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 -O2 #-}
{-# LANGUAGE BangPatterns          #-}
{-# LANGUAGE CPP                   #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE OverloadedStrings     #-}
{-# LANGUAGE RecordWildCards       #-}
{-# LANGUAGE TupleSections         #-}
{-# LANGUAGE TypeFamilies          #-}

import           Control.Applicative
import           Control.Monad
import           Control.Monad.Primitive
import           Control.Monad.ST
import           Control.Monad.State.Strict
import           Data.Bool
import qualified Data.ByteString.Char8       as B
import qualified Data.ByteString.Unsafe      as B
import           Data.Char
import           Data.Function
import qualified Data.IntMap.Strict          as IM
import qualified Data.IntSet                 as IS
import           Data.List
import qualified Data.Map.Strict             as M
import           Data.Monoid
import           Data.Ord
import           Data.Primitive.MutVar
import qualified Data.Set                    as S
import           Data.Tuple
import qualified Data.Vector                 as V
import qualified Data.Vector.Generic         as G
import qualified Data.Vector.Generic.Mutable as GM
import qualified Data.Vector.Unboxed         as U
import qualified Data.Vector.Unboxed.Mutable as UM
import           Debug.Trace
import           Foreign                     hiding (void)
import           Unsafe.Coerce

main :: IO ()
main = do
    [n, m, q] <- map read.words <$> getLine :: IO [Int]
    (lrs, qs) <- U.splitAt m.U.unfoldrN (m + q) parseInt2 <$> B.getContents
    putStr.unlines.map show $ solve n lrs qs

width :: Int
width = 512

solve :: Int -> U.Vector (Int, Int) -> U.Vector (Int, Int) -> [Int]
solve n lrs qs = U.toList $ U.map (U.unsafeIndex table . uncurry ix1) qs
  where
    ix1 x y = ix (x - 1) (y - 1)
    ix x y = x * width + y
    !table = U.create $ do
        t <- UM.replicate (width * (n + 1)) 0
        U.forM_ lrs $ \(l, r) -> do
            UM.unsafeModify t (+1) (ix 0 (r - 1))
            UM.unsafeModify t (subtract 1) (ix l (r - 1))

        rep (n + 1) $ \i ->
            for 1 (n + 1) $ \j -> do
                acc <- UM.unsafeRead t (ix i (j - 1))
                UM.unsafeModify t (+acc) (ix i j)
        for 1 (n+1) $ \i ->
            rep (n + 1) $ \j -> do
                acc <- UM.unsafeRead t (ix (i -1 ) j)
                UM.unsafeModify t (+acc) (ix i j)

        return t


-------------------------------------------------------------------------------
type Parser a = B.ByteString -> Maybe (a, B.ByteString)

parseInt :: Parser Int
parseInt = B.readInt . B.dropWhile isSpace

parseInt2 :: Parser (Int, Int)
parseInt2 = runStateT $
    (,) <$> StateT (B.readInt . B.dropWhile isSpace)
        <*> StateT (B.readInt . B.unsafeTail)

parseInt3 :: Parser (Int, Int, Int)
parseInt3 = runStateT $
    (,,) <$> StateT (B.readInt . B.dropWhile isSpace)
        <*> StateT (B.readInt . B.unsafeTail)
        <*> StateT (B.readInt . B.unsafeTail)

rep, rev :: Monad m => Int -> (Int -> m ()) -> m ()
rep !n = U.forM_ $ U.generate n id
rev !n = U.forM_ $ U.iterateN n (subtract 1) (n - 1)
for :: Monad m => Int -> Int -> (Int -> m ()) -> m ()
for !s !t = U.forM_ $ U.generate (t - s) (+s)
{-# INLINE rep #-}
{-# INLINE rev #-}
{-# INLINE for #-}