#include<bits/stdc++.h>
using namespace std;
#define ll long long
const int maxn=1e3+5;
const int maxval=2e4+5;
int w[maxn],s[maxn],arr[maxn];
ll v[maxn];
bool Less1(int a,int b)
{
	return s[a]+w[a]<s[b]+w[b];
}
ll maxx[maxn][maxval];
void fl()
{
	freopen(".in","r",stdin);
	freopen(".out","w",stdout);
}
int main()
{
//    fl();
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d%d%lld",&w[i],&s[i],&v[i]);
		arr[i]=i;
	}
	sort(arr+1,arr+n+1,Less1);
	for(int i=1;i<=n;i++)
		for(int j=0;j<=20000;j++)
		{
			maxx[i][j]=maxx[i-1][j];
			if(j>=w[arr[i]]&&j-w[arr[i]]<=s[arr[i]])
				maxx[i][j]=max(maxx[i][j],maxx[i-1][j-w[arr[i]]]+v[arr[i]]);
		}
	ll ans=0;
	for(int j=0;j<=20000;j++)
		ans=max(ans,maxx[n][j]);
	printf("%lld\n",ans);
	return 0;
}

### Prompt

Create a solution in CPP for 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 maxn=1e3+5;
const int maxval=2e4+5;
int w[maxn],s[maxn],arr[maxn];
ll v[maxn];
bool Less1(int a,int b)
{
	return s[a]+w[a]<s[b]+w[b];
}
ll maxx[maxn][maxval];
void fl()
{
	freopen(".in","r",stdin);
	freopen(".out","w",stdout);
}
int main()
{
//    fl();
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d%d%lld",&w[i],&s[i],&v[i]);
		arr[i]=i;
	}
	sort(arr+1,arr+n+1,Less1);
	for(int i=1;i<=n;i++)
		for(int j=0;j<=20000;j++)
		{
			maxx[i][j]=maxx[i-1][j];
			if(j>=w[arr[i]]&&j-w[arr[i]]<=s[arr[i]])
				maxx[i][j]=max(maxx[i][j],maxx[i-1][j-w[arr[i]]]+v[arr[i]]);
		}
	ll ans=0;
	for(int j=0;j<=20000;j++)
		ans=max(ans,maxx[n][j]);
	printf("%lld\n",ans);
	return 0;
}

```