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

int n,dp[20010];
pair<pair<int,int>,pair<int,int> > a[1010];  

signed main()
{
	ios::sync_with_stdio(false);
	cin>>n;
	for(int i=1;i<=n;i++){
		int w,s,v;
		cin>>w>>s>>v;
		a[i]=make_pair(make_pair(w+s,w),make_pair(s,v));
	}
	sort(a+1,a+n+1); 
	for(int i=1;i<=n;i++){
		for(int j=a[i].second.first;j>=0;j--){
			dp[j+a[i].first.second]=max(dp[j+a[i].first.second],dp[j]+a[i].second.second);
		}
	}
	int maxv=0;
	for(int j=0;j<=20000;j++) maxv=max(maxv,dp[j]);
	cout<<maxv<<endl;
	return 0;
}
### Prompt

In CPP, your task is to solve the following problem:

There are N blocks, numbered 1, 2, \ldots, N. For each i (1 \leq i \leq N), Block i has a weight of w_i, a solidness of s_i and a value of v_i.

Taro has decided to build a tower by choosing some of the N blocks and stacking them vertically in some order. Here, the tower must satisfy the following condition:

* For each Block i contained in the tower, the sum of the weights of the blocks stacked above it is not greater than s_i.



Find the maximum possible sum of the values of the blocks contained in the tower.

Constraints

* All values in input are integers.
* 1 \leq N \leq 10^3
* 1 \leq w_i, s_i \leq 10^4
* 1 \leq v_i \leq 10^9

Input

Input is given from Standard Input in the following format:


N
w_1 s_1 v_1
w_2 s_2 v_2
:
w_N s_N v_N


Output

Print the maximum possible sum of the values of the blocks contained in the tower.

Examples

Input

3
2 2 20
2 1 30
3 1 40


Output

50


Input

4
1 2 10
3 1 10
2 4 10
1 6 10


Output

40


Input

5
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000


Output

5000000000


Input

8
9 5 7
6 2 7
5 7 3
7 8 8
1 9 6
3 3 3
4 1 7
4 5 5


Output

22

### Response

```cpp
#include <bits/stdc++.h>
#define int long long
using namespace std;

int n,dp[20010];
pair<pair<int,int>,pair<int,int> > a[1010];  

signed main()
{
	ios::sync_with_stdio(false);
	cin>>n;
	for(int i=1;i<=n;i++){
		int w,s,v;
		cin>>w>>s>>v;
		a[i]=make_pair(make_pair(w+s,w),make_pair(s,v));
	}
	sort(a+1,a+n+1); 
	for(int i=1;i<=n;i++){
		for(int j=a[i].second.first;j>=0;j--){
			dp[j+a[i].first.second]=max(dp[j+a[i].first.second],dp[j]+a[i].second.second);
		}
	}
	int maxv=0;
	for(int j=0;j<=20000;j++) maxv=max(maxv,dp[j]);
	cout<<maxv<<endl;
	return 0;
}
```