#include<bits/stdc++.h>
using namespace std;
using ll=long long;
ll mod=1e9+7;
ll dp[1007][10009];
vector<vector<ll>> box;
vector<ll> v;
ll solve(int i,int w)
{
  if(i==0)
    return (w<=box[i][1])?box[i][2]:0;//w<=s[i]
  if(dp[i][w]!=-1)
    return dp[i][w];
  ll ans=solve(i-1,w);
  if(box[i][1]>=w)
    ans=max(ans,box[i][2]+((w+box[i][0]<=10000)?(solve(i-1,w+box[i][0])):0));
  return dp[i][w]=ans;
}
bool cmp(vector<ll>& a,vector<ll>& b)
{
  return (a[0]+a[1])>(b[0]+b[1]);
}
int main()
{
  memset(dp,-1,sizeof(dp));
  int n;
  cin>>n;
  box.resize(n,vector<ll>(3));// w and s
  for(int i=0;i<n;i++)
    cin>>box[i][0]>>box[i][1]>>box[i][2];
  sort(box.begin(),box.end(),cmp);
  cout<<solve(n-1,0)<<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>
using namespace std;
using ll=long long;
ll mod=1e9+7;
ll dp[1007][10009];
vector<vector<ll>> box;
vector<ll> v;
ll solve(int i,int w)
{
  if(i==0)
    return (w<=box[i][1])?box[i][2]:0;//w<=s[i]
  if(dp[i][w]!=-1)
    return dp[i][w];
  ll ans=solve(i-1,w);
  if(box[i][1]>=w)
    ans=max(ans,box[i][2]+((w+box[i][0]<=10000)?(solve(i-1,w+box[i][0])):0));
  return dp[i][w]=ans;
}
bool cmp(vector<ll>& a,vector<ll>& b)
{
  return (a[0]+a[1])>(b[0]+b[1]);
}
int main()
{
  memset(dp,-1,sizeof(dp));
  int n;
  cin>>n;
  box.resize(n,vector<ll>(3));// w and s
  for(int i=0;i<n;i++)
    cin>>box[i][0]>>box[i][1]>>box[i][2];
  sort(box.begin(),box.end(),cmp);
  cout<<solve(n-1,0)<<endl;
  return 0;
}

```