// failed to generate code

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

long long dp[20001];

int main(){
    ios::sync_with_stdio(false);
    int n;
    cin >> n;
    vector< tuple<int,int,int> > itms;
    for(int i = 0 ; i < n ; i++){
        int w,s,v;
        cin >> w >> s >> v;
        itms.emplace_back(w + s , s, v);
    }
    sort(itms.begin(), itms.end());
    for(int i = 0 ; i < n ; i++){
        int w,s,v;
        tie(w,s,v) = itms[i];
        w -= s;

        for(int j = s + w ; j >= w ; j--){
            dp[j] = max(dp[j], dp[j - w] + v);
        }
    }
    cout << *max_element(dp, dp + 20001) << endl;
}

### Prompt

Generate 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
// failed to generate code

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

long long dp[20001];

int main(){
    ios::sync_with_stdio(false);
    int n;
    cin >> n;
    vector< tuple<int,int,int> > itms;
    for(int i = 0 ; i < n ; i++){
        int w,s,v;
        cin >> w >> s >> v;
        itms.emplace_back(w + s , s, v);
    }
    sort(itms.begin(), itms.end());
    for(int i = 0 ; i < n ; i++){
        int w,s,v;
        tie(w,s,v) = itms[i];
        w -= s;

        for(int j = s + w ; j >= w ; j--){
            dp[j] = max(dp[j], dp[j - w] + v);
        }
    }
    cout << *max_element(dp, dp + 20001) << endl;
}

```