#include <algorithm>
#include <cassert>
#include <iostream>
#include <vector>
using namespace std;

struct block {
    int weight, solid, value;

    bool operator<(const block &other) const {
        return solid < other.solid;
    }
};

const int TOWER_MAX = 20005;

int N;
vector<block> blocks;

int main() {
    scanf("%d", &N);
    blocks.resize(N);

    for (block &b : blocks) {
        scanf("%d %d %d", &b.weight, &b.solid, &b.value);
        b.solid += b.weight;
    }

    sort(blocks.begin(), blocks.end());
    vector<long long> dp(TOWER_MAX, 0);

    for (block &b : blocks)
        for (int w = b.solid; w >= b.weight; w--)
            dp[w] = max(dp[w], dp[w - b.weight] + b.value);

    printf("%lld\n", *max_element(dp.begin(), dp.end()));
}

### Prompt

Your challenge is to write 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 <algorithm>
#include <cassert>
#include <iostream>
#include <vector>
using namespace std;

struct block {
    int weight, solid, value;

    bool operator<(const block &other) const {
        return solid < other.solid;
    }
};

const int TOWER_MAX = 20005;

int N;
vector<block> blocks;

int main() {
    scanf("%d", &N);
    blocks.resize(N);

    for (block &b : blocks) {
        scanf("%d %d %d", &b.weight, &b.solid, &b.value);
        b.solid += b.weight;
    }

    sort(blocks.begin(), blocks.end());
    vector<long long> dp(TOWER_MAX, 0);

    for (block &b : blocks)
        for (int w = b.solid; w >= b.weight; w--)
            dp[w] = max(dp[w], dp[w - b.weight] + b.value);

    printf("%lld\n", *max_element(dp.begin(), dp.end()));
}

```