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;

const int N = 1e5+7;

struct Node
{
    int l, r;
    long long c;
    friend bool operator < (const Node &x, const Node &y) {
        if (x.c != y.c) return x.c < y.c;
        return x.r > y.r;
    }
} a[N];

int n, m;
long long dis[N];
set<Node> s;

bool cmpl(const Node &x, const Node &y) { return x.l < y.l; }

int main()
{
    cin >> n >> m;
    for (int i = 1; i <= m; ++i) {
        cin >> a[i].l >> a[i].r >> a[i].c;
    }
    sort(a+1, a+m+1, cmpl);
    memset(dis, -1, sizeof dis);
    dis[1] = 0;
    for (int i = 1, p = 1; i <= n; ++i) {
        while (s.size() && s.begin()->r < i) s.erase(s.begin());
        if (i > 1) {
            if (s.empty()) break;
            dis[i] = s.begin()->c;
        }
        for ( ;p <= m && a[p].l <= i; ++p) {
            a[p].c += dis[i];
            while (s.size() && s.rbegin()->c >= a[p].c && s.rbegin()->r <= a[p].r)
                s.erase((--s.end()));
            if (s.size() && s.rbegin()-> c <= a[p].c && s.rbegin()->r >= a[p].r)
                continue;
            s.insert(a[p]);
        }
    }
    cout << dis[n] << endl;
    return 0;
}