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)

{-# OPTIONS_GHC -O #-}
{-# LANGUAGE BangPatterns #-}

import Control.Monad
import Control.Monad.ST
import Data.List
import Data.Array.Unboxed
import Data.Array.ST
import Control.Monad.Trans.State.Strict
import Data.Char (isSpace)
import Data.Maybe (fromJust)
import qualified Data.ByteString.Char8 as B

type Parser a = StateT B.ByteString Maybe a

parseInt :: Parser Int
parseInt = StateT (B.readInt . B.dropWhile isSpace)

parseInt2 :: Parser (Int,Int)
parseInt2 = liftM2 (,) parseInt parseInt

parse :: Parser (Int, [(Int,Int)], [(Int,Int)])
parse = do
  n<-parseInt
  m<-parseInt
  q<-parseInt
  lrs<-replicateM m parseInt2
  pqs<-replicateM q parseInt2
  return (n,lrs,pqs)

main=do
  (n,lrs,pqs) <- fromJust.evalStateT parse <$> B.getContents
  let !ar = f n lrs
  putStr.unlines $ map (\(p,q)->show $ ar ! (p,q)) pqs
--
f n lrs = runSTUArray $ do
  ar <- newArray ((1,1),(n+1,n)) 0 :: ST s (STUArray s (Int,Int) Int)
  forM_ lrs $ \(l,r) -> do
    writeArray ar (1,r) =<< succ <$> readArray ar (1,r)
    writeArray ar (l+1,r) =<< pred <$> readArray ar (l+1,r)
  forM_ [(l,r)|l<-[2..n],r<-[1..n]] $ \(l,r) -> do
    writeArray ar (l,r) =<< (+) <$> readArray ar (l,r) <*> readArray ar (l-1,r)
  forM_ [(l,r)|l<-[1..n],r<-[2..n]] $ \(l,r) -> do
    writeArray ar (l,r) =<< (+) <$> readArray ar (l,r) <*> readArray ar (l,r-1)
  pure ar