#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
const int N=2e4+5,M=2e4;
ll f[N];
struct dt {
	int w,s,v;
}d[N];

int main() {
	//freopen("1.in","r",stdin);
	//freopen("1.ans","w",stdout);
	
	int n; scanf("%d",&n);
	for(int i=1;i<=n;++i) scanf("%d%d%d",&d[i].w,&d[i].s,&d[i].v);
	sort(d+1,d+n+1,[](const dt &lhs,const dt &rhs){return lhs.s+lhs.w<rhs.s+rhs.w;});
	for(int i=1;i<=n;++i) {
		for(int j=d[i].s;j>=0;--j) if(j+d[i].w<=M) f[j+d[i].w]=max(f[j+d[i].w],f[j]+d[i].v);
	}
	printf("%lld\n",*max_element(f,f+M+1));
	
	return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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;

typedef long long ll;
const int N=2e4+5,M=2e4;
ll f[N];
struct dt {
	int w,s,v;
}d[N];

int main() {
	//freopen("1.in","r",stdin);
	//freopen("1.ans","w",stdout);
	
	int n; scanf("%d",&n);
	for(int i=1;i<=n;++i) scanf("%d%d%d",&d[i].w,&d[i].s,&d[i].v);
	sort(d+1,d+n+1,[](const dt &lhs,const dt &rhs){return lhs.s+lhs.w<rhs.s+rhs.w;});
	for(int i=1;i<=n;++i) {
		for(int j=d[i].s;j>=0;--j) if(j+d[i].w<=M) f[j+d[i].w]=max(f[j+d[i].w],f[j]+d[i].v);
	}
	printf("%lld\n",*max_element(f,f+M+1));
	
	return 0;
}

```