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)

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}
//usage
//input! {
//  h: i32;
//  v: [i32; n]
//  x: [[i32; n]; m]
//  f: chars <- Vec<char>
//}
pub mod at {
    pub struct UnionFind {
        parents: Vec<isize>,
    }
    use std::collections::HashMap;
    impl UnionFind {
        pub fn new(n: usize) -> UnionFind {
            let parents = vec![-1; n];
            UnionFind { parents: parents }
        }
        pub fn find(&mut self, x: usize) -> usize {
            if self.parents[x] < 0 {
                x
            } else {
                let xx = self.parents[x] as usize;
                let y = self.find(xx);
                self.parents[x] = y as isize;
                y
            }
        }
        pub fn unite(&mut self, x: usize, y: usize) -> bool {
            use std::mem::swap;
            let mut x = self.find(x);
            let mut y = self.find(y);
            if x == y {
                return false;
            }
            if self.parents[x] > self.parents[y] {
                swap(&mut x, &mut y);
            }
            self.parents[x] += self.parents[y];
            self.parents[y] = x as isize;
            true
        }
        pub fn size(&mut self, x: usize) -> usize {
            let x = self.find(x);
            (-self.parents[x]) as usize
        }
        pub fn same(&mut self, x: usize, y: usize) -> bool {
            self.find(x) == self.find(y)
        }
        pub fn members(&mut self, x: usize) -> Vec<usize> {
            let root = self.find(x);
            (0..self.parents.len())
                .into_iter()
                .filter(|i| self.find(*i) == root)
                .collect::<Vec<usize>>()
        }
        pub fn roots(&mut self) -> Vec<usize> {
            (0..self.parents.len())
                .into_iter()
                .filter(|i| self.parents[*i] < 0)
                .collect::<Vec<usize>>()
        }
        pub fn all_group_members(&mut self) -> HashMap<usize, Vec<usize>> {
            let mut groups_map = HashMap::new();
            for x in 0..self.parents.len() {
                let r = self.find(x);
                groups_map.entry(r).or_insert(vec![]).push(x);
            }
            groups_map
        }
    }
}

use at::*;

fn main() {
    input! {
        n: usize,
        m: usize,
        k: usize,
        friend: [(usize, usize); m],
        block: [(usize, usize); k],
    }

    let mut b:Vec<Vec<usize>> = vec![vec![]; n + 1];
    let mut f:Vec<Vec<usize>> = vec![vec![]; n + 1];


    for &(x, y) in &friend {
        f[x].push(y);
        f[y].push(x);
    }

    for &(x, y) in &block {
        b[x].push(y);
        b[y].push(x);
    }

    let mut union = UnionFind::new((n + 1) as usize);
    for &(x, y) in &friend {
        union.unite(x, y);
    }

    for i in 1..(n + 1) {
        let mut ans = union.size(i) - f[i].len() - 1;
        for &j in &b[i] {
            if union.same(i, j) {
                ans -= 1;
            }
        }
        println!("{}", ans);
    }
}