#include <bits/stdc++.h>
using namespace std;
#define ll long long
const int N=1005;
const int M=20005;
ll dp[2][M];
int c,p=1;
int v[N],w[N],s[N],id[N];
bool comp(int i, int j){ return w[i]+s[i]<w[j]+s[j];}
int main()
{
	int n,i,j,k;
	scanf("%i",&n);
	for(i=1;i<=n;i++) scanf("%i %i %i",&w[i],&s[i],&v[i]),id[i]=i;
	sort(id+1,id+1+n,comp);
	for(j=1;j<=n;j++)
	{
		i=id[j];
		for(k=M-1;~k;k--)
		{
			dp[c][k]=dp[p][k];
			if(k<=s[i]) dp[c][k+w[i]]=max(dp[c][k+w[i]],dp[p][k]+v[i]);
		}
		c^=1;p^=1;
	}
	ll ans=0;
	for(i=0;i<M;i++) ans=max(ans,dp[p][i]);
	printf("%lld\n",ans);
	return 0;
}
### Prompt

Generate a CPP solution to 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 ll long long
const int N=1005;
const int M=20005;
ll dp[2][M];
int c,p=1;
int v[N],w[N],s[N],id[N];
bool comp(int i, int j){ return w[i]+s[i]<w[j]+s[j];}
int main()
{
	int n,i,j,k;
	scanf("%i",&n);
	for(i=1;i<=n;i++) scanf("%i %i %i",&w[i],&s[i],&v[i]),id[i]=i;
	sort(id+1,id+1+n,comp);
	for(j=1;j<=n;j++)
	{
		i=id[j];
		for(k=M-1;~k;k--)
		{
			dp[c][k]=dp[p][k];
			if(k<=s[i]) dp[c][k+w[i]]=max(dp[c][k+w[i]],dp[p][k]+v[i]);
		}
		c^=1;p^=1;
	}
	ll ans=0;
	for(i=0;i<M;i++) ans=max(ans,dp[p][i]);
	printf("%lld\n",ans);
	return 0;
}
```