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,n) for(int i=0;i<(n);i++)
typedef long long ll;
typedef pair<int, ll> P;
#define MOD 998244353
ll gcd(ll a, ll b) {
    return (b==0) ? a : gcd(b, a%b);
}

int main() {

    int n, m;cin >> n >> m;
    /// firstがto secondがcost
    const ll INF = 1001001001;
    struct Edge {int to; ll cost;};
    ll d[n];
    vector<Edge> g[n];

    rep(i,m) {
        ll l, r, c; cin >> l >> r >> c;
        for (int s=l;s<=r-1;s++) {
            for (int t=l+1;t<=r;t++) {
                Edge edge1 = {t-1, c};
                g[s-1].push_back(edge1);
                Edge edge2 = {s-1, c};
                g[t-1].push_back(edge2);
            }
        }
    }

    priority_queue<P, vector<P>, greater<P>> pq;
    fill(d, d + n, INF);
    d[0] = 0;
    pq.push(P(0, 0));

    while(! pq.empty()){
        P p = pq.top(); pq.pop();
        int v = p.second;
        if (d[v] < p.first) continue;
        rep(i, g[v].size()) {
            auto e = g[v][i];
            if (d[e.to] > d[v] + e.cost) {
                d[e.to] = d[v] + e.cost;
                pq.push(P(d[e.to], e.to));
            }
        }
    }

    ll ans = d[n-1];
    if (ans == INF) ans = -1;
    cout << ans << endl;
}