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 <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <set>
#include <map>

using namespace std;
typedef long long ll;
typedef pair<ll, ll> P_;
typedef pair<P_, ll> P;
P p[100000];


const ll INF = 1e+15;
vector<int> G[100000];

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(10) << fixed;
    int N, M;
    cin >> N >> M;
    for(int i = 0; i < M; i++){
        int l, r;
        ll c;
        cin >> l >> r >> c;
        l--; r--;
        p[i] = P(P_(l, r), c);
    }
    sort(p, p+M);
    map<int, ll> mp;
    mp[0] = 0;
    mp[N-1] = INF;
    for(int i = 0; i < M; i++){
        int l = p[i].first.first;
        int r = p[i].first.second;
        ll c = p[i].second;
        auto ptr = mp.lower_bound(l);
        auto ptrr = mp.lower_bound(r);
        if(mp.count(r) == 0){
            mp[r] = min(ptr->second+c, ptrr->second);
        }else{
            mp[r] = min(ptr->second+c, ptrr->second);
        }
        auto ptr2 = mp.find(r);
        ll tmp = mp[r];
        while(true){
            ptr2--;
            int idx = ptr2->first;
            if(ptr2->second < tmp) break;
            else mp.erase(idx); 
        }
    }
    // for(auto itr = mp.begin(); itr != mp.end(); itr++){
    //     cout << itr->first << ' ' << itr->second << endl;
    // }
    if(mp[N-1] >= INF){
        cout << -1 << endl;
    }else{
        cout << mp[N-1] << endl;
    }
}