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: Accepted)

import Control.Monad
import Control.Applicative
import Data.List
import Data.Array
import Data.Array.IO
import Data.Maybe
import Data.Bits
import Data.Ord
import qualified Data.ByteString.Char8 as BS
import qualified Data.Set as Set
import Debug.Trace

modifyArray arr i f = readArray arr i >>= \x -> writeArray arr i (f x)

listToTuple2 [a,b] = (a,b)
listToTuple3 [a,b,c] = (a,b,c)
listToTuple4 [a,b,c,d] = (a,b,c,d)

getWords = getLine >>= return . words

readIntBS = fst . fromJust . BS.readInt


main :: IO ()
main = do
  (n,m,query) <- listToTuple3 . map read . words <$> getLine :: IO (Int,Int,Int)

  dat <- map (listToTuple2 . map readIntBS . BS.words) <$> (replicateM m BS.getLine) :: IO [(Int,Int)]

  arr <- newArray ((0,0),(n,n)) 0 :: IO (IOArray (Int,Int) Int)

  forM_ dat $ \(l,r) -> do
    modifyArray arr (l,r) (+1)

  forM_ [0..n] $ \l -> do
    forM_ [1..n] $ \r -> do
      ((+) <$> readArray arr (l,r-1) <*> readArray arr (l,r)) >>= \x -> writeArray arr (l,r) x

  forM_ [1..n] $ \l -> do
    forM_ [0..n] $ \r -> do
      ((+) <$> readArray arr (l-1,r) <*> readArray arr (l,r)) >>= \x -> writeArray arr (l,r) x


  replicateM query $ do
    (p,q) <- listToTuple2 . map readIntBS . BS.words <$> BS.getLine :: IO (Int,Int)

    a <- readArray arr (q,q)
    b <- readArray arr (p-1,q)
    c <- readArray arr (q,p-1)
    d <- readArray arr (p-1,p-1)

    print $ a - b - c + d
  
  return ()