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 heapq


def main():
    n, m = map(int, input().split())
    lrc = [list(map(int, input().split())) for _ in range(m)]

    adj = [[(0, i-1)] for i in range(n)]
    adj[0] = []

    for l, r, c in lrc:
        l -= 1
        r -= 1
        adj[l].append((c, r))

    WHITE = 0
    GRAY = 1
    BLACK = 2

    def dijkstra(s):
        colors = [WHITE] * n
        ds = [float("inf")] * n
        ps = [-1] * n
        pq = []

        ds[s] = 0
        ps[s] = -1
        heapq.heappush(pq, (0, s))

        while pq:
            d, u = heapq.heappop(pq)
            colors[u] = BLACK

            if ds[u] < d:
                continue

            for c, v in adj[u]:
                if colors[v] != BLACK:
                    if ds[u] + c < ds[v]:
                        ds[v] = ds[u] + c
                        ps[v] = u
                        colors[v] = GRAY
                        heapq.heappush(pq, (ds[v], v))

        return ds, ps

    ds, ps = dijkstra(0)

    ans = ds[-1]
    if ans == float("inf"):
        ans = -1

    print(ans)


if __name__ == "__main__":
    main()