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;
}

$bridges = eval_bridge($requests, $b_count);
$cut_bridges = [];
$end_flg = false;

for ($i=1; $i <= $b_count; $i++) {
	$result = $i;
	if ($i == 1) {
		foreach ($bridges as $bridge) {
			if (count($bridge["inc_reqs"]) == $request_cnt) {
				$end_flg = true;
				$result = 1;
				break;
			}
		}
	}else{
		$kumiawase = kumiawase($b_array, $i);
		foreach ($kumiawase as $value) {
			$resolved = [];
			foreach ($value as $index) {
				$tmp_b = $bridges[$index];
				$resolved = array_merge($resolved, $tmp_b["inc_reqs"]);
			}
			$resolved = array_unique($resolved, SORT_REGULAR);

			if(count($resolved) == $request_cnt){
				$end_flg = true;
				$result = $i;
				break;
			}
		}
	}
	if ($end_flg == true) {
		break;
	}
}

out($result);



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


function eval_bridge($requests, $b_count){
	$bridges = [];

	for ($i=1; $i <= $b_count; $i++) {
		$inc_count = 0;
		$inc_req = [];
		foreach ($requests as $request) {
			if (_include($request, $i)) {
				++$inc_count;
				$inc_req[] = $request;
			}
		}
		$bridges[(int)$i] = [
			"inc_count" => $inc_count,
			"inc_reqs" => $inc_req,
		];
	}
	return $bridges;
}
function _include($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;
}