Contest Duration: ~ (local time) (120 minutes) Back to Home
D - Shortest Path on a Line /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

• 1 以上 N 以下の整数 L_i, R_i 及び正整数 C_i を用いる。 L_i ≦ s < t ≦ R_i なる整数の組 (s,t) すべてに対し、頂点 s と頂点 t の間に長さ C_i の辺を追加する。

ただし、L_1,...,L_M, R_1,...,R_M, C_1,...,C_M はすべて入力で与えられます。

### 制約

• 2 ≦ N ≦ 10^5
• 1 ≦ M ≦ 10^5
• 1 ≦ L_i < R_i ≦ N
• 1 ≦ C_i ≦ 10^9

### 入力

N M
L_1 R_1 C_1
:
L_M R_M C_M


### 入力例 1

4 3
1 3 2
2 4 3
1 4 6


### 出力例 1

5


### 入力例 2

4 2
1 2 1
3 4 2


### 出力例 2

-1


### 入力例 3

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


### 出力例 3

28


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