#include <bits/stdc++.h>

using namespace std;

#define ll long long
ll input(){
	ll x=0,f=0;char ch=getchar();
	while(ch<'0'||ch>'9') f|=ch=='-',ch=getchar();
	while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
	return f? -x:x;
}

const int N=1e4+7;

ll dp[N];
struct node{
	ll w,s,v;
}a[1007];

bool cmp(node a,node b){
	return a.s-b.w>b.s-a.w;
}

int main(){
	int n=input();
	for(int i=1;i<=n;i++){
		a[i].w=input(),a[i].s=input(),a[i].v=input();
	}

	sort(a+1,a+1+n,cmp);

	for(int i=1;i<=n;i++){
		for(int j=a[i].w;j<=10000;j++)
			dp[min(j-a[i].w,a[i].s)]=max(dp[min(j-a[i].w,a[i].s)],dp[j]+a[i].v);
		dp[a[i].s]=max(dp[a[i].s],a[i].v);
	}
	ll Ans=0;
	for(int i=0;i<=10000;i++) Ans=max(Ans,dp[i]);
	printf("%lld\n",Ans);
}
### Prompt

Construct a CPP code solution to the problem outlined:

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
ll input(){
	ll x=0,f=0;char ch=getchar();
	while(ch<'0'||ch>'9') f|=ch=='-',ch=getchar();
	while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
	return f? -x:x;
}

const int N=1e4+7;

ll dp[N];
struct node{
	ll w,s,v;
}a[1007];

bool cmp(node a,node b){
	return a.s-b.w>b.s-a.w;
}

int main(){
	int n=input();
	for(int i=1;i<=n;i++){
		a[i].w=input(),a[i].s=input(),a[i].v=input();
	}

	sort(a+1,a+1+n,cmp);

	for(int i=1;i<=n;i++){
		for(int j=a[i].w;j<=10000;j++)
			dp[min(j-a[i].w,a[i].s)]=max(dp[min(j-a[i].w,a[i].s)],dp[j]+a[i].v);
		dp[a[i].s]=max(dp[a[i].s],a[i].v);
	}
	ll Ans=0;
	for(int i=0;i<=10000;i++) Ans=max(Ans,dp[i]);
	printf("%lld\n",Ans);
}
```