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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

import sys
from heapq import heappop, heappush

def main():
    input = sys.stdin.readline
    INF = 10**15
    ans = INF
    N, M = map(int, input().split())
    heap = []
    for _ in range(M):
        l, r, c = map(int, input().split())
        heappush(heap, (l-1, r-1, c))
    
    front = []
    heappush(front, (0, 0))
    while heap:
        l, r, c = heappop(heap)

        front_ = []
        while front:
            r_, c_ = heappop(front)
            if r_ < l:
                continue
            
            heappush(front_, (r_, c_))
            heappush(front_, (r, c+c_))
            if r == N-1:
                ans = min(ans, c+c_)
        
        front = front_
            
    if ans == INF:
        return -1
    
    return ans

if __name__ == '__main__':
    print(main())