#include <bits/stdc++.h>
#define rep(i,n) for(int i = 0; i < (n); ++i)
#define srep(i,s,t) for (int i = s; i < t; ++i)
#define drep(i,n) for(int i = (n)-1; i >= 0; --i)
using namespace std;
typedef long long int ll;
typedef pair<int,int> P;
#define yn {puts("Yes");}else{puts("No");}
#define MAX_N 200005

int main() {
    ll n;
    cin >> n;
    vector<vector<ll>> a;
    rep(i,n){
        vector<ll> b(4);
        cin >> b[1] >> b[2] >> b[3];
        b[0] = b[1] + b[2];
        a.push_back(b);
    }
    sort(a.begin(), a.end());

    ll dp[20005] = {};
    ll ans = 0;
    rep(i,n){
        vector<ll> b = a[i];
        ll w = b[1], s = b[2], v = b[3];
        drep(j,s+1){
            dp[j+w] = max(dp[j+w], dp[j] + v);
            ans = max(ans, dp[j+w]);
        }
    }

    cout << ans << endl;
    return 0;
}



### 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
#include <bits/stdc++.h>
#define rep(i,n) for(int i = 0; i < (n); ++i)
#define srep(i,s,t) for (int i = s; i < t; ++i)
#define drep(i,n) for(int i = (n)-1; i >= 0; --i)
using namespace std;
typedef long long int ll;
typedef pair<int,int> P;
#define yn {puts("Yes");}else{puts("No");}
#define MAX_N 200005

int main() {
    ll n;
    cin >> n;
    vector<vector<ll>> a;
    rep(i,n){
        vector<ll> b(4);
        cin >> b[1] >> b[2] >> b[3];
        b[0] = b[1] + b[2];
        a.push_back(b);
    }
    sort(a.begin(), a.end());

    ll dp[20005] = {};
    ll ans = 0;
    rep(i,n){
        vector<ll> b = a[i];
        ll w = b[1], s = b[2], v = b[3];
        drep(j,s+1){
            dp[j+w] = max(dp[j+w], dp[j] + v);
            ans = max(ans, dp[j+w]);
        }
    }

    cout << ans << endl;
    return 0;
}



```