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 (1.42.0) (judge verdict: Time Limit Exceeded)

use proconio::input;
use proconio::marker::Usize1;
use smallvec::alloc::collections::{BTreeSet, BTreeMap};
use std::ops::Bound::{Included, Excluded};
use itertools::Itertools;

#[proconio::fastout]
fn main() {
    input! {
        N: usize,
        M: usize,
        Q: usize,
        trains: [(Usize1, Usize1); M],
        queries: [(Usize1, Usize1); Q]
    }

    let mut ordered_trains:BTreeMap<(usize, usize), i128> = BTreeMap::new();
    for train in trains {
        let q = ordered_trains.entry(train).or_insert(0);
        *q += 1;
    }
    for (s, t) in queries {
        let x = (Included((s, s)), Included((t, t)));
        println!("{:?}", ordered_trains.range(x).into_iter().filter(|&((u, v), _)| s <= *u && *v <= t).map(|(_, x)| *x).sum::<i128>());
    }
}