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: Wrong Answer)

import Data.List
import Control.Monad

data KdTree = Branch {isBegBrch :: {-# UNPACK #-} !Bool,
                      pivotBeg :: {-# UNPACK #-} !Int,
                      pivotEnd :: {-# UNPACK #-} !Int,
                      size_ :: {-# UNPACK #-} !Int,
                      leftChild :: KdTree,
                      rightChild :: KdTree } | Nil

size :: KdTree -> Int
size Branch{size_ = s} = s
size Nil = 0
                                               
pivot (Branch _ b e _ _ _) = (b,e)

branch :: Bool -> (Int,Int) -> KdTree -> KdTree -> KdTree
branch b (pb,pe) lc rc = Branch b pb pe (size lc + size rc + 1) lc rc

selector :: Bool -> (a,a) -> a
selector True = fst
selector False = snd

makeKdTree_ :: Bool -> [(Int,Int)] -> Int -> KdTree
makeKdTree_ _ [] _ = Nil
makeKdTree_ flag ls len = Branch flag pb pe len
                                           (makeKdTree_ (not flag) ls1 len1)
                                           (makeKdTree_ (not flag) ls2 len2)
 where
   ls' = sortOn (selector flag) ls
   (ls1, (pb,pe):ls2) = splitAt len1 ls 
   len1 = len `div` 2
   len2 = len - len1 - 1

makeKdTree :: [(Int,Int)] -> KdTree
makeKdTree ls = makeKdTree_ True ls (length ls)

query :: (Bool,Bool) -> KdTree -> (Int,Int) -> Int
query _ Nil _ = 0
query (True,True) b _ = size b
query (True,False) (b@(Branch True _ pe _ lc rc)) t@(_,te)
  = (if pe <= te then 1 else 0)
     + query (True,False) lc t
     + query (True,False) rc t
query (False,True) (b@(Branch False pb _ _ lc rc)) t@(tb,_)
   = (if tb <= pb then 1 else 0)
     + query (False,True) lc t
     + query (False,True) rc t
query (False,flg2) (b@(Branch True pb pe _ lc rc)) t@(tb,te)
   = if tb <= pb
     then
       (if pe <= te then 1 else 0)
       + query (False,flg2) lc t
       + query (True,flg2) rc t
     else
       query (False,flg2) rc t
query (flg1,False) (b@(Branch False pb pe _ lc rc)) t@(tb,te)
   = if pe <= te
     then
       (if tb <= pb then 1 else 0)
       + query (flg1,True) lc t
       + query (flg1,False) rc t
     else
       query (flg1,False) lc t

main :: IO ()
main = do
  [n,m,q] <- (map read . words) <$> getLine
  ls <- map ((\[x,y]->(x,y)) . map read . words) <$> replicateM m getLine
  let tr = makeKdTree ls
  replicateM_ q $ do
    t <- ((\[x,y]->(x,y)) . map read . words) <$> getLine
    let a = query (False,False) tr t
    putStrLn $ show a