#if 1

#include <bits/stdc++.h>
using namespace std;
int n;
long long d[20005];

struct XY
{
    int w,s,v;
}a[1005];

bool cmp(XY x,XY y)
{
    return x.w+x.s < y.w+y.s;
}

int main()
{
    scanf("%d",&n);
    for(int i = 1;i <= n;i++)
    {
        scanf("%d %d %d", &a[i].w, &a[i].s, &a[i].v);
    }
    sort(a+1,a+n+1,cmp);
    long long ans = 0;
    for(int i = 1;i <= n;i++)
    {
        for(int j = a[i].s;j >= 0;j--)
        {
            d[j+a[i].w] = max(d[j+a[i].w],d[j]+a[i].v);

        }
        //for(int j = 0;j <= 30;j++) cout << d[j] << " ";
        //cout << '\n';
    }
    for(int i = 0;i <= 20004;i++)
    {
        //cout << d[i] << " ";
        ans = max(ans,d[i]);
    }
    printf("%lld",ans);
}

#endif // 1
### Prompt

Please create a solution in CPP 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
#if 1

#include <bits/stdc++.h>
using namespace std;
int n;
long long d[20005];

struct XY
{
    int w,s,v;
}a[1005];

bool cmp(XY x,XY y)
{
    return x.w+x.s < y.w+y.s;
}

int main()
{
    scanf("%d",&n);
    for(int i = 1;i <= n;i++)
    {
        scanf("%d %d %d", &a[i].w, &a[i].s, &a[i].v);
    }
    sort(a+1,a+n+1,cmp);
    long long ans = 0;
    for(int i = 1;i <= n;i++)
    {
        for(int j = a[i].s;j >= 0;j--)
        {
            d[j+a[i].w] = max(d[j+a[i].w],d[j]+a[i].v);

        }
        //for(int j = 0;j <= 30;j++) cout << d[j] << " ";
        //cout << '\n';
    }
    for(int i = 0;i <= 20004;i++)
    {
        //cout << d[i] << " ";
        ans = max(ans,d[i]);
    }
    printf("%lld",ans);
}

#endif // 1
```