#include <bits/stdc++.h>

using namespace std;

using ll = long long;

const int MAXS = 10000;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n;
    cin >> n;
    vector<int> idxs(n), w(n), s(n);
    vector<ll> v(n);
    for (int i = 0; i < n; i++) {
        cin >> w[i] >> s[i] >> v[i];
        idxs[i] = i;
    }
    sort(idxs.begin(), idxs.end(), [&](const int i1, const int i2){return w[i1] + s[i1] < w[i2] + s[i2];});

    ll ans = 0;
    vector<ll> dp(MAXS + 1, 0);
    for (int i : idxs) {
        for (int j = s[i]; j >= 0; j--) {
            ans = max(ans, dp[j] + v[i]);
            if (j + w[i] <= MAXS) dp[j + w[i]] = max(dp[j + w[i]], dp[j] + v[i]);
        }
    }
    
    for (int i = 0; i <= MAXS; i++) ans = max(ans, dp[i]);
    cout << ans << endl;
    return 0;
}
### Prompt

Create a solution in CPP for 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 <bits/stdc++.h>

using namespace std;

using ll = long long;

const int MAXS = 10000;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n;
    cin >> n;
    vector<int> idxs(n), w(n), s(n);
    vector<ll> v(n);
    for (int i = 0; i < n; i++) {
        cin >> w[i] >> s[i] >> v[i];
        idxs[i] = i;
    }
    sort(idxs.begin(), idxs.end(), [&](const int i1, const int i2){return w[i1] + s[i1] < w[i2] + s[i2];});

    ll ans = 0;
    vector<ll> dp(MAXS + 1, 0);
    for (int i : idxs) {
        for (int j = s[i]; j >= 0; j--) {
            ans = max(ans, dp[j] + v[i]);
            if (j + w[i] <= MAXS) dp[j + w[i]] = max(dp[j + w[i]], dp[j] + v[i]);
        }
    }
    
    for (int i = 0; i <= MAXS; i++) ans = max(ans, dp[i]);
    cout << ans << endl;
    return 0;
}
```