#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
const int MM = 2e4 + 4;
int main() {
	int n;
	cin >> n;
	vector <int> w(n), s(n), v(n), p(n);
	for(int i = 0; i < n; i++) {
		cin >> w[i] >> s[i] >> v[i];
		p[i] = i;
	}
	sort(p.begin(), p.end(), [&](int i, int j) {
		return w[i] + s[i] < w[j] + s[j];
	});
	vector <ll> DP(MM, 0);
	for(int i : p) {
		vector <ll> ls = DP;
		for(int j = 0; j <= s[i]; j++) {
			if(j + w[i] < MM) {
				DP[j + w[i]] = max(DP[j + w[i]], ls[j] + v[i]);
			}
		}
	}
	cout << *max_element(DP.begin(), DP.end());
	return 0;
}
### Prompt

Please formulate 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 "bits/stdc++.h"
using namespace std;
typedef long long ll;
const int MM = 2e4 + 4;
int main() {
	int n;
	cin >> n;
	vector <int> w(n), s(n), v(n), p(n);
	for(int i = 0; i < n; i++) {
		cin >> w[i] >> s[i] >> v[i];
		p[i] = i;
	}
	sort(p.begin(), p.end(), [&](int i, int j) {
		return w[i] + s[i] < w[j] + s[j];
	});
	vector <ll> DP(MM, 0);
	for(int i : p) {
		vector <ll> ls = DP;
		for(int j = 0; j <= s[i]; j++) {
			if(j + w[i] < MM) {
				DP[j + w[i]] = max(DP[j + w[i]], ls[j] + v[i]);
			}
		}
	}
	cout << *max_element(DP.begin(), DP.end());
	return 0;
}
```