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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

namespace ConsoleApp
{
    class Program
    {
        static void Main(string[] args)
        {
            Input();
            Initialize();

            for (int i = 0; i < Q; i++)
            {
                var x = p[i];
                var y = q[i];
                Console.WriteLine(Count(y, y) - Count(x - 1, y) - Count(y, x - 1) + Count(x - 1, x - 1));
            }
        }

        // L<=x, Q<=y を満たす電車区間の個数
        static int Count(int x, int y)
        {
            if (dp[x, y] != -1) return dp[x, y];
            if (x == 0 || y == 0) return 0;

            dp[x, y] = trains[x, y] + Count(x - 1, y) + Count(x, y - 1) - Count(x - 1, y - 1);
            return dp[x, y];
        }

        static int N;
        static int M;
        static int Q;
        static int[,] trains;
        static int[] p;
        static int[] q;
        static int[,] dp;

        static void Input()
        {
            var input = Console.ReadLine().Split().Select(int.Parse).ToArray();
            N = input[0];
            M = input[1];
            Q = input[2];
            trains = new int[N + 1, N + 1];
            p = new int[Q];
            q = new int[Q];

            for (int i = 0; i < M; i++)
            {
                var inputLR = Console.ReadLine().Split().Select(int.Parse).ToArray();
                trains[inputLR[0], inputLR[1]]++;
            }

            for (int i = 0; i < Q; i++)
            {
                var inputPQ = Console.ReadLine().Split().Select(int.Parse).ToArray();
                p[i] = inputPQ[0];
                q[i] = inputPQ[1];
            }
        }

        static void Initialize()
        {
            dp = new int[N + 1, N + 1];
            for (int i = 0; i <= N; i++)
            {
                for (int j = 0; j <= N; j++)
                {
                    dp[i, j] = -1;
                }
            }
        }
    }
}