#include <bits/stdc++.h>
using namespace std;
const int N = 1003, m = 10004;
struct ban
{
    int w, s;
    int g;
};
bool operator<(const ban& a, const ban& b)
{
    return a.w + a.s < b.w + b.s;
}

int n;
ban a[N];

long long dp[m];
int main()
{
    scanf("%d", &n);
    for (int i = 0; i < n; ++i)
        scanf("%d%d%d", &a[i].w, &a[i].s, &a[i].g);
    sort(a, a + n);
    long long ans = 0;
    for (int i = 0; i < n; ++i)
    {
        for (int j = a[i].s; j >= 0; --j)
        {
            ans = max(ans, dp[j] + a[i].g);
            if (j + a[i].w < m)
                dp[j + a[i].w] = max(dp[j + a[i].w], dp[j] + a[i].g);
        }
    }
    cout << ans << endl;
    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;
const int N = 1003, m = 10004;
struct ban
{
    int w, s;
    int g;
};
bool operator<(const ban& a, const ban& b)
{
    return a.w + a.s < b.w + b.s;
}

int n;
ban a[N];

long long dp[m];
int main()
{
    scanf("%d", &n);
    for (int i = 0; i < n; ++i)
        scanf("%d%d%d", &a[i].w, &a[i].s, &a[i].g);
    sort(a, a + n);
    long long ans = 0;
    for (int i = 0; i < n; ++i)
    {
        for (int j = a[i].s; j >= 0; --j)
        {
            ans = max(ans, dp[j] + a[i].g);
            if (j + a[i].w < m)
                dp[j + a[i].w] = max(dp[j + a[i].w], dp[j] + a[i].g);
        }
    }
    cout << ans << endl;
    return 0;
}

```