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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
#define rep(i,j,n) for(int i=(int)(j);i<(int)(n);i++)
#define REP(i,j,n) for(int i=(int)(j);i<=(int)(n);i++)
#define MOD 1000000007
#define int long long
#define ALL(a) (a).begin(),(a).end()
#define vi vector<int>
#define vii vector<vi>
#define pii pair<int,int>
#define priq priority_queue<int>
#define disup(A,key) distance(A.begin(),upper_bound(ALL(A),(int)(key)))
#define dislow(A,key) distance(A.begin(),lower_bound(ALL(A),(int)(key)))
#define tii tuple<int,int,int>
#define Priq priority_queue<int,vi,greater<int>>
#define pb push_back
#define mp make_pair
#define INF (1ll<<60)
signed main(){
  int N,M; cin>>N>>M;
  vector<pair<pii,int>> A(M);
  rep(i,0,M) cin>>A[i].first.first>>A[i].first.second>>A[i].second;
  sort(ALL(A));
  vi dp(N+1,-1);
  dp[1]=0;
  priority_queue<pii,vector<pii>,greater<pii>> Q;
  int memo=0;
  REP(i,1,N){
    for(memo;memo<M;memo++){
      if(A[memo].first.first>i) break;
      Q.push(mp(A[memo].first.second,A[memo].second));
    }
    while(Q.size()>0){
      int X=Q.top().first;
      if(X>i) break;
      Q.pop();
    }
    if(dp[i]!=-1){
      queue<pii> q;
      rep(i,0,Q.size()){
        q.push(Q.top());
        int X=Q.top().first,Y=Q.top().second;
        Q.pop();
        if(dp[X]==-1) dp[X]=Y+dp[i];
        else dp[X]=min(dp[X],Y+dp[i]);
      }
      while(q.size()>0){
        Q.push(q.front());
        q.pop();
      }
    }
  }
  cout<<dp[N]<<endl;
  }