#include <iostream>
#include <algorithm>
#include <vector>

using Int = long long int;
using std::vector;

constexpr Int INF = std::numeric_limits<Int>::max() / 3;
constexpr int S = 10000;

struct Block {
    int w, s;
    Int v;
    bool operator<(const Block& b) const {
        return w + s < b.w + b.s;
    }
};

int main() {
    int n;
    std::cin >> n;
    
    vector<Block> blocks(n);
    for(auto& b : blocks) {
        std::cin >> b.w >> b.s >> b.v;
    }
    std::sort(blocks.begin(), blocks.end());

    vector<Int> dp(S * 2 + 1, -INF);
    dp[0] = 0;
    // key is weight

    for(const auto& b : blocks) {
        for(int w = b.s; w >= 0; --w) {
            dp[w + b.w] = std::max(dp[w + b.w], dp[w] + b.v);
        }
    }

    std::cout << *std::max_element(dp.begin(), dp.end()) << std::endl;
    return 0;
}

### 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 <iostream>
#include <algorithm>
#include <vector>

using Int = long long int;
using std::vector;

constexpr Int INF = std::numeric_limits<Int>::max() / 3;
constexpr int S = 10000;

struct Block {
    int w, s;
    Int v;
    bool operator<(const Block& b) const {
        return w + s < b.w + b.s;
    }
};

int main() {
    int n;
    std::cin >> n;
    
    vector<Block> blocks(n);
    for(auto& b : blocks) {
        std::cin >> b.w >> b.s >> b.v;
    }
    std::sort(blocks.begin(), blocks.end());

    vector<Int> dp(S * 2 + 1, -INF);
    dp[0] = 0;
    // key is weight

    for(const auto& b : blocks) {
        for(int w = b.s; w >= 0; --w) {
            dp[w + b.w] = std::max(dp[w + b.w], dp[w] + b.v);
        }
    }

    std::cout << *std::max_element(dp.begin(), dp.end()) << std::endl;
    return 0;
}

```