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.split.map(&:to_i)
events = []
n.times do
  l, r = gets.split.map(&:to_i)
  events << [l, +1]
  events << [r, -1]
end
events.sort_by!(&:first)
k = 0
best = 0
until events.empty?
  t = events[0][0]
  while !events.empty? && events[0][0] == t
    _, diff = events.shift
    k += diff
  end
  best = k if k > best
end
p best