#include <bits/stdc++.h>

using namespace std;

struct trio{
    int wt, sz, v;
    bool operator <(const trio &t) const{
        return sz+wt < t.sz+t.wt;
    }
};

int N;
trio arr[1005];
long long dp[30005];

int main(){
    cin >> N;
    for(int i = 1; i<=N; i++){
        cin >> arr[i].wt >> arr[i].sz >> arr[i].v;
    }
    sort(arr+1, arr+N+1);
    long long ans = 0;
    for(int i = 1; i<=N; i++){
        for(int j = arr[i].sz; j>=0; j--){
            dp[j+arr[i].wt] = max(dp[j+arr[i].wt], dp[j]+arr[i].v);
            ans = max(dp[j+arr[i].wt], ans);
        }
    }
    cout << ans << endl;
}

### 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;

struct trio{
    int wt, sz, v;
    bool operator <(const trio &t) const{
        return sz+wt < t.sz+t.wt;
    }
};

int N;
trio arr[1005];
long long dp[30005];

int main(){
    cin >> N;
    for(int i = 1; i<=N; i++){
        cin >> arr[i].wt >> arr[i].sz >> arr[i].v;
    }
    sort(arr+1, arr+N+1);
    long long ans = 0;
    for(int i = 1; i<=N; i++){
        for(int j = arr[i].sz; j>=0; j--){
            dp[j+arr[i].wt] = max(dp[j+arr[i].wt], dp[j]+arr[i].v);
            ans = max(dp[j+arr[i].wt], ans);
        }
    }
    cout << ans << endl;
}

```