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 Python (3.4.3) (judge verdict: Accepted)

import numpy as np
from scipy.sparse import csr_matrix
from scipy.sparse.csgraph import dijkstra
import sys
readline = sys.stdin.readline
readlines = sys.stdin.readlines

N, M = map(int, readline().split())
lines = readlines()
edge = np.array([line.split() for line in lines], dtype = np.int64)
edge = sorted(edge,key=lambda x:(x[0],x[1],x[2]))

for i in range(1,M):
  if edge[i][0] == edge[i-1][0] and edge[i][1] == edge[i-1][1]:
    edge[i][2] = 0
#print(edge)
x = np.arange(N,1,-1)
y = np.arange(N-1,0,-1)
z = np.zeros(N-1,int)
X = np.vstack([x,y,z]).T
edge = np.concatenate([X,edge]).T
graph = csr_matrix((edge[2], (edge[:2] - 1)), (N, N))
distance_mat = dijkstra(graph, directed = True, indices = 0)
#print(distance_mat)
print(-1 if distance_mat[-1] == float("inf") else int(distance_mat[-1]))