/*
 *  Lang    : C++
 *  Author  : little_angel
 */
#include <bits/stdc++.h>

using namespace std;
#define int long long

struct box {
    int w, s, v;

    bool operator<(const box &b) const {
        return w + s < b.w + b.s;
    }
};

istream &operator>>(istream &in, box &b) {
    in >> b.w >> b.s >> b.v;
    return in;
}

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);

    int n;
    cin >> n;
    vector<box> a(n);
    for (int i = 0; i < n; ++i) cin >> a[i];
    sort(a.begin(), a.end());
    int dp[200010];
    memset(dp, -1, sizeof(dp));
    dp[0] = 0;
    for (auto &b:a) {
        for (int i = b.s; i >= 0; --i) {
            if (~dp[i])dp[i + b.w] = max(dp[i + b.w], dp[i] + b.v);
        }
    }
    cout << *max_element(dp, dp + 200010) << endl;
}
### Prompt

In CPP, your task is to solve 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
/*
 *  Lang    : C++
 *  Author  : little_angel
 */
#include <bits/stdc++.h>

using namespace std;
#define int long long

struct box {
    int w, s, v;

    bool operator<(const box &b) const {
        return w + s < b.w + b.s;
    }
};

istream &operator>>(istream &in, box &b) {
    in >> b.w >> b.s >> b.v;
    return in;
}

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);

    int n;
    cin >> n;
    vector<box> a(n);
    for (int i = 0; i < n; ++i) cin >> a[i];
    sort(a.begin(), a.end());
    int dp[200010];
    memset(dp, -1, sizeof(dp));
    dp[0] = 0;
    for (auto &b:a) {
        for (int i = b.s; i >= 0; --i) {
            if (~dp[i])dp[i + b.w] = max(dp[i + b.w], dp[i] + b.v);
        }
    }
    cout << *max_element(dp, dp + 200010) << endl;
}
```