#include <bits/stdc++.h>

int N;
long long dp[1001][10001];
std::pair<long long, int> a[1000];
int w[1000];
int s[1000];
long long v[1000];

int main(){
  
  std::cin>>N;
  for(int i=0;i<N;++i){
    std::cin>>w[i]>>s[i]>>v[i];
    a[i]={w[i]+s[i],i};
  }
  std::sort(a,a+N);
  long long ans=0;
  for(int i=0;i<N;++i){
    int pos=a[i].second;
    for(int j=0;j<=s[pos];++j){
      long long ne=std::max((i>0?dp[i-1][j]:0)+v[pos],dp[i][j+w[pos]]);
      if(j+w[pos]<=10000){
		dp[i][j+w[pos]]=ne;
      }
      ans=std::max(ans,ne);
    }
    for(int j=0;i>0&&j<=10000;++j){
      dp[i][j]=std::max(dp[i][j],dp[i-1][j]);
    }
  }
  std::cout<<ans<<std::endl;
  return 0;
}

### Prompt

Please create a solution in cpp 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>

int N;
long long dp[1001][10001];
std::pair<long long, int> a[1000];
int w[1000];
int s[1000];
long long v[1000];

int main(){
  
  std::cin>>N;
  for(int i=0;i<N;++i){
    std::cin>>w[i]>>s[i]>>v[i];
    a[i]={w[i]+s[i],i};
  }
  std::sort(a,a+N);
  long long ans=0;
  for(int i=0;i<N;++i){
    int pos=a[i].second;
    for(int j=0;j<=s[pos];++j){
      long long ne=std::max((i>0?dp[i-1][j]:0)+v[pos],dp[i][j+w[pos]]);
      if(j+w[pos]<=10000){
		dp[i][j+w[pos]]=ne;
      }
      ans=std::max(ans,ne);
    }
    for(int j=0;i>0&&j<=10000;++j){
      dp[i][j]=std::max(dp[i][j],dp[i-1][j]);
    }
  }
  std::cout<<ans<<std::endl;
  return 0;
}

```