#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define sz(x) (int)x.size()
#define int long long
typedef pair<int,int>pii;
typedef vector<int> vi;
typedef vector<vi> vii;
const int mxN=1e4+5,M=1e9+7,mxW=2e4+5;
//did u check when n=1?
//is mxN correct?
int dp[mxW],n;
struct t{
    int  w,s,v;
    bool operator<(const t &o) const{
        return w+s<o.w+o.s;
    }
} a[mxN];
int32_t main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cin>>n;
    for(int i=0;i<n;i++){
        cin>>a[i].w>>a[i].s>>a[i].v;
    }
    sort(a,a+n);
    for(int i=0;i<n;i++){
        for(int j=a[i].s;j>=0;j--){
            dp[j+a[i].w]=max(dp[j+a[i].w],dp[j]+a[i].v);
        }
    }
    int ans=0;
    for(int i=0;i<mxW;i++)ans=max(ans,dp[i]);
    cout<<ans;


}
### Prompt

Generate 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>
using namespace std;
#define ll long long
#define pb push_back
#define sz(x) (int)x.size()
#define int long long
typedef pair<int,int>pii;
typedef vector<int> vi;
typedef vector<vi> vii;
const int mxN=1e4+5,M=1e9+7,mxW=2e4+5;
//did u check when n=1?
//is mxN correct?
int dp[mxW],n;
struct t{
    int  w,s,v;
    bool operator<(const t &o) const{
        return w+s<o.w+o.s;
    }
} a[mxN];
int32_t main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cin>>n;
    for(int i=0;i<n;i++){
        cin>>a[i].w>>a[i].s>>a[i].v;
    }
    sort(a,a+n);
    for(int i=0;i<n;i++){
        for(int j=a[i].s;j>=0;j--){
            dp[j+a[i].w]=max(dp[j+a[i].w],dp[j]+a[i].v);
        }
    }
    int ans=0;
    for(int i=0;i<mxW;i++)ans=max(ans,dp[i]);
    cout<<ans;


}
```