#include <bits/stdc++.h>

using namespace std;

//#define FILE_IO

typedef long long LL;

struct Block
{
    int w, s, v;
}a[1005];

int N;
LL dp[20005];

int main()
{
    #ifdef FILE_IO
    freopen("1.in", "r", stdin);
    //freopen("1.out", "w", stdout);
    #endif

    cin >> N;
    for(int i = 1; i <= N; i++)
        cin >> a[i].w >> a[i].s >> a[i].v;

    sort(a + 1, a + N + 1,
         [](Block x, Block y) { return (x.w + x.s) < (y.w + y.s); });

    for(int i = 1; i <= N; i++)
    {
        for(int j = a[i].s; j >= 0; j--)
            if(j + a[i].w <= 20000)
                dp[j + a[i].w] = max(dp[j + a[i].w], dp[j] + a[i].v);
    }

    LL ans = 0;
    for(int i = 0; i <= 20000; i++)
        ans = max(ans, dp[i]);
    cout << ans << '\n';

    return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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 FILE_IO

typedef long long LL;

struct Block
{
    int w, s, v;
}a[1005];

int N;
LL dp[20005];

int main()
{
    #ifdef FILE_IO
    freopen("1.in", "r", stdin);
    //freopen("1.out", "w", stdout);
    #endif

    cin >> N;
    for(int i = 1; i <= N; i++)
        cin >> a[i].w >> a[i].s >> a[i].v;

    sort(a + 1, a + N + 1,
         [](Block x, Block y) { return (x.w + x.s) < (y.w + y.s); });

    for(int i = 1; i <= N; i++)
    {
        for(int j = a[i].s; j >= 0; j--)
            if(j + a[i].w <= 20000)
                dp[j + a[i].w] = max(dp[j + a[i].w], dp[j] + a[i].v);
    }

    LL ans = 0;
    for(int i = 0; i <= 20000; i++)
        ans = max(ans, dp[i]);
    cout << ans << '\n';

    return 0;
}

```