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
#input = sys.stdin.readline
sys.setrecursionlimit(10**7)
N, M = map(int, input().split())
LRC = [list(map(int, input().split())) for _ in range(M)]

adjm = [[float('inf')] * N for _ in range(N)]

for lrc in LRC:
    l = lrc[0]-1
    r = lrc[1]-1
    c = lrc[2]

    for i in range(l, r):
        for j in range(i+1, r+1):
            if adjm[i][j] > c:
                adjm[i][j] = c
                adjm[j][i] = c

def warshall_floyd(d):
    for k in range(N):
        for i in range(N):
            for j in range(N):
                d[i][j] = min(d[i][j],d[i][k] + d[k][j])

warshall_floyd(adjm)

res = adjm[0][N-1]
if res == float('inf'):
    print(-1)
else:
    print(res)