#include <iostream>
#include <algorithm>
#include<vector>
using namespace std;

long long int dp[21005];

int N;
int w[1003], s[1003];
long long int v[1003];

vector<pair<int, pair<int, long long int>> > V;

int main(void) {

	cin >> N;

	for (int i = 1; i <= N; i++) {
		cin >> w[i] >> s[i] >> v[i];
		V.push_back(make_pair(s[i]+w[i], make_pair(w[i], v[i])));
	}

	sort(V.begin(), V.end());

	for (int i = 1; i <= N; i++) {
		int vs = V[i - 1].first-V[i-1].second.first;
		int vw = V[i - 1].second.first;

		long long int val = V[i - 1].second.second;
		for (int W = 20000; W >= 0; W--) {
			if (dp[W] > 0 && W <= vs) { dp[W + vw] = max(dp[W + vw], dp[W] + val); }
		}
		dp[vw] = max(dp[vw], val);
	}

	long long int ans = 0;

	for (int W = 20000; W >= 0; W--) {
		ans = max(ans, dp[W]);
	}

	cout << ans << endl;

	return 0;
}
### Prompt

Please create a solution in cpp 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 <algorithm>
#include<vector>
using namespace std;

long long int dp[21005];

int N;
int w[1003], s[1003];
long long int v[1003];

vector<pair<int, pair<int, long long int>> > V;

int main(void) {

	cin >> N;

	for (int i = 1; i <= N; i++) {
		cin >> w[i] >> s[i] >> v[i];
		V.push_back(make_pair(s[i]+w[i], make_pair(w[i], v[i])));
	}

	sort(V.begin(), V.end());

	for (int i = 1; i <= N; i++) {
		int vs = V[i - 1].first-V[i-1].second.first;
		int vw = V[i - 1].second.first;

		long long int val = V[i - 1].second.second;
		for (int W = 20000; W >= 0; W--) {
			if (dp[W] > 0 && W <= vs) { dp[W + vw] = max(dp[W + vw], dp[W] + val); }
		}
		dp[vw] = max(dp[vw], val);
	}

	long long int ans = 0;

	for (int W = 20000; W >= 0; W--) {
		ans = max(ans, dp[W]);
	}

	cout << ans << endl;

	return 0;
}
```