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

fscanf(STDIN, "%d %d", $n, $m);

for($i = 0; $i<$m; $i++){
    $temp= explode(" ",trim(fgets(STDIN)));
    if(isset($map[$temp[0]][$temp[2]])){
        $map[$temp[0]][$temp[2]] = max($map[$temp[0]][$temp[2]], $temp[1]);
    }else {
        $map[$temp[0]][$temp[2]] = $temp[1];
    }
    if(isset($mmap[$temp[0]])){
        $mmap[$temp[0]] = max($mmap[$temp[0]], $temp[1]);
    }else{
        $mmap[$temp[0]] = $temp[1];
    }

}

ksort($map);
$cmap = array_fill(2,$n-1,PHP_INT_MAX);
$cmap[1] = 0;

foreach($map as $start => $value){
    ksort($value);
    $startcost = $cmap[$start];
    if($startcost == PHP_INT_MAX){
        echo -1;
        exit;
    }
    $k=0;
    foreach($value as $cost=>$end){
        if($k==0){
            $k=1;
            $mincost = $startcost + $cost;
            $update = 0;
            for($i=$start;$i<=$mmap[$start];$i++){
                if($cmap[$i] >= $mincost){
                    $update = $i;
                    break;
                }
            }
            if($update == 0){
                break;
            }
        }
        $cmap = array_replace($cmap, array_fill($update,$end - $update + 1, $startcost + $cost));
        $update = $end + 1;

    }
}
if($cmap[$n]==PHP_INT_MAX){
    echo -1;
}else{
    echo $cmap[$n];
}