D - AtCoder Express 2

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 $q_i$.

2 3 1
1 1
1 2
2 2
1 2

3

As all the trains runs within the section from City $1$ to City $2$, the answer to the only query is $3$.

10 3 2
1 5
2 8
7 10
1 7
3 10

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 $3$.

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

7
9
10
6
8
9
6
7
8
10