#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 1087, C = 2e4 + 87;
ll dp[C];
tuple<int, int, int> a[N];
int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    int n;
    cin >> n;
    for (int i = 0; i < n; ++i) {
        int w, s, v;
        cin >> w >> s >> v;
        s += w;
        a[i] = make_tuple(s, w, v);
    }
    sort(a, a + n);
    for (int i = 0; i < n; ++i) {
        int s, w, v;
        tie(s, w, v) = a[i];
        for (int j = s; j >= w; --j)
            dp[j] = max(dp[j], dp[j - w] + v);
        for (int j = s + 1; j < C; ++j)
            dp[j] = max(dp[j], dp[j - 1]);
    }
    cout << dp[C - 1] << endl;
}

### Prompt

Please provide a CPP coded solution 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;
typedef long long ll;
const int N = 1087, C = 2e4 + 87;
ll dp[C];
tuple<int, int, int> a[N];
int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    int n;
    cin >> n;
    for (int i = 0; i < n; ++i) {
        int w, s, v;
        cin >> w >> s >> v;
        s += w;
        a[i] = make_tuple(s, w, v);
    }
    sort(a, a + n);
    for (int i = 0; i < n; ++i) {
        int s, w, v;
        tie(s, w, v) = a[i];
        for (int j = s; j >= w; --j)
            dp[j] = max(dp[j], dp[j - w] + v);
        for (int j = s + 1; j < C; ++j)
            dp[j] = max(dp[j], dp[j - 1]);
    }
    cout << dp[C - 1] << endl;
}

```