#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

struct block {
    ll w, s, v;

    block() : w(0), s(0), v(0) {}

    bool operator<(const block& other) const {
        return w + s > other.w + other.s;
    }
};

const int MAXS = 10000;

int N;
ll dp[MAXS + 1];
vector<block> b;

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cin >> N;
    b.resize(N);
    for (int i = 0; i < N; i++)
        cin >> b[i].w >> b[i].s >> b[i].v;
    sort(b.begin(), b.end());
    ll result = 0;
    for (int i = N - 1; i >= 0; i--) {
        result = max(result, b[i].v + dp[b[i].s]);
        for (int j = MAXS; j >= 0; j--)
            if (b[i].w <= j)
                dp[j] = max(dp[j], b[i].v + dp[min(b[i].s, j - b[i].w)]);
    }
    cout << result << endl;
}

### 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;

typedef long long ll;

struct block {
    ll w, s, v;

    block() : w(0), s(0), v(0) {}

    bool operator<(const block& other) const {
        return w + s > other.w + other.s;
    }
};

const int MAXS = 10000;

int N;
ll dp[MAXS + 1];
vector<block> b;

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cin >> N;
    b.resize(N);
    for (int i = 0; i < N; i++)
        cin >> b[i].w >> b[i].s >> b[i].v;
    sort(b.begin(), b.end());
    ll result = 0;
    for (int i = N - 1; i >= 0; i--) {
        result = max(result, b[i].v + dp[b[i].s]);
        for (int j = MAXS; j >= 0; j--)
            if (b[i].w <= j)
                dp[j] = max(dp[j], b[i].v + dp[min(b[i].s, j - b[i].w)]);
    }
    cout << result << endl;
}

```