Problem:
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The Maximum Number of Customers

$N$ persons visited a restaurant. The restaurant is open from 0 to $T$. The $i$-th person entered the restaurant at $l_i$ and left at $r_i$. Find the maximum number of persons during the business hours.

Constraints

$ 1 \leq N \leq 10^5 $

$ 1 \leq T \leq 10^5 $

$ 0 \leq l_i < r_i \leq T $

Input

The input is given in the following format.

$N$ $T$

$l_1$ $r_1$

$l_2$ $r_2$

:

$l_N$ $r_N$

Output

Print the maximum number of persons in a line.

Sample Input 1

6 10
0 2
1 3
2 6
3 8
4 10
5 10

Sample Output 1

4

Sample Input 2

2 2
0 1
1 2

Sample Output 2

1

Solution in Haskell (judge verdict: Accepted)

import Control.Applicative
import Control.Monad
import Data.List
data Count = In Int | Out Int deriving (Show)

countNum (In n) = n
countNum (Out n) = n

instance Eq Count where
    a == b = countNum a == countNum b
instance Ord Count where
    compare (In a) (Out b) = case compare a b of
                               EQ -> GT
                               _  -> compare a b
    compare (Out a) (In b) = case compare a b of
                               EQ -> LT
                               _  -> compare a b
    compare  a b = compare (countNum a) (countNum b)

main = do
    [n,t] <- map read.words<$>getLine
    customers <- replicateM n ((\[l,t] -> [In l, Out t]).map read.words<$>getLine)
    print $ maximum.cumSum.sort.concat$customers

cumSum :: [Count] -> [Int]
cumSum = scanl (\acc c -> case c of
                             (In _) -> acc+1
                             (Out _) -> acc-1) 0