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
N,M = map(int,input().split())
LRC = [tuple(map(int,input().split())) for i in range(M)]

es = [[] for i in range(N)]
for l,r,c in LRC:
    l,r = l-1,r-1
    es[l].append((r,c))
for i in range(N-1):
    es[i+1].append((i,0))

INF = float('inf')
dist = [INF]*N
dist[0] = 0
hq = [(0,0)]
heapq.heapify(hq)

while(hq):
    d,v = heapq.heappop(hq)
    if v==N-1:
        print(d)
        exit()
    for to,c in es[v]:
        if d+c >= dist[to]: continue
        dist[to] = d+c
        heapq.heappush(hq, (d+c, to))
print(-1)