    fn new(n: usize) -> Self {
        UnionFind {
            parents: (0..n).map(|i| i).collect(),
            ranks: vec![1; n],
            weights: vec![T::from(0u8); n],
        }
    }
    fn find(&mut self, x: usize) -> usize {
        if x == self.parents[x] { return x; }
        let root = self.find(self.parents[x]);
        self.weights[x] = self.weights[x] + self.weights[self.parents[x]];
        self.parents[x] = root;
        return root;
    }

    fn unite(&mut self, x: usize, y: usize, weight: T) -> bool {
        // weights[x]+ weight = weights[y]
        let x_root = self.find(x);
        let y_root = self.find(y);
        if x_root == y_root { return false; }
        let (smaller, bigger, new_weight) = if self.size(x_root) >= self.size(y_root) {
            (y_root, x_root, self.weights[x] - self.weights[y] + weight)
        } else {
            (x_root, y_root, -(self.weights[x] - self.weights[y] + weight))
        };
        self.parents[smaller] = bigger;
        self.ranks[bigger] += self.ranks[smaller];
        self.weights[smaller] = new_weight;
        return true;
    }

    fn diff(&mut self, x: usize, y: usize) -> T {
        self.find(x);
        self.weights[y] - self.weights[x]
    }
    fn size(&mut self, x: usize) -> usize {
        let root = self.find(x);
        self.ranks[root]
    }
    fn equiv(&mut self, x: usize, y: usize) -> bool {
        self.find(x) == self.find(y)
    }
}

fn main() {
    input! {
        n: usize,
        m: usize,
        k: usize,
        ab: [(Usize1, Usize1); m],
        cd: [(Usize1, Usize1); k],
    }
    let mut uf = UnionFind::new(n + 1);
    let mut friends = vec![Vec::new(); n + 1];
    let mut blocks = vec![Vec::new(); n + 1];
    for i in 0..m {
        friends[ab[i].0].push(ab[i].1);
        friends[ab[i].1].push(ab[i].0);
    }
    for i in 0..k {
        blocks[cd[i].0].push(cd[i].1);
        blocks[cd[i].1].push(cd[i].0);
    }
    for i in 0..m {
        uf.unite(ab[i].0, ab[i].1, 0);
    }
    let mut ans = Vec::new();
    for i in 0..n {
        let cand = uf.size(i)
            - friends[i].iter().filter(|&&j| uf.equiv(i, j)).count()
            - blocks[i].iter().filter(|&&j| uf.equiv(i, j)).count()
            - 1;
        ans.push(cand);
    }
    println!("{}", ans.iter().join(" "));
}
*/

fn main() {
    let exe = "/tmp/bin05D3C160";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";