Problem:
Score: 400 points

Problem Statement

In Takahashi Kingdom, there is a east-west railroad and N cities along it, numbered 1, 2, 3, ..., N from west to east.
A company called AtCoder Express possesses M trains, and the train i runs from City L_i to City R_i (it is possible that L_i = R_i).
Takahashi the king is interested in the following Q matters:

The number of the trains that runs strictly within the section from City p_i to City q_i, that is, the number of trains j such that p_i \leq L_j and R_j \leq q_i.

Although he is genius, this is too much data to process by himself. Find the answer for each of these Q queries to help him.

Constraints

N is an integer between 1 and 500 (inclusive).

M is an integer between 1 and 200 \ 000 (inclusive).

Q is an integer between 1 and 100 \ 000 (inclusive).

1 \leq L_i \leq R_i \leq N (1 \leq i \leq M)

1 \leq p_i \leq q_i \leq N (1 \leq i \leq Q)

Input

Input is given from Standard Input in the following format:

N M Q
L_1 R_1
L_2 R_2
:
L_M R_M
p_1 q_1
p_2 q_2
:
p_Q q_Q

Output

Print Q lines. The i-th line should contain the number of the trains that runs strictly within the section from City p_i to City q_i.

Sample Input 1

2 3 1
1 1
1 2
2 2
1 2

Sample Output 1

3

As all the trains runs within the section from City 1 to City 2, the answer to the only query is 3.

Sample Input 2

10 3 2
1 5
2 8
7 10
1 7
3 10

Sample Output 2

1
1

The first query is on the section from City 1 to 7. There is only one train that runs strictly within that section: Train 1.
The second query is on the section from City 3 to 10. There is only one train that runs strictly within that section: Train 3.

Sample Input 3

10 10 10
1 6
2 9
4 5
4 7
4 7
5 8
6 6
6 7
7 9
10 10
1 8
1 9
1 10
2 8
2 9
2 10
3 8
3 9
3 10
1 10

Sample Output 3

7
9
10
6
8
9
6
7
8
10

Solution in Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_macros)]
macro_rules! vec_md {
    ( $ init : expr ; $ ( $ dim : expr ) ;* ) => { vec_md ! ( $ ( $ dim ) ;* => $ init ) };
    ( $ head : expr ; $ ( $ tail : expr ) ;* => $ init : expr ) => { vec ! [ vec_md ! ( $ ( $ tail ) ;* => $ init ) ; $ head ] };
    ( $ head : expr => $ init : expr ) => { vec ! [ $ init ; $ head ] };
}

#[allow(dead_code)]
pub const D: usize = 23;

fn main() {
    use std::io::Read;
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    
    let _n: usize = iter.next().unwrap().parse().unwrap();
    let m: usize = iter.next().unwrap().parse().unwrap();
    let q: usize = iter.next().unwrap().parse().unwrap();
    
    let mut ranges: Vec<Data> = Vec::with_capacity(m+q);
    for _ in 0..m {
        let l: usize = iter.next().unwrap().parse().unwrap();
        let r: usize = iter.next().unwrap().parse().unwrap();
        ranges.push(Data {l:l, r:r, query_index: None});
    }
    for i in 0..q {
        let l: usize = iter.next().unwrap().parse().unwrap();
        let r: usize = iter.next().unwrap().parse().unwrap();
        ranges.push(Data {l:l, r:r, query_index: Some(i)});
    }
    ranges.sort();
    let mut sq = vec_md![0;D;D];
    let mut sq2 = vec![0;D];
    let mut ret = vec![0;q];
    for Data{l,r,query_index} in ranges {
        if let Some(i) = query_index {
            ret[i] = sum(&sq, &sq2, r+1) - sum(&sq, &sq2, l);
        } else {
            sq[l/D][l%D] += 1;
            sq2[l/D] += 1;
        }
    }

    for i in 0..q {
        println!("{}", ret[i]);
    }
}

fn sum(sq: &[Vec<usize>], sq2: &[usize], n: usize) -> usize {
    let mut ret = 0;
    for i in 0..(n/D) {
        ret += sq2[i];
    }
    for i in 0..(n%D) {
        ret += sq[n/D][i];
    }
    ret
}

#[derive(PartialEq, Eq, Debug)]
pub struct Data{
    l: usize,
    r: usize,
    query_index: Option<usize>
}
impl PartialOrd for Data {
    fn partial_cmp(&self, other: &Data) -> Option<std::cmp::Ordering> {
        Some(self.cmp(other))
    }
}
impl Ord for Data {
    fn cmp(&self, other: &Data) -> std::cmp::Ordering {
        match self.r.cmp(&other.r) {
            std::cmp::Ordering::Equal => self.query_index.cmp(&other.query_index),
            other => other
        }
    }
}