#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<ll> vec;
typedef vector<vec> mat;
typedef pair<ll,ll> pll;
const ll mod=1e9+7;
//const ll mod=998244353;
const ll inf=1LL<<61;

int main() {
  ll n;
  cin >> n;
  vec w(n),s(n),v(n);
  vector<pll> a(n);
  for(ll i=0;i<n;i++) {
    cin >> w[i] >> s[i] >> v[i];
    a[i]={w[i]+s[i],i};
  }
  sort(a.begin(),a.end());
  mat dp(n+1,vec(2e4+10));
  for(ll i=0;i<n;i++) {
    ll idx=a[i].second;
    for(ll j=0;j<=2e4;j++) {
      dp[i+1][j]=max(dp[i+1][j],dp[i][j]);
      if(j) dp[i+1][j]=max(dp[i+1][j],dp[i+1][j-1]);
      if(j<=s[idx]&&j+w[idx]<=2e4) {
        dp[i+1][j+w[idx]]=max(dp[i+1][j+w[idx]],dp[i][j]+v[idx]);
      }
    }
  }
  cout << dp[n][2e4] << 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
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<ll> vec;
typedef vector<vec> mat;
typedef pair<ll,ll> pll;
const ll mod=1e9+7;
//const ll mod=998244353;
const ll inf=1LL<<61;

int main() {
  ll n;
  cin >> n;
  vec w(n),s(n),v(n);
  vector<pll> a(n);
  for(ll i=0;i<n;i++) {
    cin >> w[i] >> s[i] >> v[i];
    a[i]={w[i]+s[i],i};
  }
  sort(a.begin(),a.end());
  mat dp(n+1,vec(2e4+10));
  for(ll i=0;i<n;i++) {
    ll idx=a[i].second;
    for(ll j=0;j<=2e4;j++) {
      dp[i+1][j]=max(dp[i+1][j],dp[i][j]);
      if(j) dp[i+1][j]=max(dp[i+1][j],dp[i+1][j-1]);
      if(j<=s[idx]&&j+w[idx]<=2e4) {
        dp[i+1][j+w[idx]]=max(dp[i+1][j+w[idx]],dp[i][j]+v[idx]);
      }
    }
  }
  cout << dp[n][2e4] << endl;
}
```