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 heapq

INF = 2**62-1

class Dijkstra:
    def __init__(self, rote_map, start_point):
        self.rote_map = rote_map
        self.start_point = start_point

    def execute(self):
        num_of_city = len(self.rote_map)
        dist = [INF for _ in range(num_of_city)]

        dist[self.start_point] = 0
        heap_q = []
        heapq.heappush(heap_q, (0, self.start_point))
        while heap_q:
            prev_cost, src = heapq.heappop(heap_q)

            # if dist[src] < prev_cost:
                # continue

            for dest, cost in self.rote_map[src].items():
                if dist[dest] > dist[src] + cost:
                    dist[dest] = dist[src] + cost
                    heapq.heappush(heap_q, (dist[dest], dest))
        return dist

n, m = map(int, input().split())
route_map = [{} for _ in range(n)]

for i in range(m):
    u, v, a = map(int, input().split())
    u, v = u - 1, v - 1
    route_map[u][v] = a

for i in range(n-1):
    u, v = i+1, i
    route_map[u][v] = 0

# ゴールまでの最短経路
dijkstra_result = Dijkstra(route_map,0).execute()

if dijkstra_result[-1] != INF:
    print(dijkstra_result[-1])
else:
    print(-1)