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)

from heapq import heappush, heappop

n, m = map(int, input().split())
edge = [list(map(int, input().split())) for _ in range(m)]
edge.sort(key=lambda x: (x[1], x[0]))

q = [(1, 0)]
for l, r, c in edge:
    # print((l, r, c), q)

    cand = float("inf")
    while q:
        y, z = heappop(q)
        if y >= l:
            heappush(q, (y, z))
            break

    for y, z in q:
        if y < r:
            cand = min(cand, z)
        else:
            heappush(q, (y, z))
            break

    if cand != float("inf"):
        heappush(q, (r, cand + c))

# print(q)

ans = -1
for y, z in q:
    if y == n:
        if ans == -1:
            ans = z
        else:
            ans = min(ans, z)

print(ans)