#include <bits/stdc++.h>

#define N_MAX 1002
#define W_MAX 20002
#define ll long long

using namespace std;

const int W = 10000;

int n;

struct Block
{
    int w, s, v;
};

Block blocks[N_MAX];

bool operator < (Block a, Block b)
{
    return a.w + a.s < b.w + b.s;
}

ll mxv[W_MAX];

int main()
{
    cin >> n;
    for(int i = 1; i <= n; i++)
        cin >> blocks[i].w >> blocks[i].s >> blocks[i].v;
    sort(blocks + 1, blocks + n + 1);
    for(int i = 1; i <= n; i++)
        for(int j = W; j >= 0; j--)
        {
            if(j <= blocks[i].s)
                mxv[j + blocks[i].w] = max(mxv[j + blocks[i].w],  mxv[j] + blocks[i].v);
        }
    ll ans = 0;
    for(int i = 0; i <= W * 2; i++)
        ans = max(ans, mxv[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>

#define N_MAX 1002
#define W_MAX 20002
#define ll long long

using namespace std;

const int W = 10000;

int n;

struct Block
{
    int w, s, v;
};

Block blocks[N_MAX];

bool operator < (Block a, Block b)
{
    return a.w + a.s < b.w + b.s;
}

ll mxv[W_MAX];

int main()
{
    cin >> n;
    for(int i = 1; i <= n; i++)
        cin >> blocks[i].w >> blocks[i].s >> blocks[i].v;
    sort(blocks + 1, blocks + n + 1);
    for(int i = 1; i <= n; i++)
        for(int j = W; j >= 0; j--)
        {
            if(j <= blocks[i].s)
                mxv[j + blocks[i].w] = max(mxv[j + blocks[i].w],  mxv[j] + blocks[i].v);
        }
    ll ans = 0;
    for(int i = 0; i <= W * 2; i++)
        ans = max(ans, mxv[i]);
    cout << ans << "\n";
    return 0;
}

```