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;

class Edge {
  public:
    int from;
    int to;
    int cost;
    Edge(int _from, int _to, int _cost) {
      from = _from;
      to = _to;
      cost = _cost;
    }
};

bool has_smaller_from(const Edge& a, const Edge& b)
{
  return a.from < b.from;
}

int main()
{
  int nnode, nedge;
  cin >> nnode >> nedge;
  vector<Edge> edge;
  for (int i = 0; i < nedge; i++) {
    int from, to, cost;
    cin >> from >> to >> cost;
    edge.emplace_back(from, to, cost);
  }
  sort(edge.begin(), edge.end(), has_smaller_from);
  map<int, int> d;
  d[1] = 0;
  for (const auto& e : edge) {
    auto it = d.lower_bound(e.from);
    if (it == d.end()) {
      cout << "-1\n";
      return 0;
    }
    int cost = it->second + e.cost;
    vector<decltype(it)> to_be_erased;
    for (it = next(it, 1); it != d.end(); it++) {
      if (e.to < it->first) {
        break;
      }
      if (it->second < cost) {
        break;
      }
      to_be_erased.push_back(it);
    }
    for (auto i : to_be_erased) {
      d.erase(i);
    }
    if (it == d.end()) {
      d[e.to] = cost;
    } else {
      auto iter = d.find(e.to);
      if (iter == d.end()) {
        d[e.to] = cost;
      } else {
        d[e.to] = min(d[e.to], cost);
      }
    }
  }
  auto it = d.find(nnode);
  if (it == d.end()) {
    cout << "-1\n";
  } else {
    cout << it->second << '\n';
  }
  return 0;
}