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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

N, M = gets.split.map(&:to_i)
lrcs = M.times.map { gets.split.map(&:to_i) }
imos = Array.new(N, 0)
graph = Array.new(N) { [] }
lrcs.each do |(l, r, c)|
  l -= 1
  r -= 1
  graph[l].push([r, c])
  imos[l] += 1
  imos[r] -= 1 if r < N
end
current = 0
used = Array.new(N)
imos.each.with_index do |n, i|
  current += n
  used[i] = current > 0
end

used.each.with_index do |b, i|
  graph[i + 1].push([i, 0]) if b
end

MAX = 10 ** 9 * N + 1

def shortest_path(graph, s)
  c_list = Array.new(graph.size, MAX)
  c_list[s] = 0
  queue = [[s, 0]]
  while !queue.empty?
    v, c = queue.shift
    next if c > c_list[v]
    graph[v].each do |(u, c)|
      if c_list[u] > c_list[v] + c
        c_list[u] = c_list[v] + c
        queue.push([u, c_list[u]])
      end
    end
  end
  c_list
end

ans = shortest_path(graph, 0)[N - 1]
if ans == MAX
  puts '-1'
else
  puts ans
end