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: Time Limit Exceeded)

#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
using namespace std;
#define ll long long
#define rep(i,n) for(int i=0;i<(n);i++)
#define repp(i,n) for(int i=1;i<=n;i++)
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}
typedef pair<int,ll> P;
const int MAX=100100;
const ll INF=1001001001001001;

struct edge{
    int to;
    ll cost;
};

int main(){
    int v,n;
    cin >> v >> n;
    ll d[v];
    vector<edge> G[v];
    rep(i,n){
        int a,b;
        ll c;
        cin >> a >> b >> c;
        a--; b--;
        for(int j=a;j<=b;j++){
            for(int k=j;k<=b;k++){
                edge e = {k,c};
                G[j].push_back(e);
            }
        }
    }
    priority_queue<P,vector<P>,greater<P>> pq;
    rep(i,v) d[i]=INF;
    d[0]=0;
    pq.push(P(0,0));
    while(!pq.empty()){
        P p=pq.top();
        pq.pop();
        ll c = p.second;
        if(d[c]<p.first) continue;
        rep(i,G[c].size()){
            edge e = G[c][i];
            if(d[e.to] > d[c]+e.cost){
                d[e.to] = d[c] + e.cost;
                pq.push(P(d[e.to],e.to));
            }
        }
    }
    if(d[v-1]!=INF) cout << d[v-1] << endl;
    else cout << -1 << endl;
}