#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
const ll MOD = 1e9 + 7;
const double PI = 3.141592653589793238;
const double EPS = 1e-10;
typedef pair<int, int> P;
ll dp[2][20001];
ll w[1000], s[1000], v[1000];
int main() {
	int N;
	cin >> N;
	vector<P> vec;
	for (int i = 0; i < N; i++) {
		cin >> w[i] >> s[i] >> v[i];
		vec.emplace_back(w[i] + s[i], i);
	}
	sort(vec.begin(), vec.end());
	dp[0][w[vec[0].second]] = v[vec[0].second];
	for (int i = 0; i + 1 < N; i++) {
		int x = vec[i + 1].second;
		for (int j = 0; j <= 20000; j++) dp[(i + 1) & 1][j] = dp[i & 1][j];
		for (int j = 0; j <= s[x]; j++) {
			dp[(i + 1) & 1][j + w[x]] = max(dp[(i + 1) & 1][j + w[x]], dp[i & 1][j] + v[x]);
		}
	}
	ll ans = 0;
	for (int i = 0; i <= 20000; i++) ans = max(ans, dp[(N - 1) & 1][i]);
	cout << ans << endl;
}
### 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 ll MOD = 1e9 + 7;
const double PI = 3.141592653589793238;
const double EPS = 1e-10;
typedef pair<int, int> P;
ll dp[2][20001];
ll w[1000], s[1000], v[1000];
int main() {
	int N;
	cin >> N;
	vector<P> vec;
	for (int i = 0; i < N; i++) {
		cin >> w[i] >> s[i] >> v[i];
		vec.emplace_back(w[i] + s[i], i);
	}
	sort(vec.begin(), vec.end());
	dp[0][w[vec[0].second]] = v[vec[0].second];
	for (int i = 0; i + 1 < N; i++) {
		int x = vec[i + 1].second;
		for (int j = 0; j <= 20000; j++) dp[(i + 1) & 1][j] = dp[i & 1][j];
		for (int j = 0; j <= s[x]; j++) {
			dp[(i + 1) & 1][j + w[x]] = max(dp[(i + 1) & 1][j + w[x]], dp[i & 1][j] + v[x]);
		}
	}
	ll ans = 0;
	for (int i = 0; i <= 20000; i++) ans = max(ans, dp[(N - 1) & 1][i]);
	cout << ans << endl;
}
```