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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Control.Monad
import Data.Array
import Data.Array.ST

main = do
  [n,m,q] <- (map read . words) <$> getLine
  lr0 <- replicateM m (getLine >>= return . map read . words)
  pq0 <- replicateM q (getLine >>= return . map read . words)
  let lrlist = map (\l -> (head l, head $ tail l)) lr0
  let pqlist = map (\l -> (head l, head $ tail l)) pq0
  let train2dimsum = train_number_array_from n lrlist
  forM_ pqlist (query train2dimsum)

query train2dimsum (p, q) =
  print answer
  where answer =
          train2dimsum!(q,q) -
            if p == 1 then
              0
            else
              train2dimsum!(q,p-1) + train2dimsum!(p-1,q) - train2dimsum!(p-1,p-1)

train_number_array_from n lrlist = runSTArray $ do
  tstarray <- newArray ((1,1), (n,n)) 0
  forM_ lrlist (update_train_number_array tstarray)
  forM_ [1 .. n] $ \x -> do
    forM_ [1 .. n] $ \y -> do
      v <- readArray tstarray (x,y)
      s <- if x == 1 then return 0 else readArray tstarray (x-1,y)
      writeArray tstarray (x,y) (s+v)
  forM_ [1 .. n] $ \x -> do
    forM_ [1 .. n] $ \y -> do
      v <- readArray tstarray (x,y)
      s <- if y == 1 then return 0 else readArray tstarray (x,y-1)
      writeArray tstarray (x,y) (s+v)
  return tstarray

update_train_number_array tstarray lr = do
  num <- readArray tstarray lr
  writeArray tstarray lr (num + 1)