#include <bits/stdc++.h>
#define ll long long
#define ppll pair < pair<ll,ll> , pair<ll,ll> >

#define fr first
#define sc second

#define sw fr.fr
#define v fr.sc
#define w sc.fr
#define s sc.sc

using namespace std;

const ll N = 1010;
const ll W = 30100;
const ll Inf = 1e18;

ppll a[N];
ll Dp[N][W];

int main()
{
    ll n;   cin>>n;

    for(ll i=1;i<=n;i++)    scanf("%I64d%I64d%I64d",&a[i].w,&a[i].s,&a[i].v) , a[i].sw = a[i].s + a[i].w ;

    sort(a+1,a+n+1);

    for(ll i=1;i<=n;i++)
        for(ll We=0;We<W;We++)
            Dp[i][We] = max( Dp[i-1][We] , We>=a[i].w ? a[i].v + Dp[i-1][min(We-a[i].w,a[i].s)] : -Inf );

    cout<<Dp[n][W-1];
}
### Prompt

Please formulate 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 ll long long
#define ppll pair < pair<ll,ll> , pair<ll,ll> >

#define fr first
#define sc second

#define sw fr.fr
#define v fr.sc
#define w sc.fr
#define s sc.sc

using namespace std;

const ll N = 1010;
const ll W = 30100;
const ll Inf = 1e18;

ppll a[N];
ll Dp[N][W];

int main()
{
    ll n;   cin>>n;

    for(ll i=1;i<=n;i++)    scanf("%I64d%I64d%I64d",&a[i].w,&a[i].s,&a[i].v) , a[i].sw = a[i].s + a[i].w ;

    sort(a+1,a+n+1);

    for(ll i=1;i<=n;i++)
        for(ll We=0;We<W;We++)
            Dp[i][We] = max( Dp[i-1][We] , We>=a[i].w ? a[i].v + Dp[i-1][min(We-a[i].w,a[i].s)] : -Inf );

    cout<<Dp[n][W-1];
}
```