#include <bits/stdc++.h>
using namespace std;

const int N = 1001;
struct TW 
{
    int w,s,v;

    bool operator  < (const TW &h) const 
    {
        if (s!=h.s)return s < h.s;
        if (w!=h.w)return w < h.w;
        return v  > h.v;
    }
} a[N];
int n;

#define lint long long 
lint f[20001], f_[20001];

int main() 
{
    cin >> n;
    for (int i=1; i<=n; ++i) 
    {
        cin >> a[i].w >> a[i].s >> a[i].v;
        a[i].s += a[i].w;
    }
    sort (a+1, a+1+n);
    for (int i=1; i<=n; ++i) 
    {
        for (int j=a[i].w ; j <= a[i].s; ++j) 
            f_[j] = f[j - a[i].w] + a[i].v;
        for (int j=1; j<=20000; ++j)    
            f[j] = max(f[j], f_[j]);
    }
    lint ans = 0;
    for (int i=1; i<=20000; ++i) 
        ans = max(ans, f[i]);
    cout << ans;
}
### Prompt

Your challenge is to write 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;

const int N = 1001;
struct TW 
{
    int w,s,v;

    bool operator  < (const TW &h) const 
    {
        if (s!=h.s)return s < h.s;
        if (w!=h.w)return w < h.w;
        return v  > h.v;
    }
} a[N];
int n;

#define lint long long 
lint f[20001], f_[20001];

int main() 
{
    cin >> n;
    for (int i=1; i<=n; ++i) 
    {
        cin >> a[i].w >> a[i].s >> a[i].v;
        a[i].s += a[i].w;
    }
    sort (a+1, a+1+n);
    for (int i=1; i<=n; ++i) 
    {
        for (int j=a[i].w ; j <= a[i].s; ++j) 
            f_[j] = f[j - a[i].w] + a[i].v;
        for (int j=1; j<=20000; ++j)    
            f[j] = max(f[j], f_[j]);
    }
    lint ans = 0;
    for (int i=1; i<=20000; ++i) 
        ans = max(ans, f[i]);
    cout << ans;
}
```