#include <bits/stdc++.h>
#define int long long
#define maxc 20005
#define maxn 1005
using namespace std;
struct Pt {
    int w, s, v;
    void RD() {
        cin >> w >> s >> v;
    }
    bool operator < (const Pt &a) const {
        return w + s < a.w + a.s;
    }
};

int dp[maxc] = {};
Pt arr[maxn];
int n;

int32_t main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cin >> n;
    for(int i = 1; i <= n; i++) {
        arr[i].RD();
    }
    sort(arr + 1, arr + n + 1);
    for(int i = 1; i <= n; i++) {
        int mx = arr[i].s + arr[i].w;
        for(int j = mx; j >= arr[i].w; j--) {
            dp[j] = max(dp[j], dp[j - arr[i].w] + arr[i].v);
        }

    }
    cout << *max_element(dp, dp + maxc) << '\n';
    return 0;
}

### Prompt

Your task is to create 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>
#define int long long
#define maxc 20005
#define maxn 1005
using namespace std;
struct Pt {
    int w, s, v;
    void RD() {
        cin >> w >> s >> v;
    }
    bool operator < (const Pt &a) const {
        return w + s < a.w + a.s;
    }
};

int dp[maxc] = {};
Pt arr[maxn];
int n;

int32_t main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cin >> n;
    for(int i = 1; i <= n; i++) {
        arr[i].RD();
    }
    sort(arr + 1, arr + n + 1);
    for(int i = 1; i <= n; i++) {
        int mx = arr[i].s + arr[i].w;
        for(int j = mx; j >= arr[i].w; j--) {
            dp[j] = max(dp[j], dp[j - arr[i].w] + arr[i].v);
        }

    }
    cout << *max_element(dp, dp + maxc) << '\n';
    return 0;
}

```