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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

int N, M, Q;
int L[271828], R[271828];
int p[114514], q[114514];

int kitaeri[512][512];
int asumisu[512];

int main(void) {
	int i, j;
	if (scanf("%d%d%d", &N, &M, &Q) != 3) return 1;
	for (i = 0; i < M; i++) {
		if (scanf("%d%d", &L[i], &R[i]) != 2) return 1;
	}
	for (i = 0; i < Q; i++) {
		if (scanf("%d%d", &p[i], &q[i]) != 2) return 1;
	}

	for (i = 0; i < M; i++) {
		kitaeri[L[i]][R[i]]++;
		kitaeri[R[i] + 1][R[i]]--;
		asumisu[R[i]]++;
	}
	/* 都市iを走る(すなわち、始点が都市1～i)、都市jが終点の列車は何本あるか */
	for (i = 1; i <= N + 1; i++) {
		for (j = 1; j <= N; j++) {
			kitaeri[i][j] += kitaeri[i - 1][j];
		}
	}
	/* 都市iを走る、都市j～都市Nが終点の列車は何本あるか */
	for (i = 1; i <= N; i++) {
		for (j = N - 1; j >= 1; j--) {
			kitaeri[i][j] += kitaeri[i][j + 1];
		}
	}
	/* 都市j～都市Nが終点の列車は何本あるか */
	for (i = N - 1; i >= 1; i--) {
		asumisu[i] += asumisu[i + 1];
	}

	for (i = 0; i < Q; i++) {
		/* 都市p[i]～都市q[i]が終点の列車 */
		int satorina = asumisu[p[i]] - asumisu[q[i] + 1];
		/* そのうち、都市(p[i]-1)を走っているもの */
		int zaasan = kitaeri[p[i] - 1][p[i]] - kitaeri[p[i] - 1][q[i] + 1];
		/* 都市p[i]～都市Nが始発で、都市p[i]～都市q[i]が終点の列車 */
		printf("%d\n", satorina - zaasan);
	}

	return 0;
}

/*

Nが小さい
それぞれの地点において、「どこまでの列車が何本あるか」という情報を積む

*/

/* ↓の方法は方程式が解なしになってダメそう */

/*

完全に含まれないとは？

a. L <= R < p
b. L      < p      <= R <= q
c. L      < p           <= q < R
d.          p <= L      <= q < R
e.          p           <= q < L <= R

完全に含まれるとは？

f.          p <= L <= R <= q

x1. L < p               : a+b+c
x2.     p <= L <= q     :       d  +f
x3.               q < L :         e

x4. R < p               : a
x5.     p <= R <= q     :   b      +f
x6.               q < R :     c+d+e

a : x1           + x4           = 1
b : x1                + x5      = 1
c : x1                     + x6 = 1
d :      x2                + x6 = 1
e :           x3           + x6 = 1
f :      x2           + x5      = 0

1 0 0 1 0 0 | 1
1 0 0 0 1 0 | 1
1 0 0 0 0 1 | 1
0 1 0 0 0 1 | 1
0 0 1 0 0 1 | 1
0 1 0 0 1 0 | 0

1 0 0  1 0 0 | 1
0 0 0 -1 1 0 | 0
0 0 0 -1 0 1 | 0
0 1 0  0 0 1 | 1
0 0 1  0 0 1 | 1
0 1 0  0 1 0 | 0

1 0 0  1 0  0 |  1
0 1 0  0 0  1 |  1
0 0 0 -1 1  0 |  0
0 0 0 -1 0  1 |  0
0 0 1  0 0  1 |  1
0 0 0  0 1 -1 | -1

1 0 0  1 0  0 | 1
0 1 0  0 0  1 | 1
0 0 1  0 0  1 | 1
0 0 0 -1 1  0 | 0
0 0 0 -1 0  1 | 0
0 0 0  0 1 -1 |-1

1 0 0  1  0  0 | 1
0 1 0  0  0  1 | 1
0 0 1  0  0  1 | 1
0 0 0  1 -1  0 | 0
0 0 0  0 -1  1 | 0
0 0 0  0  1 -1 |-1

1 0 0  1  0  0 | 1
0 1 0  0  0  1 | 1
0 0 1  0  0  1 | 1
0 0 0  1 -1  0 | 0
0 0 0  0  1 -1 | 0
0 0 0  0  0  0 |-1

*/