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: Time Limit Exceeded)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
#![allow(non_snake_case)]
#![allow(unused_imports)]
 
use proconio::{input, fastout};
use std::collections::*;
use whiteread::parse_line;

#[derive(Debug, Clone)]
struct FriendsMap {
    friends_map: HashMap<usize, HashSet<usize>>,
    seen: HashSet<usize>,
    friends_num: HashSet<usize>,
    block_num: HashSet<usize>,
}

impl FriendsMap {
    fn dfs(&mut self, start:usize, fix_start:usize, blocks_map: &HashMap<usize, HashSet<usize>>) {
        for next_start in self.friends_map.clone().get(&start).unwrap() {
            // println!("start: {}, next_start: {}", start, next_start);
            self.seen.insert(start);
            if self.friends_map.get(&fix_start).unwrap().contains(&start) {
                self.friends_num.insert(start);
            }
            if blocks_map.contains_key(&fix_start) {
                if blocks_map.get(&fix_start).unwrap().contains(&start) {
                    self.block_num.insert(start);
                }
            }

            if self.seen.contains(&next_start) {
                continue;
            } else {
                self.dfs(*next_start, fix_start, &blocks_map)
            }
        }
    }
}




#[fastout]
fn main() {
    let (N, M, K): (usize, usize, usize) = parse_line().unwrap();
    
    let mut friends_map: HashMap<usize, HashSet<usize>> = HashMap::new();
    let mut blocks_map: HashMap<usize, HashSet<usize>> = HashMap::new();

    for _i in 0..M {
        let (A, B): (usize, usize) = parse_line().unwrap();
        friends_map.entry(A).or_insert(HashSet::new());
        friends_map.entry(B).or_insert(HashSet::new());
        friends_map.get_mut(&A).unwrap().insert(B);
        friends_map.get_mut(&B).unwrap().insert(A);
    }

    for _i in 0..K {
        let (C, D): (usize, usize) = parse_line().unwrap();
        blocks_map.entry(C).or_insert(HashSet::new());
        blocks_map.entry(D).or_insert(HashSet::new());
        blocks_map.get_mut(&C).unwrap().insert(D);
        blocks_map.get_mut(&D).unwrap().insert(C);
    }

    // println!("{:?}", friends_map);


    let mut ans: Vec<usize> = Vec::new();

    for i in 1..=N {
        if friends_map.contains_key(&i) {
            let mut graph = FriendsMap{
                friends_map: friends_map.clone(),
                seen: HashSet::new(),
                friends_num: HashSet::new(),
                block_num: HashSet::new(),
            };

            graph.dfs(i, i, &blocks_map);
            // println!("{:?}", graph);
            ans.push(graph.seen.len() - graph.friends_num.len() - graph.block_num.len() - 1);
        } else {
            ans.push(0)
        }
    }

    let ans_for_print: Vec<String> = ans.iter().map(|x| x.to_string()).collect();

    println!("{}", ans_for_print.connect(" "));    
}
*/

fn main() {
    let exe = "/tmp/bin47F4797F";
    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>";