Problem:
Score : 600 points

Problem Statement

We have N points numbered 1 to N arranged in a line in this order.

Takahashi decides to make an undirected graph, using these points as the vertices.
In the beginning, the graph has no edge. Takahashi will do M operations to add edges in this graph.
The i-th operation is as follows:

The operation uses integers L_i and R_i between 1 and N (inclusive), and a positive integer C_i. For every pair of integers (s, t) such that L_i \leq s < t \leq R_i, add an edge of length C_i between Vertex s and Vertex t.

The integers L_1, ..., L_M, R_1, ..., R_M, C_1, ..., C_M are all given as input.

Takahashi wants to solve the shortest path problem in the final graph obtained. Find the length of the shortest path from Vertex 1 to Vertex N in the final graph.

Constraints

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq L_i < R_i \leq N

1 \leq C_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N M
L_1 R_1 C_1
:
L_M R_M C_M

Output

Print the length of the shortest path from Vertex 1 to Vertex N in the final graph.
If there is no shortest path, print -1 instead.

Sample Input 1

4 3
1 3 2
2 4 3
1 4 6

Sample Output 1

5

We have an edge of length 2 between Vertex 1 and Vertex 2, and an edge of length 3 between Vertex 2 and Vertex 4, so there is a path of length 5 between Vertex 1 and Vertex 4.

Sample Input 2

4 2
1 2 1
3 4 2

Sample Output 2

-1

Sample Input 3

10 7
1 5 18
3 4 8
1 3 5
4 7 10
5 9 8
6 10 5
8 10 3

Sample Output 3

28

Solution in PHP7 (7.0.15) (judge verdict: Accepted)

<?php
list($n, $m) = array_map("intval", explode(" ", trim(fgets(STDIN))));
$di = new Di($n);
for($i = 0; $i < $m; $i++){
  list($from, $to, $d) = array_map("intval", explode(" ", trim(fgets(STDIN))));
  $di->connect($from, $to, $d);
}
for($i = 2; $i <= $n; $i++){
  $di->connect($i, $i - 1, 0);
}
$di->solve(1);
$distance = $di->distance[$n];
if($distance == $di->inf){
  echo -1;
}else{
  echo $distance;
}

/**
 * Dijkstra
 * Attention: 1-origin
 **/
class Di{
  public $pq;
  public $distance;
  public $G;
  public $from;
  public $inf = 10**18;
  function __construct($n) {
    $this->pq = new SplPriorityQueue();
    for($i = 1; $i <= $n; $i++){
      $this->distance[$i] = $this->inf;
      $this->from[$i] = 0;
    }
  }
  function connect($from, $to, $cost){
    $this->G[$from][] = [$to, $cost];
  }
  function solve($from){
    $this->pq->insert($from, 0);
    $this->distance[$from] = 0;
    while($this->pq->count()){
      $f = $this->pq->extract();
      if(!isset($this->G[$f]))continue;
      foreach($this->G[$f] as list($t, $dist)){
        $new = $this->distance[$f] + $dist;
        if($this->distance[$t] > $new){
          $this->distance[$t] = $new;
          $this->from[$t] = $f;
          $this->pq->insert($t, -$new);
        }
      }
    }
  }
}