#include <iostream>
#include <vector>
#include <map>
#include <algorithm>
using namespace std;

long long dp[1111][22222];

int main(){
    int N;
    cin >> N;
    vector<tuple<int, int, int, int>> A(N);
    for(int i=0; i<N; i++){
        int w, s, v;
        cin >> w >> s >> v;
        A[i] = make_tuple(w+s, w, s, v);
    }
    sort(A.begin(), A.end());

    for(int i=0; i<N; i++){
        int ws, w, s, v;
        tie(ws, w, s, v) = A[i];

        for(int j=0; j<22222; j++)
            dp[i+1][j] = dp[i][j];

        for(int j=0; j<=s; j++){
            if(j+w >= 22222) continue;
            dp[i+1][j+w] = max(dp[i+1][j+w], dp[i][j] + v);
        }
    }
    long long ans = 0;
    for(int i=0; i<22222; i++)
        ans = max(ans, dp[N][i]);
    cout << ans << endl;
    return 0;
}
### Prompt

In Cpp, your task is to solve 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
#include <iostream>
#include <vector>
#include <map>
#include <algorithm>
using namespace std;

long long dp[1111][22222];

int main(){
    int N;
    cin >> N;
    vector<tuple<int, int, int, int>> A(N);
    for(int i=0; i<N; i++){
        int w, s, v;
        cin >> w >> s >> v;
        A[i] = make_tuple(w+s, w, s, v);
    }
    sort(A.begin(), A.end());

    for(int i=0; i<N; i++){
        int ws, w, s, v;
        tie(ws, w, s, v) = A[i];

        for(int j=0; j<22222; j++)
            dp[i+1][j] = dp[i][j];

        for(int j=0; j<=s; j++){
            if(j+w >= 22222) continue;
            dp[i+1][j+w] = max(dp[i+1][j+w], dp[i][j] + v);
        }
    }
    long long ans = 0;
    for(int i=0; i<22222; i++)
        ans = max(ans, dp[N][i]);
    cout << ans << endl;
    return 0;
}
```