#include <bits/stdc++.h>
#define fst first
#define snd second
#define fore(i,a,b) for(int i=a,ThxDem=b;i<ThxDem;++i)
#define pb push_back
#define ALL(s) s.begin(),s.end()
#define FIN ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define SZ(n) ((int)(n).size())
using namespace std;
typedef long long ll;
typedef pair<ll,ll> ii;

ll dp[200000];
pair<ii,ll> a[1001];

bool cmp(pair<ii,ll> &x, pair<ii,ll> &y){
    return x.fst.fst+x.fst.snd < y.fst.fst+y.fst.snd;
}

int main(){FIN;
    ll n,ans=0; cin >> n;
    fore(i,0,n) cin >> a[i].fst.fst >> a[i].fst.snd >> a[i].snd;
    sort(a,a+n,cmp);
    fore(i,0,n){
        for(int j = a[i].fst.snd; j >= 0; j--){
            dp[j+a[i].fst.fst] = max(dp[j+a[i].fst.fst], dp[j]+a[i].snd);
        }
    }
    fore(i,0,200000) ans = max(ans,dp[i]);
    cout << ans << endl;
}
### Prompt

Your task is to create 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 fst first
#define snd second
#define fore(i,a,b) for(int i=a,ThxDem=b;i<ThxDem;++i)
#define pb push_back
#define ALL(s) s.begin(),s.end()
#define FIN ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define SZ(n) ((int)(n).size())
using namespace std;
typedef long long ll;
typedef pair<ll,ll> ii;

ll dp[200000];
pair<ii,ll> a[1001];

bool cmp(pair<ii,ll> &x, pair<ii,ll> &y){
    return x.fst.fst+x.fst.snd < y.fst.fst+y.fst.snd;
}

int main(){FIN;
    ll n,ans=0; cin >> n;
    fore(i,0,n) cin >> a[i].fst.fst >> a[i].fst.snd >> a[i].snd;
    sort(a,a+n,cmp);
    fore(i,0,n){
        for(int j = a[i].fst.snd; j >= 0; j--){
            dp[j+a[i].fst.fst] = max(dp[j+a[i].fst.fst], dp[j]+a[i].snd);
        }
    }
    fore(i,0,200000) ans = max(ans,dp[i]);
    cout << ans << endl;
}
```