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: Wrong Answer)

import sys
input = sys.stdin.readline


def main():
    N, M = map(int, input().split())
    A = []
    for _ in range(M):
        A.append(list(map(int, input().split())))
    A.sort(key=lambda x: x[1])
    A.sort(key=lambda x: x[0])
#    print(A)
    dp = [[float("inf")]*N for _ in range(M+1)]
    dp[0][0] = 0
    for i, (s, t, c) in enumerate(A):
        for j in range(t+1):
            if j < s:
                dp[i+1][j-1] = dp[i][j-1]
            else:
                dp[i+1][j-1] = min(dp[i][j-1], dp[i][s-1] + c)
    ans = dp[M][N-1]
#    for x in dp:
#        print(x)
    if ans == float("inf"):
        print(-1)
    else:
        print(ans)


if __name__ == '__main__':
    main()