#include <bits/stdc++.h>
using namespace std;
#define int int64_t
int dp[1005][20005];
tuple<int,int,int> arr[1005];
bool cmp(tuple<int,int,int>a,tuple<int,int,int>b)
{
	return get<0>(a)+get<1>(a)<get<0>(b)+get<1>(b);
}
signed main()
{
	int n,i,j;
	cin>>n;
	for(i=1;i<=n;i++)
	{
		int w,s,v;
		cin>>w>>s>>v;
		arr[i]=make_tuple(w,s,v);
	}
	sort(arr+1,arr+n+1,cmp);
	for(i=1;i<=n;i++)
	{
		int w,s,v;
		tie(w,s,v)=arr[i];
		for(j=1;j<=20000;j++)
		{
			dp[i][j]=max(dp[i-1][j],dp[i][j-1]);
			if(s>=j-w&&j>=w)
			{
			dp[i][j]=max(dp[i-1][j-w]+v,dp[i][j]);
		}
		}
	}
	
	cout<<dp[n][20000]<<"\n";
}
### 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>
using namespace std;
#define int int64_t
int dp[1005][20005];
tuple<int,int,int> arr[1005];
bool cmp(tuple<int,int,int>a,tuple<int,int,int>b)
{
	return get<0>(a)+get<1>(a)<get<0>(b)+get<1>(b);
}
signed main()
{
	int n,i,j;
	cin>>n;
	for(i=1;i<=n;i++)
	{
		int w,s,v;
		cin>>w>>s>>v;
		arr[i]=make_tuple(w,s,v);
	}
	sort(arr+1,arr+n+1,cmp);
	for(i=1;i<=n;i++)
	{
		int w,s,v;
		tie(w,s,v)=arr[i];
		for(j=1;j<=20000;j++)
		{
			dp[i][j]=max(dp[i-1][j],dp[i][j-1]);
			if(s>=j-w&&j>=w)
			{
			dp[i][j]=max(dp[i-1][j-w]+v,dp[i][j]);
		}
		}
	}
	
	cout<<dp[n][20000]<<"\n";
}
```