#include <bits/stdc++.h>
using namespace std;

using ll = long long;

struct block {
    int w, s, v;
    bool operator<(block const& other) const {
        return w + s < other.w + other.s;
    }
};

int main() {
    int n; cin >> n;
    vector<block> bs(n);
    for(int i = 0; i < n; ++i) {
        cin >> bs[i].w >> bs[i].s >> bs[i].v;
    }
    sort(begin(bs), end(bs));

    const int max_s = 1 << 15;
    vector<ll> dp(max_s);
    for(int i = 0; i < n; ++i) {
        for(int j = max_s - 1 - bs[i].w; j >= 0; --j) {
            if(bs[i].s < j) continue;
            dp[j + bs[i].w] = max(dp[j + bs[i].w], dp[j] + bs[i].v);
        }
    }

    cout << *max_element(begin(dp), end(dp)) << endl;
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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;

struct block {
    int w, s, v;
    bool operator<(block const& other) const {
        return w + s < other.w + other.s;
    }
};

int main() {
    int n; cin >> n;
    vector<block> bs(n);
    for(int i = 0; i < n; ++i) {
        cin >> bs[i].w >> bs[i].s >> bs[i].v;
    }
    sort(begin(bs), end(bs));

    const int max_s = 1 << 15;
    vector<ll> dp(max_s);
    for(int i = 0; i < n; ++i) {
        for(int j = max_s - 1 - bs[i].w; j >= 0; --j) {
            if(bs[i].s < j) continue;
            dp[j + bs[i].w] = max(dp[j + bs[i].w], dp[j] + bs[i].v);
        }
    }

    cout << *max_element(begin(dp), end(dp)) << endl;
}

```