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

#define MAX_N 1003
#define MAX_NW 10000007

struct box{
    int w ,s ,v;
    bool operator<(const box&rhs) const{
        return s+w < rhs.s+rhs.w;
    }
};

int n;
box bs[MAX_N];
long long dp[MAX_NW];

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

    memset(dp ,-1 ,sizeof dp);
    dp[0] = 0;
    for(int i=0; i<n; i++)
    for(int j=bs[i].s; ~j; j--)
        if(~dp[j])
            dp[j+bs[i].w] = max(dp[j+bs[i].w] ,dp[j]+bs[i].v);

    printf("%lld\n",*max_element(dp ,dp+MAX_NW));
}

### Prompt

Create a solution in CPP for 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;

#define MAX_N 1003
#define MAX_NW 10000007

struct box{
    int w ,s ,v;
    bool operator<(const box&rhs) const{
        return s+w < rhs.s+rhs.w;
    }
};

int n;
box bs[MAX_N];
long long dp[MAX_NW];

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

    memset(dp ,-1 ,sizeof dp);
    dp[0] = 0;
    for(int i=0; i<n; i++)
    for(int j=bs[i].s; ~j; j--)
        if(~dp[j])
            dp[j+bs[i].w] = max(dp[j+bs[i].w] ,dp[j]+bs[i].v);

    printf("%lld\n",*max_element(dp ,dp+MAX_NW));
}

```