#include <stdio.h>
#include <algorithm>
#include <string>
#include <vector>
using namespace std;

struct block{
	int w,s,v;
	bool operator <(const block &t)const{
		return w + s < t.w + t.s;
	}
}B[1010];

long long V[20101]; int N;

int main()
{
	scanf ("%d",&N);
	for (int i=0;i<N;i++) scanf ("%d %d %d",&B[i].w,&B[i].s,&B[i].v);
	sort(B,B+N);

	for (int i=0;i<N;i++){
		for (int j=B[i].s;j>=0;j--){
			if (V[j+B[i].w] < V[j] + B[i].v)
				V[j+B[i].w] = V[j] + B[i].v;
		}
	}

	long long A = 0;
	for (int i=0;i<20101;i++) if (A < V[i]) A = V[i];
	printf ("%lld\n",A);
	return 0;
}

### Prompt

Generate 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 <stdio.h>
#include <algorithm>
#include <string>
#include <vector>
using namespace std;

struct block{
	int w,s,v;
	bool operator <(const block &t)const{
		return w + s < t.w + t.s;
	}
}B[1010];

long long V[20101]; int N;

int main()
{
	scanf ("%d",&N);
	for (int i=0;i<N;i++) scanf ("%d %d %d",&B[i].w,&B[i].s,&B[i].v);
	sort(B,B+N);

	for (int i=0;i<N;i++){
		for (int j=B[i].s;j>=0;j--){
			if (V[j+B[i].w] < V[j] + B[i].v)
				V[j+B[i].w] = V[j] + B[i].v;
		}
	}

	long long A = 0;
	for (int i=0;i<20101;i++) if (A < V[i]) A = V[i];
	printf ("%lld\n",A);
	return 0;
}

```