#include <bits/stdc++.h>
using namespace std;
#define int long long
typedef long long ll;
 
struct block {
    int w, s, v;
};
 
bool cmp(const block &x, const block &y) {
    return x.w + x.s > y.w + y.s;
}
 
const int N = 2e4+10;
int memo[N];
 
signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int n;
    cin >> n;
    vector<block> arr(n);
    for(int i = 0; i < n; ++i) {
        cin >> arr[i].w >> arr[i].s >> arr[i].v;
    }
    sort(arr.begin(), arr.end(), cmp);
    int res = 0;
    for(int i = 0; i < n; ++i) {
        for(int j = 0; j < N; ++j) {
            if(j <= arr[i].s) {
                memo[j] = max(memo[j], arr[i].v + memo[j+arr[i].w]);
                res = max(res, memo[j]);
            }
        }
    }
    cout << res << '\n';
}
 
 
 
 
 
### Prompt

Develop a solution in CPP 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;
#define int long long
typedef long long ll;
 
struct block {
    int w, s, v;
};
 
bool cmp(const block &x, const block &y) {
    return x.w + x.s > y.w + y.s;
}
 
const int N = 2e4+10;
int memo[N];
 
signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int n;
    cin >> n;
    vector<block> arr(n);
    for(int i = 0; i < n; ++i) {
        cin >> arr[i].w >> arr[i].s >> arr[i].v;
    }
    sort(arr.begin(), arr.end(), cmp);
    int res = 0;
    for(int i = 0; i < n; ++i) {
        for(int j = 0; j < N; ++j) {
            if(j <= arr[i].s) {
                memo[j] = max(memo[j], arr[i].v + memo[j+arr[i].w]);
                res = max(res, memo[j]);
            }
        }
    }
    cout << res << '\n';
}
 
 
 
 
 
```