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

const int N = 20004;
const int mod = 1000000007;
typedef long long  ll;

ll dp[N];
int n;

struct node
{
    int w,s,b;
};
bool cmp(node x,node y)
{
    return x.w+x.s<y.s+y.w;
}
node arr[N];


int main()
{
    scanf("%d",&n);
    for(int i=1; i<=n; i++) scanf("%d %d %d",&arr[i].w,&arr[i].s,&arr[i].b);
    sort(arr+1,arr+n+1,cmp);
    dp[0]=0;
    for(int i=1; i<N; i++) dp[i]=-1e17;
    for(int i=1; i<=n; i++)
    {
        for(int j=arr[i].s; j>=0; j--)
        {
            dp[j+arr[i].w]=max(dp[j+arr[i].w],arr[i].b+dp[j]);
        }
    }
    ll ans=0;
    for(int i=0; i<N; i++) ans=max(ans,dp[i]);
    printf("%lld\n",ans);


}

### 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>
using namespace std;

const int N = 20004;
const int mod = 1000000007;
typedef long long  ll;

ll dp[N];
int n;

struct node
{
    int w,s,b;
};
bool cmp(node x,node y)
{
    return x.w+x.s<y.s+y.w;
}
node arr[N];


int main()
{
    scanf("%d",&n);
    for(int i=1; i<=n; i++) scanf("%d %d %d",&arr[i].w,&arr[i].s,&arr[i].b);
    sort(arr+1,arr+n+1,cmp);
    dp[0]=0;
    for(int i=1; i<N; i++) dp[i]=-1e17;
    for(int i=1; i<=n; i++)
    {
        for(int j=arr[i].s; j>=0; j--)
        {
            dp[j+arr[i].w]=max(dp[j+arr[i].w],arr[i].b+dp[j]);
        }
    }
    ll ans=0;
    for(int i=0; i<N; i++) ans=max(ans,dp[i]);
    printf("%lld\n",ans);


}

```