#include <bits/stdc++.h>
#define endl "\n"
using namespace std;
typedef long long int lli;
const lli N=1e3+5;
vector<pair<pair<lli,lli>,lli>> v;
lli dp[20005];

bool cmp(const pair<pair<lli,lli>,lli> &a,const pair<pair<lli,lli>,lli> &b)
{
    return a.first.first+a.first.second < b.first.first+b.first.second;
}
int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    lli n;
    cin>>n;
    lli i,j,ans=0,w,s,va;
    
    for(i=0;i<n;i++) 
    {
        cin>>w>>s>>va;
        v.push_back({{w,s},va});
    }
    sort(v.begin(), v.end(), cmp);
    
    for(i=0;i<n;i++)
    {
        for(j=v[i].first.second;j>=0;j--)
        {
            dp[j+v[i].first.first]=max(dp[j+v[i].first.first], dp[j]+v[i].second);
        }
    }
    
    for(i=0;i<20005;i++) ans=max(ans, dp[i]);
    cout<<ans;
    return 0;
}
### Prompt

Your challenge is to write 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 endl "\n"
using namespace std;
typedef long long int lli;
const lli N=1e3+5;
vector<pair<pair<lli,lli>,lli>> v;
lli dp[20005];

bool cmp(const pair<pair<lli,lli>,lli> &a,const pair<pair<lli,lli>,lli> &b)
{
    return a.first.first+a.first.second < b.first.first+b.first.second;
}
int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    lli n;
    cin>>n;
    lli i,j,ans=0,w,s,va;
    
    for(i=0;i<n;i++) 
    {
        cin>>w>>s>>va;
        v.push_back({{w,s},va});
    }
    sort(v.begin(), v.end(), cmp);
    
    for(i=0;i<n;i++)
    {
        for(j=v[i].first.second;j>=0;j--)
        {
            dp[j+v[i].first.first]=max(dp[j+v[i].first.first], dp[j]+v[i].second);
        }
    }
    
    for(i=0;i<20005;i++) ans=max(ans, dp[i]);
    cout<<ans;
    return 0;
}
```