#include<cstdio>
#include<algorithm>
#define int long long
const int N=1003,S=20003;
struct block{int w,s,v;}a[N];
inline bool Cmp(const block&a,const block&b){return a.s+a.w<b.s+b.w;}
int dp[N][S],n,ans;
signed main(){
	scanf("%lld",&n);
	for(int i=1;i<=n;i++)scanf("%lld%lld%lld",&a[i].w,&a[i].s,&a[i].v);
	std::sort(a+1,a+1+n,Cmp);
	for(int i=1;i<=n;i++)
	  for(int j=0;j<S;j++){
		dp[i][j]=dp[i-1][j];
		if(j>=a[i].w&&a[i].s>=j-a[i].w)
		  dp[i][j]=std::max(dp[i][j],dp[i-1][j-a[i].w]+a[i].v);
		if(i==n)ans=std::max(ans,dp[i][j]);
	  }
	printf("%lld",ans);
	return 0;
}
### Prompt

Please formulate 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<algorithm>
#define int long long
const int N=1003,S=20003;
struct block{int w,s,v;}a[N];
inline bool Cmp(const block&a,const block&b){return a.s+a.w<b.s+b.w;}
int dp[N][S],n,ans;
signed main(){
	scanf("%lld",&n);
	for(int i=1;i<=n;i++)scanf("%lld%lld%lld",&a[i].w,&a[i].s,&a[i].v);
	std::sort(a+1,a+1+n,Cmp);
	for(int i=1;i<=n;i++)
	  for(int j=0;j<S;j++){
		dp[i][j]=dp[i-1][j];
		if(j>=a[i].w&&a[i].s>=j-a[i].w)
		  dp[i][j]=std::max(dp[i][j],dp[i-1][j-a[i].w]+a[i].v);
		if(i==n)ans=std::max(ans,dp[i][j]);
	  }
	printf("%lld",ans);
	return 0;
}
```