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 Ruby (judge verdict: Accepted)

n, t = gets.chomp.split.map(&:to_i)
arr = Array.new(t + 1, 0)
n.times{
    l, r = gets.chomp.split.map(&:to_i)
    arr[l] += 1
    arr[r] -= 1
}
cum, max = 0, 0
arr.each{|x|
    cum += x
    max = cum if max < cum
}
puts max