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

typedef long long ll;

struct state
{
    ll w,s,v;
    state(ll w, ll s, ll v) : w(w), s(s), v(v) {}
    state(){}
    bool operator < (const state &x ) const
    {
        return x.w + x.s > w + s;
    }
};

state v[10005];

const int maxm = 3e4 + 400;

ll dp[maxm];

int main()
{
    int n;
    scanf("%d",&n);
    for(int i = 0; i < n ; i++)
    {
        scanf("%lld %lld %lld",&v[i].w, &v[i].s, &v[i].v);
    }
    sort(v,v+n);

    for(int i = 0; i < n ; i++)
    {
        for(int j = v[i].s; j >= 0; j--)
        {
            int pos = j+v[i].w;
            if(pos < maxm)
                dp[pos] = max(dp[pos], dp[j] + v[i].v); 
        }
    }
    printf("%lld\n",*max_element(dp, dp + maxm));
    return 0; 
}
### 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;

typedef long long ll;

struct state
{
    ll w,s,v;
    state(ll w, ll s, ll v) : w(w), s(s), v(v) {}
    state(){}
    bool operator < (const state &x ) const
    {
        return x.w + x.s > w + s;
    }
};

state v[10005];

const int maxm = 3e4 + 400;

ll dp[maxm];

int main()
{
    int n;
    scanf("%d",&n);
    for(int i = 0; i < n ; i++)
    {
        scanf("%lld %lld %lld",&v[i].w, &v[i].s, &v[i].v);
    }
    sort(v,v+n);

    for(int i = 0; i < n ; i++)
    {
        for(int j = v[i].s; j >= 0; j--)
        {
            int pos = j+v[i].w;
            if(pos < maxm)
                dp[pos] = max(dp[pos], dp[j] + v[i].v); 
        }
    }
    printf("%lld\n",*max_element(dp, dp + maxm));
    return 0; 
}
```