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 (1.42.0) (judge verdict: Accepted)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use std::collections::BTreeMap;

use comp::union_find::UnionFind;
use std::collections::BTreeSet;

fn main() {
    use proconio::input;
    use proconio::marker::Usize1;
    input!(n: usize, m: usize, k: usize);
    let builder = |n| {
        let mut ret: BTreeMap<usize, BTreeSet<usize>> = BTreeMap::new();
        for _ in 0..n {
            input!(a: Usize1, b: Usize1);
            ret.entry(a).or_insert(BTreeSet::new()).insert(b);
            ret.entry(b).or_insert(BTreeSet::new()).insert(a);
        }
        ret
    };
    let friends = builder(m);
    let blockers = builder(k);
    let mut uf = UnionFind::new(n);
    for (&a, bs) in friends.iter() {
        for &b in bs.iter() {
            uf.unite(a, b);
        }
    }

    let cnt = uf.counts();

    // println!("f {:?}", friends);
    // println!("b {:?}", blockers);
    // println!("{:?}", uf.v);
    let ans = (0..n)
        .map(|i| {
            let r = uf.root(i);
            let mut ans = *cnt.get(&r).unwrap() - 1;
            let direct_friends = friends.get(&i).map_or(0, |s| {
                // println!("direct friends: {:?}", s);
                s.len()
            });
            // println!("uf.v[33]    {}", uf.root(33));
            // println!("uf.v[29430] {}", uf.root(2930));
            // println!("33 cnt {:?}", cnt.get(&33));
            // println!("29430 cnt {:?}", cnt.get(&29430));
            // println!("29430 f {:?}", friends.get(&29430));
            // println!(
            //     "for {}: r = {}, ans = {}, direct_friends = {}",
            //     i, r, ans, direct_friends
            // );
            ans -= direct_friends;

            // println!("{:?}", blockers.get(&i));

            if let Some(bs) = blockers.get(&i) {
                for &b in bs {
                    if uf.root(b) == r {
                        ans -= 1;
                    }
                }
            }

            ans.to_string()
        })
        .collect::<Vec<String>>()
        .join(" ");
    println!("{}", ans);
}
*/

fn main() {
    let exe = "/tmp/binB35CE194";
    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>";