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)

use std::io::*;
use std::str::*;

fn main() {
    let n: usize = read_one();
    let m: u32 = read_one();
    let q: u32 = read_one();

    let lr: Vec<(usize, usize)> = read2_lines(m);
    let pq: Vec<(usize, usize)> = read2_lines(q);

    let mut mat1: Vec<Vec<u32>> = vec![vec![0; n]; n];
    let mut mat2: Vec<Vec<u32>> = vec![vec![0; n]; n];

    for &(l, r) in lr.iter() {
        mat1[l - 1][r - 1] += 1;
    }

    for r in 0..n {
        for l in (0..n).rev() {
            let r_ofst = if r == 0 { 0 } else { mat2[l][r - 1] };
            mat2[l][r] += mat1[l][r] + r_ofst;
        }
    }

    for l in (0..n).rev() {
        for r in 0..n {
            let l_ofst = if l == n - 1 { 0 } else { mat2[l + 1][r] };
            mat2[l][r] += l_ofst;
        }
    }

    for &(p, q) in pq.iter() {
        println!("{}", mat2[p - 1][q - 1]);
    }
}

fn read_one<T: std::str::FromStr>() -> T {
    let s = stdin().bytes().map(|c| c.unwrap() as char)
                   .skip_while(|c| c.is_whitespace())
                   .take_while(|c| !c.is_whitespace())
                   .collect::<String>();
    s.trim().parse().ok().unwrap()
}

fn read2<T: FromStr, T2: FromStr>() -> (T, T2) {
    let mut s = String::new();
    stdin().read_line(&mut s).ok();
    let mut iter = s.trim().split_whitespace();
    (iter.next().unwrap().parse().ok().unwrap(), iter.next().unwrap().parse().ok().unwrap())
}

fn read2_lines<T: FromStr, T2: FromStr>(n: u32) -> Vec<(T, T2)> {
    (0..n).map(|_| read2()).collect()
}