#include<cstdio>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N=1e3+10;
const int M=2e4+10;
int n;ll dp[N][M],ans;
struct node{int w,s,v;bool operator <(const node&e)const{return (w+s)<(e.w+e.s)||(w+s==e.w+e.s&&v>e.v);}}k[N];
int main(){
	scanf("%d",&n);
	for(register int i=1;i<=n;i++)
		scanf("%d%d%d",&k[i].w,&k[i].s,&k[i].v);
	sort(k+1,k+n+1);
	for(register int i=1;i<=n;i++){
		for(register int j=0;j<=k[i-1].s+k[i-1].w;j++)
			dp[i][j]=max(dp[i][j],dp[i-1][j]);
		for(register int j=0;j<=min(k[i].s,k[i-1].s+k[i-1].w);j++)
			dp[i][j+k[i].w]=max(dp[i][j+k[i].w],dp[i-1][j]+k[i].v);
	}
	for(register int i=1;i<=n;i++)
		for(register int j=0;j<=k[i].s+k[i].w;j++)
			ans=max(ans,dp[i][j]);
	printf("%lld\n",ans);
	return 0;
}
### Prompt

Your challenge is to write 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<cstdio>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N=1e3+10;
const int M=2e4+10;
int n;ll dp[N][M],ans;
struct node{int w,s,v;bool operator <(const node&e)const{return (w+s)<(e.w+e.s)||(w+s==e.w+e.s&&v>e.v);}}k[N];
int main(){
	scanf("%d",&n);
	for(register int i=1;i<=n;i++)
		scanf("%d%d%d",&k[i].w,&k[i].s,&k[i].v);
	sort(k+1,k+n+1);
	for(register int i=1;i<=n;i++){
		for(register int j=0;j<=k[i-1].s+k[i-1].w;j++)
			dp[i][j]=max(dp[i][j],dp[i-1][j]);
		for(register int j=0;j<=min(k[i].s,k[i-1].s+k[i-1].w);j++)
			dp[i][j+k[i].w]=max(dp[i][j+k[i].w],dp[i-1][j]+k[i].v);
	}
	for(register int i=1;i<=n;i++)
		for(register int j=0;j<=k[i].s+k[i].w;j++)
			ans=max(ans,dp[i][j]);
	printf("%lld\n",ans);
	return 0;
}
```