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

struct S {
    int w, s , v;
    bool operator <(const S &he) const
    {
        return w + s < he.w + he.s;
    }
};
int max_W = 2e4;
int main()
{
    int n;  scanf("%d",&n);
    vector < S > a(n);
    for(int i = 0 ; i < n; i++)
        scanf("%d%d%d",&a[i].w,&a[i].s,&a[i].v);
    sort(a.begin(),a.end());

    vector < ll > dp(20005,0);
    for(int i = n-1 ; i >= 0 ; i--)
        for(int w = 0 ; w <= min(a[i].s,max_W - a[i].w); w++)
            dp[w] = max(dp[w] , dp[w+a[i].w] + a[i].v);

    printf("%lld\n",dp[0]);
    return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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>
#define ll long long
using namespace std;

struct S {
    int w, s , v;
    bool operator <(const S &he) const
    {
        return w + s < he.w + he.s;
    }
};
int max_W = 2e4;
int main()
{
    int n;  scanf("%d",&n);
    vector < S > a(n);
    for(int i = 0 ; i < n; i++)
        scanf("%d%d%d",&a[i].w,&a[i].s,&a[i].v);
    sort(a.begin(),a.end());

    vector < ll > dp(20005,0);
    for(int i = n-1 ; i >= 0 ; i--)
        for(int w = 0 ; w <= min(a[i].s,max_W - a[i].w); w++)
            dp[w] = max(dp[w] , dp[w+a[i].w] + a[i].v);

    printf("%lld\n",dp[0]);
    return 0;
}

```