#include<bits/stdc++.h>
using namespace std;
using Int = long long;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}

//INSERT ABOVE HERE
signed main(){
  Int n;
  cin>>n;
  vector<Int> w(n),s(n),v(n);
  for(Int i=0;i<n;i++) cin>>w[i]>>s[i]>>v[i];
  
  vector<Int> ord(n);
  iota(ord.begin(),ord.end(),0);
  auto cmp=[&](Int i,Int j){return w[i]+s[i]<w[j]+s[j];};
  sort(ord.begin(),ord.end(),cmp);
  
  const Int MAX = 2e4+100;
  vector<Int> dp(MAX+1,0);
  for(Int p:ord)
    for(Int j=s[p];j>=0;j--)
      chmax(dp[j+w[p]],dp[j]+v[p]);
    
  cout<<*max_element(dp.begin(),dp.end())<<endl;
  return 0;
}

### 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;
using Int = long long;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}

//INSERT ABOVE HERE
signed main(){
  Int n;
  cin>>n;
  vector<Int> w(n),s(n),v(n);
  for(Int i=0;i<n;i++) cin>>w[i]>>s[i]>>v[i];
  
  vector<Int> ord(n);
  iota(ord.begin(),ord.end(),0);
  auto cmp=[&](Int i,Int j){return w[i]+s[i]<w[j]+s[j];};
  sort(ord.begin(),ord.end(),cmp);
  
  const Int MAX = 2e4+100;
  vector<Int> dp(MAX+1,0);
  for(Int p:ord)
    for(Int j=s[p];j>=0;j--)
      chmax(dp[j+w[p]],dp[j]+v[p]);
    
  cout<<*max_element(dp.begin(),dp.end())<<endl;
  return 0;
}

```