#include<bits/stdc++.h>
using namespace std;
struct inp{
	int w,s;
	long long v;
	inline bool operator <(const inp &a) const{
		return min(s-a.w,a.s)>min(a.s-w,s);
	}
}a[1005];
long long dp[1005][10005];
int main(){
	int n;
	cin>>n;
	for(int i=0;i<n;i++){
		scanf("%d %d %lld",&a[i].w,&a[i].s,&a[i].v);
	}
	sort(a,a+n);
	for(int i=0;i<n;i++){
		for(int j=1;j<n;j++){
			dp[i][j]=-1e18;
		}
	}
	long long ma=0;
	dp[0][a[0].s]=a[0].v;
	ma=max(a[0].v,ma);
	for(int i=1;i<n;i++){
		for(int j=0;j<=10000;j++) dp[i][j]=dp[i-1][j];
		dp[i][a[i].s]=max(dp[i][a[i].s],a[i].v);
		for(int j=a[i].w;j<=10000;j++){
			dp[i][min(a[i].s,j-a[i].w)]=max(dp[i][min(a[i].s,j-a[i].w)],dp[i-1][j]+a[i].v);
		}
		for(int j=0;j<=10000;j++) ma=max(ma,dp[i][j]);
	}
	cout<<ma;
}
### 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;
struct inp{
	int w,s;
	long long v;
	inline bool operator <(const inp &a) const{
		return min(s-a.w,a.s)>min(a.s-w,s);
	}
}a[1005];
long long dp[1005][10005];
int main(){
	int n;
	cin>>n;
	for(int i=0;i<n;i++){
		scanf("%d %d %lld",&a[i].w,&a[i].s,&a[i].v);
	}
	sort(a,a+n);
	for(int i=0;i<n;i++){
		for(int j=1;j<n;j++){
			dp[i][j]=-1e18;
		}
	}
	long long ma=0;
	dp[0][a[0].s]=a[0].v;
	ma=max(a[0].v,ma);
	for(int i=1;i<n;i++){
		for(int j=0;j<=10000;j++) dp[i][j]=dp[i-1][j];
		dp[i][a[i].s]=max(dp[i][a[i].s],a[i].v);
		for(int j=a[i].w;j<=10000;j++){
			dp[i][min(a[i].s,j-a[i].w)]=max(dp[i][min(a[i].s,j-a[i].w)],dp[i-1][j]+a[i].v);
		}
		for(int j=0;j<=10000;j++) ma=max(ma,dp[i][j]);
	}
	cout<<ma;
}
```