#include<bits/stdc++.h>
using namespace std;

struct Block {
  int w, s;
  long long v;
  Block(int w, int s, int v) : w(w), s(s), v(v) {}
  bool operator<(const Block& oth) const { return w + s < oth.w + oth.s; }
};

long long dp[1<<16] = {0};
int main() {
  ios_base::sync_with_stdio(false); cin.tie(0);
  int n; cin >> n;
  vector<Block> Bs;
  for (int i = 0; i < n; ++i) {
    int w, s, v; cin >> w >> s >> v;
    Bs.emplace_back(w, s, v);
  }
  sort(Bs.begin(), Bs.end());
  for (auto B : Bs) {
    int W = B.w, s = B.s;
    for (int w = s; w >= 0; --w) {
      dp[w + W] = max(dp[w] + B.v, dp[w + W]);
    }
  }
  cout << *max_element(dp, dp + (1<<16)) << '\n';
}

### 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;

struct Block {
  int w, s;
  long long v;
  Block(int w, int s, int v) : w(w), s(s), v(v) {}
  bool operator<(const Block& oth) const { return w + s < oth.w + oth.s; }
};

long long dp[1<<16] = {0};
int main() {
  ios_base::sync_with_stdio(false); cin.tie(0);
  int n; cin >> n;
  vector<Block> Bs;
  for (int i = 0; i < n; ++i) {
    int w, s, v; cin >> w >> s >> v;
    Bs.emplace_back(w, s, v);
  }
  sort(Bs.begin(), Bs.end());
  for (auto B : Bs) {
    int W = B.w, s = B.s;
    for (int w = s; w >= 0; --w) {
      dp[w + W] = max(dp[w] + B.v, dp[w + W]);
    }
  }
  cout << *max_element(dp, dp + (1<<16)) << '\n';
}

```