#include <algorithm>
#include <stdio.h>
#include <math.h>
#include <string>
#include <iostream>
#include <vector>
#include <iomanip>
using namespace std;

struct Block {
    int w, s, v;
    bool operator< (const Block & b) const {
        return w + s > b.w + b.s;
    }
} bt[1010];

long long rucsac[20100];

int main()
{
    int n;
    scanf("%d", &n);

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

    sort(bt, bt + n);

    for (int i = 0; i < n; i++) {
        for (int j = bt[i].w; j <= 20000; j++) {
            long long & v = rucsac[min(j - bt[i].w, bt[i].s)];
            v = max(v, rucsac[j] + bt[i].v);
        }
    }

    cout << rucsac[0] << '\n';

    return 0;
}

### Prompt

Please formulate 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 <algorithm>
#include <stdio.h>
#include <math.h>
#include <string>
#include <iostream>
#include <vector>
#include <iomanip>
using namespace std;

struct Block {
    int w, s, v;
    bool operator< (const Block & b) const {
        return w + s > b.w + b.s;
    }
} bt[1010];

long long rucsac[20100];

int main()
{
    int n;
    scanf("%d", &n);

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

    sort(bt, bt + n);

    for (int i = 0; i < n; i++) {
        for (int j = bt[i].w; j <= 20000; j++) {
            long long & v = rucsac[min(j - bt[i].w, bt[i].s)];
            v = max(v, rucsac[j] + bt[i].v);
        }
    }

    cout << rucsac[0] << '\n';

    return 0;
}

```