#include <bits/stdc++.h>

using namespace std;
typedef pair<int, int> ii;

bool comp(pair<ii, int> a, pair<ii, int> b) {
    return a.first.first + a.first.second > b.first.first + b.first.second;
}


int main() {
    int n; cin >> n;

    pair<ii, int> arr[n];

    for(int i = 0; i < n; ++i) {
        int w, s, v; cin >> w >> s >> v;
        arr[i] = pair<ii, int>(ii(w, s), v);
    }
    sort(arr, arr + n, comp);

    vector<long long> dp(20004);


    for(int i = n-1; i >= 0; --i) {

        for(int j = min(arr[i].first.second, 20001 - arr[i].first.first); j >= 0; --j) {

            dp[j + arr[i].first.first] = max(dp[ j + arr[i].first.first] , dp[j] + arr[i].second);
        }
    }

    long long ans = 0;

    for(int i = 0; i <= 20001; ++i) {
        ans = max(ans, dp[i]);
    }
    cout << ans;



}
### Prompt

Generate a CPP solution to 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;
typedef pair<int, int> ii;

bool comp(pair<ii, int> a, pair<ii, int> b) {
    return a.first.first + a.first.second > b.first.first + b.first.second;
}


int main() {
    int n; cin >> n;

    pair<ii, int> arr[n];

    for(int i = 0; i < n; ++i) {
        int w, s, v; cin >> w >> s >> v;
        arr[i] = pair<ii, int>(ii(w, s), v);
    }
    sort(arr, arr + n, comp);

    vector<long long> dp(20004);


    for(int i = n-1; i >= 0; --i) {

        for(int j = min(arr[i].first.second, 20001 - arr[i].first.first); j >= 0; --j) {

            dp[j + arr[i].first.first] = max(dp[ j + arr[i].first.first] , dp[j] + arr[i].second);
        }
    }

    long long ans = 0;

    for(int i = 0; i <= 20001; ++i) {
        ans = max(ans, dp[i]);
    }
    cout << ans;



}
```