/*
 *    author:  Gary Shih
 *    created: 2020-05-07 15:29:12
 */
#pragma GCC optimize("O3")
#include <bits/stdc++.h>

using namespace std;

int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.setf(ios::fixed), cout.precision(9);
  int n;
  cin >> n;
  vector<tuple<int, int, int, int>> a(n);
  for (int i = 0; i < n; ++i) {
    cin >> get<1>(a[i]) >> get<2>(a[i]) >> get<3>(a[i]);
    get<0>(a[i]) = get<1>(a[i]) + get<2>(a[i]);
  }
  sort(a.rbegin(), a.rend());
  vector<long long> dp(2e4 + 1);
  for (int i = 0; i < n; ++i) {
    int w = get<1>(a[i]), s = get<2>(a[i]), v = get<3>(a[i]);
    for (int j = 0; j <= s; ++j)
      if (j + w < (int)dp.size()) dp[j] = max(dp[j], dp[j + w] + v);
    for (int j = dp.size() - 2; j >= 0; --j) dp[j] = max(dp[j], dp[j + 1]);
  }
  cout << dp[0] << '\n';
}

### 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
/*
 *    author:  Gary Shih
 *    created: 2020-05-07 15:29:12
 */
#pragma GCC optimize("O3")
#include <bits/stdc++.h>

using namespace std;

int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.setf(ios::fixed), cout.precision(9);
  int n;
  cin >> n;
  vector<tuple<int, int, int, int>> a(n);
  for (int i = 0; i < n; ++i) {
    cin >> get<1>(a[i]) >> get<2>(a[i]) >> get<3>(a[i]);
    get<0>(a[i]) = get<1>(a[i]) + get<2>(a[i]);
  }
  sort(a.rbegin(), a.rend());
  vector<long long> dp(2e4 + 1);
  for (int i = 0; i < n; ++i) {
    int w = get<1>(a[i]), s = get<2>(a[i]), v = get<3>(a[i]);
    for (int j = 0; j <= s; ++j)
      if (j + w < (int)dp.size()) dp[j] = max(dp[j], dp[j + w] + v);
    for (int j = dp.size() - 2; j >= 0; --j) dp[j] = max(dp[j], dp[j + 1]);
  }
  cout << dp[0] << '\n';
}

```