#include<bits/stdc++.h>
using namespace std;
#define ll long long
const ll inf=1e18L+5;
struct block{
int w,s;ll v;
};
int main()
{
    int n;
    cin>>n;
    vector<block> vec(n);
    int max_w=0;
    for(int i=0;i<n;i++)
    {
        cin>>vec[i].w>>vec[i].s>>vec[i].v;
        max_w+=vec[i].w;
    }
    sort(vec.begin(),vec.end(),[](block a,block b){
        return a.w+a.s<b.w+b.s;
    });
    //dp[i] max value with total weight i so far
    vector<ll> dp(max_w+5);
    for(int i=0;i<n;i++)
    {
        for(int j=min(vec[i].s,max_w-vec[i].w);j>=0;j--)
        {            
                dp[j+vec[i].w]=max(dp[j+vec[i].w],dp[j]+vec[i].v);
        }
    }
    ll ans=-1;
    for(int j=max_w;j>=0;j--)
    {
        ans=max(ans,dp[j]);
    }
    cout<<ans<<endl;

}

### 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;
#define ll long long
const ll inf=1e18L+5;
struct block{
int w,s;ll v;
};
int main()
{
    int n;
    cin>>n;
    vector<block> vec(n);
    int max_w=0;
    for(int i=0;i<n;i++)
    {
        cin>>vec[i].w>>vec[i].s>>vec[i].v;
        max_w+=vec[i].w;
    }
    sort(vec.begin(),vec.end(),[](block a,block b){
        return a.w+a.s<b.w+b.s;
    });
    //dp[i] max value with total weight i so far
    vector<ll> dp(max_w+5);
    for(int i=0;i<n;i++)
    {
        for(int j=min(vec[i].s,max_w-vec[i].w);j>=0;j--)
        {            
                dp[j+vec[i].w]=max(dp[j+vec[i].w],dp[j]+vec[i].v);
        }
    }
    ll ans=-1;
    for(int j=max_w;j>=0;j--)
    {
        ans=max(ans,dp[j]);
    }
    cout<<ans<<endl;

}

```