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! 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 ) * } };
}
#[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 , chars ) => { read_value ! ( $ next , String ) . chars ( ) . collect ::< Vec < char >> ( ) };
    ( $ next : expr , usize1 ) => { read_value ! ( $ next , usize ) - 1 };
    ( $ next : expr , $ t : ty ) => { $ next ( ) . parse ::<$ t > ( ) . expect ( "Parse error" ) };
}

fn main() {
    input! {
        n: usize, m: usize, q: usize,
        rails: [(usize, usize); m],
        queries: [(usize, usize); q]
    }

    let mut ranges = rails.into_iter().map(|(l,r)| (l,r,None)) .collect::<Vec<_>>();
    let mut iqueries = queries.into_iter().enumerate().map(|(i, (l,r))| (l,r,Some(i))) .collect::<Vec<_>>();
    ranges.append(&mut iqueries);
    ranges.sort_by_key(|&(_,r,qi)| (r, qi));
    let mut sqd = SqDecomposition::new(n+1, |a,b| a + b, 0);
    let mut ret = vec![0u64;q];
    for &(l,r,qi) in ranges.iter() {
        if let Some(src) = qi {
            ret[src] = sqd.fold(r+1) - sqd.fold(l);
        } else {
            sqd.update(l, 1);
        }
    }

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

#[allow(dead_code)]
struct SqDecomposition {
    all: Vec<u64>,
    sq: Vec<u64>,
    d: usize,
    op: Box<Fn(u64, u64) -> u64>,
    init: u64,
}
#[allow(dead_code)]
impl SqDecomposition {
    fn new<B>(n: usize, op: B, init: u64) -> SqDecomposition
    where
        B: Fn(u64, u64) -> u64 + 'static,
    {
        let d = (n as f64).sqrt().ceil() as usize;
        SqDecomposition {
            all: vec![init; n],
            sq: vec![init; d],
            d: d,
            op: Box::new(op),
            init: init,
        }
    }
    fn update(&mut self, i: usize, a: u64) {
        self.all[i] = (self.op)(self.all[i], a);
        self.sq[i / self.d] = (self.op)(self.sq[i / self.d], a);
    }
    #[doc = " [0,n)"]
    fn fold(&self, n: usize) -> u64 {
        let mut ret = self.init;
        for i in 0..n / self.d {
            ret = (self.op)(ret, self.sq[i]);
        }
        for i in 0..n % self.d {
            ret = (self.op)(ret, self.all[n - n % self.d + i]);
        }
        ret
    }
}