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<bits/stdc++.h>
using namespace std;
using Int = long long;
signed main(){
    Int N,M;
    cin >> N >> M;
    using tp = tuple<Int,Int>;
    vector<vector<tp>>edge(N);
    for(Int v = 0; v + 1 < N; ++v){
        edge[v + 1].emplace_back(v,0LL);
    }
    for(int i = 0; i < M; ++i){
        Int u,v,c;
        cin >> u >> v >> c; --u; --v;
        edge[u].emplace_back(v,c);
        edge[v].emplace_back(u,c);
    }
    constexpr Int inf = (1LL << 60);
    vector<Int>d(N,inf);

    priority_queue<tp,vector<tp>,greater<>>que;
    que.emplace(0,0);
    d[0] = 0;
    while(not que.empty()) {
        auto p = que.top(); que.pop();
        Int crt,v;
        tie(crt,v) = p;
        if(crt > d[v]) continue;
        for(auto tup : edge[v]){
            
            Int nv,cost;
            tie(nv,cost) = tup;
            if(cost + crt >= d[nv]) continue;
            d[nv] = cost + crt;
            que.emplace(d[nv],nv);
        }
    }
    cout << (d.back() == inf ? -1 : d.back()) << endl;
}