Problem:
Score : 400 points

Problem Statement

There are N islands lining up from west to east, connected by N-1 bridges.

The i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.

One day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:

Request i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.

You decided to remove some bridges to meet all these M requests.

Find the minimum number of bridges that must be removed.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq a_i < b_i \leq N

All pairs (a_i, b_i) are distinct.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print the minimum number of bridges that must be removed.

Sample Input 1

5 2
1 4
2 5

Sample Output 1

1

The requests can be met by removing the bridge connecting the second and third islands from the west.

Sample Input 2

9 5
1 8
2 7
3 5
4 6
7 9

Sample Output 2

2

Sample Input 3

5 10
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5

Sample Output 3

4

Solution in PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php

while (true) {
	$input = trim(fgets(STDIN));
	$input = explode(" ", $input);
	foreach ($input as $value) {
		$args[] = $value;
		if (count($args) >= 2) {
			break;
		}
	}
	if (count($args) >= 2) {
		break;
	}
}


$islands = (int)$args[0];
$request_cnt = (int)$args[1];
$b_count = $islands-1;
$b_array = [];
$cnt = 0;
$requests=[];

while ($cnt < $request_cnt) {
	$input = trim(fgets(STDIN));
	$input = explode(" ", $input);
	$requests[] = [(int)$input[0], (int)$input[1]];
	++$cnt;
}

for ($i=1; $i <= $b_count; $i++) { 
	$b_array[] = $i;
}

$cut_num = 0;
$end_flg = false;
for ($bridge=1; $bridge <= $b_count; $bridge++) { 
	$cut_num = $bridge;
	$kumi = kumiawase($b_array, $cut_num);
	foreach ($kumi as $value) {
		if ($value === []) {
			continue;
		}
		if (is_resolved($requests, $value)) {
			$end_flg = true;
			break;
		}
	}
	if($end_flg == true){
		break;
	}
}


out($cut_num);

function out($var){
	echo $var , PHP_EOL;
}


function is_resolved($requests, $cut_bridge_array){
	$resolved = [];
	foreach ($requests as $key => $request) {
		foreach ($cut_bridge_array as $value) {
			if(_is_resolved($request, $value)){
				$resolved[$key] = $request;
			}
		}
	}
	if (count($requests) == count($resolved)) {
		return true;
	}
	return false;
}

function _is_resolved($request, $cut_bridge){
	if (!_include($request, $cut_bridge)) {
		return false;
	}
	return true;
}


function _include($request, $bridge){
	if ($bridge >= $request[0] && $bridge < $request[1]) {
		return true;
	}
	return false;
}

function kumiawase($zentai,$nukitorisu){
  $zentaisu=count($zentai);
  $arrs = [];
  if($zentaisu<$nukitorisu){
    return [];
  }elseif($nukitorisu==1){
    for($i=0;$i<$zentaisu;$i++){
      $arrs[$i]=array($zentai[$i]);
    }
  }elseif($nukitorisu>1){
    $j=0;
    for($i=0;$i<$zentaisu-$nukitorisu+1;$i++){
      $ts=kumiawase(array_slice($zentai,$i+1),$nukitorisu-1);
      foreach($ts as $t){
        array_unshift($t,$zentai[$i]);
        $arrs[$j]=$t;
        $j++;
      }
    }
  }
  return $arrs;
}