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
list($n, $m) = ints();
for($i = 2; $i <= $n; $i++){
  $map[$i][$i-1] = 0;
}
for($i = 0; $i < $m; $i++){
  list($from, $to, $d) = ints();
  $map[$from][$to] = $d;
}
$D = [];
for($i = 1; $i <= $n; $i++){
  $D[$i] = $i == 1 ? 0 : 10**18;
}
$pq = new SplPriorityQueue();
$pq->insert(1, 0);
while($pq->count()){
  $node = $pq->extract();
  foreach($map[$node] as $to => $length){
    if($D[$node] == 10**18)continue;
    $alt = $D[$node] + $length;
    if($D[$to] > $alt){
      $D[$to] = $alt;
      $pq->insert($to, -$alt);
    }
  }
}
printf("%d", $D[$n] == 10**18 ? -1 : $D[$n]);

function str(){
  return trim(fgets(STDIN));
}
function ints(){
  return array_map("intval", explode(" ", trim(fgets(STDIN))));
}
function int(){
  return intval(trim(fgets(STDIN)));
}
function o(...$val){
    if(count($val)==1)$val = array_shift($val);
    $trace = debug_backtrace();
    echo $trace[0]['line'].")";
    if(is_array($val)){
        if(count($val) == 0){
            echo "empty array";
        }elseif(!is_array(current($val))){
            echo "array:";
            echo implode(" ", $val)."\n";
        }else{
            echo "array:array\n";
            foreach($val as $row){
                echo implode(" ", $row)."\n";
            }
        }
    }else{
        echo $val."\n";
    }
}