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: Runtime Error)

import qualified Data.Vector.Unboxed as V
import Data.Vector.Unboxed ((!))
import qualified Data.Vector.Unboxed.Mutable as VM
import Data.List
import Control.Monad
import Data.IORef

coordN :: Int -> (Int, Int) -> Int
coordN n (x,y) = x*n+y

main :: IO ()
main = do
  [n,m,q] <- map read . words <$> getLine
  let cd = coordN n
  vecm <- VM.replicate (n*n) 0 :: IO (VM.IOVector Int)
  replicateM_ m $ do
    [x,y] <- map read . words <$> getLine
    VM.modify vecm (+1) $ cd (x,y)
  forM_ [1..n-1] $ \x -> do
    let slice0 = VM.slice ((x-1)*n) n vecm
        slice1 = VM.slice (x*n) n vecm
    forM_ [0..n-1] $ \y -> do
      val <- VM.read slice0 y
      VM.modify slice1 (val+) y
  forM_ [0..n-1] $ \x -> do
    let slice = VM.slice (x*n) n vecm
    forM_ [1..n-1] $ \y -> do
      val <- VM.read slice (y-1)
      VM.modify slice (val+) y
  vec <- V.unsafeFreeze vecm :: IO (V.Vector Int)
  replicateM_ q $ do
    [x,y] <- map read . words <$> getLine
    putStrLn $ show $ query vec n x y

query :: V.Vector Int -> Int -> Int -> Int -> Int
query vec n x y =
  vec ! cd (y,y) - chk (vec ! cd (x-1,y)) - chk (vec ! cd (y,x-1))
  + chk (vec ! cd (x-1,x-1))
 where
   cd = coordN n
   chk = if x <= 0 then const 0 else id