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: Wrong Answer)

<?php
define("inf", 10**15);
list($n, $m) = array_map("intval", explode(" ", trim(fgets(STDIN))));
for($i = 2; $i <= $n; $i++){
  $map[$i][$i-1] = 0;
}
for($i = 0; $i < $m; $i++){
  list($from, $to, $d) = array_map("intval", explode(" ", trim(fgets(STDIN))));;
  $map[$from][$to] = $d;
}
$D[1] = 0;
for($i = 2; $i <= $n; $i++){
  $D[$i] = inf ;
}
$pq = new SplPriorityQueue();
$pq->insert(1, 0);
while($pq->count()){
  $from = $pq->extract();
  foreach($map[$from] as $to => $length){
    $alt = $D[$from] + $length;
    if($D[$to] > $alt){
      $D[$to] = $alt;
      $pq->insert($to, -$alt);
    }
  }
}
printf("%d", $D[$n] == inf ? -1 : $D[$n]);