#include <bits/stdc++.h>
#define int long long
#define inf 100000000000000000
#define f first
#define s second
using namespace std;
int32_t main(){
	// freopen("input.txt", "r", stdin);
	// freopen("output.txt", "w", stdout);
	int n,m;
	cin >> n >> m;
	pair <pair<int,int>,int> v[m];
	for(int i=0;i<m;++i)
		cin >> v[i].f.f >> v[i].s >> v[i].f.s ;
	sort(v,v+m);
	int d[n+1];
	for(int i=1;i<=n;i++)
		d[i]=inf;
	d[1]=0;
	set <int> s;
	s.insert(1);
	s.insert(n);
	for(int i=0;i<m;++i){
		int l=v[i].f.f,r=v[i].s,c=v[i].f.s;
		set <int> :: iterator itl,itr,t;
		itr=s.lower_bound(r);
		itl=s.lower_bound(l);
		int x=d[*itl]+c;
		if(x>=d[*itr])
			continue;
		t=--itr;
		while(d[*t]>=x){
			if(t==s.begin()){
				s.erase(t);
				break;
			}
			t--;
			s.erase(itr);
			itr=t;
		}
		s.insert(r);
		d[r]=x;
	}
	// for(int i=1;i<=n;i++)
	// 	cout << d[i] << " ";
	if(d[n]==inf)
		d[n]=-1;
	cout << d[n] << endl;
}
### Prompt

Create a solution in cpp for the following problem:

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.

Examples

Input

4 3
1 3 2
2 4 3
1 4 6


Output

5


Input

4 2
1 2 1
3 4 2


Output

-1


Input

10 7
1 5 18
3 4 8
1 3 5
4 7 10
5 9 8
6 10 5
8 10 3


Output

28

### Response

```cpp
#include <bits/stdc++.h>
#define int long long
#define inf 100000000000000000
#define f first
#define s second
using namespace std;
int32_t main(){
	// freopen("input.txt", "r", stdin);
	// freopen("output.txt", "w", stdout);
	int n,m;
	cin >> n >> m;
	pair <pair<int,int>,int> v[m];
	for(int i=0;i<m;++i)
		cin >> v[i].f.f >> v[i].s >> v[i].f.s ;
	sort(v,v+m);
	int d[n+1];
	for(int i=1;i<=n;i++)
		d[i]=inf;
	d[1]=0;
	set <int> s;
	s.insert(1);
	s.insert(n);
	for(int i=0;i<m;++i){
		int l=v[i].f.f,r=v[i].s,c=v[i].f.s;
		set <int> :: iterator itl,itr,t;
		itr=s.lower_bound(r);
		itl=s.lower_bound(l);
		int x=d[*itl]+c;
		if(x>=d[*itr])
			continue;
		t=--itr;
		while(d[*t]>=x){
			if(t==s.begin()){
				s.erase(t);
				break;
			}
			t--;
			s.erase(itr);
			itr=t;
		}
		s.insert(r);
		d[r]=x;
	}
	// for(int i=1;i<=n;i++)
	// 	cout << d[i] << " ";
	if(d[n]==inf)
		d[n]=-1;
	cout << d[n] << endl;
}
```