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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

use v5.18;
use warnings;
use Data::Dumper;
use List::Util qw( sum0 );
sub read_line { chomp(my $s = <>); $s }
sub splited_read_line { split / /, read_line }

my ($town_num, $train_num, $question_num) = splited_read_line;

my @service_sections = map {
  my ($l, $r) = splited_read_line;
  +{
    left  => $l,
    right => $r,
  };
} 0 .. $train_num - 1;

my @questions = map {
  my ($l, $r) = splited_read_line;
  +{
    left  => $l,
    right => $r,
  };
} 0 .. $question_num - 1;

my $X = [ map { [ map { 0 } 0 .. $town_num ] } 0 .. $town_num ];
my $C = [ map { [ map { 0 } 0 .. $town_num ] } 0 .. $town_num ];

for my $service_section (@service_sections) {
  $X->[ $service_section->{left} ][ $service_section->{right} ]++;
}

for my $i (1 .. $town_num) {
  for my $j (1 .. $town_num) {
    $C->[$i][$j] = $C->[$i][ $j - 1 ] + $X->[$i][$j];
  }
}

for my $question (@questions) {
  my $sum = sum0 map {
    $C->[$_][ $question->{right} ] - $C->[$_][ $question->{left} - 1 ];
  } $question->{left} .. $question->{right};
  say $sum;
}