#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i, a, b) for (int i = (a); i < (b); i++)

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);

    int n;
    cin >> n;
    vector<tuple<int, int, int, ll>> z(n);
    rep(i, 0, n) {
        int w, s, v;
        cin >> w >> s >> v;
        z[i] = make_tuple(w + s, w, s, v);
    }
    sort(z.begin(), z.end());
    vector<vector<ll>> dp(n + 1, vector<ll>(20010, -1e18));
    dp[0][0] = 0;

    rep(i, 0, n) {
        dp[i + 1] = dp[i];
        int s = get<2>(z[i]), w = get<1>(z[i]);
        ll v = get<3>(z[i]);
        rep(j, 0, s + 1) {
            dp[i + 1][j + w] = max(dp[i + 1][j + w], dp[i][j] + v);
        }
    }

    cout << *max_element(dp[n].begin(), dp[n].end()) << endl;

    return 0;
}
### Prompt

Construct a cpp code solution to the problem outlined:

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;
using ll = long long;
#define rep(i, a, b) for (int i = (a); i < (b); i++)

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);

    int n;
    cin >> n;
    vector<tuple<int, int, int, ll>> z(n);
    rep(i, 0, n) {
        int w, s, v;
        cin >> w >> s >> v;
        z[i] = make_tuple(w + s, w, s, v);
    }
    sort(z.begin(), z.end());
    vector<vector<ll>> dp(n + 1, vector<ll>(20010, -1e18));
    dp[0][0] = 0;

    rep(i, 0, n) {
        dp[i + 1] = dp[i];
        int s = get<2>(z[i]), w = get<1>(z[i]);
        ll v = get<3>(z[i]);
        rep(j, 0, s + 1) {
            dp[i + 1][j + w] = max(dp[i + 1][j + w], dp[i][j] + v);
        }
    }

    cout << *max_element(dp[n].begin(), dp[n].end()) << endl;

    return 0;
}
```