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: Wrong Answer)

require 'pp'
n,m = gets.split.map(&:to_i)

a = Array.new(n+1){ {e: [], e2: []} }
# b = Array.new(n+1){999}
m.times do
  l,r,c = gets.split.map(&:to_i) # l, r, cost
  a[r][:e] << [l,c] # l, cost
  a[l][:e2] << [r,c]
  # l.upto(r) do |i|
  #   b[i] = [b[i],c].min
  # end
end
# p n
# pp a
dp = Array.new(n+1){10**9 + 1} # n番目の店までのこすと
dp [1] = 0
1.upto(dp.size-1) do |i|
  min = a[i][:e].map{|x| dp[x[0]] >= (10**9 + 1) ? nil : dp[x[0]] + x[1] }.compact.min
  dp[i] = min if min
end
# p dp

# p '--'
# pp b
# pp dp.zip(b).map{|d,bb|d+bb}

dpr = Array.new(n+1){(10**9 + 1)} # i~-1までのコスト
dpr[-1] = 0

(dpr.size-1).downto(1) do |i|
  min = a[i][:e2].map{|x| dpr[x[0]] >= (10**9 + 1) ? nil : dpr[x[0]] + x[1] }.compact.min
  dpr[i] = min if min
end
# p dpr

# p '-----'




# if a[-1][:e].empty?# || a[-1][:e].select{|ee|dp[ee[0]] != 999}.empty?
#   p -1
#   exit
# end

xxx = dp.zip([(10**9 + 1)] + dpr[0..-1]).map{|s,t|s+t}
# pp xxx
min = xxx.min
if min >= (10**9 + 1)
  p -1
  exit
else
  p min
end

# pp dp.zip([999] + dpr[0..-1]).map{|s,t|s+t}.min

# 5 -1 28