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: Accepted)

#include <stdio.h>
#include <algorithm>
#include <utility>
#include <functional>
#include <cstring>
#include <queue>
#include <stack>
#include <cmath>
#include <iterator>
#include <vector>
#include <string>
#include <set>
#include <iostream>
#include <random>
#include <map>
#include <iomanip>
#include <stdlib.h>
#include <list>
#include <typeinfo>
#include <list>
#include <set>
#include <cassert>
#include <fstream>
#include <unordered_map>
#include <cstdlib>
#include <complex>
#include <cctype>
#include <bitset>
using namespace std;

using ll = long long;
using vll = vector<long long>;
using pll = pair<long long, long long>;
#define rep(i,n) for(long long i(0);(i)<(n);(i)++)
ll INF = 1LL<<50;

struct edge{
    ll to;
    ll cost;
    edge(ll t, ll c){
        to = t;
        cost = c;
    }
};

//* dijkstra algorithm with adjacency list
void dijkstra(vector<vector<edge> > &G, vll &dist, ll s){
    fill(dist.begin(), dist.end(), INF);
    priority_queue<pll, vector<pll>, greater<pll> > que;
    dist[s] = 0;
    que.push(pll(0, s));
    while(!que.empty()){
        ll score = que.top().first;
        ll u = que.top().second;
        que.pop();
        for(ll i=0; i< G[u].size(); i++){
            edge e = G[u][i];
            if(dist[e.to] > score + e.cost){
                dist[e.to] = score + e.cost;
                que.push(pll(dist[e.to], e.to));
            }
        }
    }
    return;
}

void solve(long long N, long long M, std::vector<long long> L, std::vector<long long> R, std::vector<long long> C){
    vector<vector<edge> > G(N);
    rep(i, M){
        G[L[i]].push_back(edge(R[i], C[i]));
    }
    for(ll i=1; i< N; i++){
        G[i].push_back(edge(i-1, 0));
    }
    vll dist(N, INF);
    dijkstra(G, dist, 0);


    cout << (dist[N-1]>=INF? -1: dist[N-1]) << endl;
}

int main(){
    long long N;
    scanf("%lld",&N);
    long long M;
    scanf("%lld",&M);
    std::vector<long long> L(M);
    std::vector<long long> R(M);
    std::vector<long long> C(M);
    for(int i = 0 ; i < M ; i++){
        scanf("%lld",&L[i]);
        scanf("%lld",&R[i]);
        scanf("%lld",&C[i]);
        L[i]--; R[i]--;
    }
    solve(N, M, std::move(L), std::move(R), std::move(C));
    return 0;
}