#include <iostream>
#include <vector>
#include <algorithm>
#define llint long long

using namespace std;

struct block{
	llint w, s, v;
	block(){};
	bool operator<(const block &obj)const{
		return w+s < obj.w+obj.s;
	}
};

llint n;
block b[1005];
llint dp[1005][20005];

int main(void)
{
	cin >> n;
	for(int i = 1; i <= n; i++){
		cin >> b[i].w >> b[i].s >> b[i].v;
	}
	sort(b+1, b+n+1);
	
	for(int i = 1; i <= n; i++){
		for(int j = 0; j < 20005; j++){
			dp[i][j] = dp[i-1][j];
			if(j-b[i].w >= 0 && b[i].s >= j-b[i].w){
				dp[i][j] = max(dp[i][j], dp[i-1][j-b[i].w] + b[i].v);
			}
		}
	}
	
	llint ans = 0;
	for(int i = 0; i < 20005; i++) ans = max(ans, dp[n][i]);
	cout << ans << endl;
	
	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 <iostream>
#include <vector>
#include <algorithm>
#define llint long long

using namespace std;

struct block{
	llint w, s, v;
	block(){};
	bool operator<(const block &obj)const{
		return w+s < obj.w+obj.s;
	}
};

llint n;
block b[1005];
llint dp[1005][20005];

int main(void)
{
	cin >> n;
	for(int i = 1; i <= n; i++){
		cin >> b[i].w >> b[i].s >> b[i].v;
	}
	sort(b+1, b+n+1);
	
	for(int i = 1; i <= n; i++){
		for(int j = 0; j < 20005; j++){
			dp[i][j] = dp[i-1][j];
			if(j-b[i].w >= 0 && b[i].s >= j-b[i].w){
				dp[i][j] = max(dp[i][j], dp[i-1][j-b[i].w] + b[i].v);
			}
		}
	}
	
	llint ans = 0;
	for(int i = 0; i < 20005; i++) ans = max(ans, dp[n][i]);
	cout << ans << endl;
	
	return 0;
}
```