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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define INF 2000000000000000000
#define ll long long
using namespace std;

struct edge {ll to, cost;};
//=============dijkstra============================
vector<ll> dijkstra(ll s, ll V, vector<vector<edge>>& G)
{
  vector<ll> d(V, INF);
  typedef pair<ll, ll> P;// first は最短距離　second は頂点の番号
  priority_queue<P, vector<P>, greater<P>> que;
  d.at(s) = 0;
  que.push(P(0, s));
  while (!que.empty())
  {
    P p = que.top();
    que.pop();
    ll v = p.second;
    if (d.at(v) < p.first) continue;
    for (ll i = 0; i < G.at(v).size(); ++i)
    {
      edge e = G.at(v).at(i);
      if (d.at(e.to) > d.at(v) + e.cost)
      {
        d.at(e.to) = d.at(v) + e.cost;
        que.push(P(d.at(e.to), e.to));
      }
    }
  }
  return d;
}
//=================================================

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  ll N, M;
  cin >> N >> M;
  vector<vector<edge>> G(N);
  for (ll i = 0; i < M; ++i) {
    ll L, R, C;
    cin >> L >> R >> C;
    L -= 1;R -= 1;
    G.at(L).push_back({R, C});
  }
  for (ll i = 1; i < N - 1; ++i) {
    G.at(i + 1).push_back({i, 0});
  }
  ll ans = dijkstra(0, N, G).at(N - 1);
  if (ans == INF) {
    cout << -1 << "\n";
  }
  else {
    cout << ans << "\n";
  }
}