#include <iostream>
#include <vector>
#include <algorithm>
using ll = long long;
struct Block
{
    int w, s;
    ll v;
    bool operator<(const Block& b) const { return w + s < b.w + b.s; };
};
int main()
{
    int N;
    std::cin >> N;
    std::vector<Block> b(N);
    for (int i = 0; i < N; i++) { std::cin >> b[i].w >> b[i].s >> b[i].v; }
    std::sort(b.begin(), b.end());
    std::vector<ll> dp(20001, -(1LL << 60));
    dp[0] = 0;
    for (int i = 0; i < N; i++) {
        for (int j = std::min(b[i].s, 20000 - b[i].w); j >= 0; j--) { dp[j + b[i].w] = std::max(dp[j + b[i].w], dp[j] + b[i].v); }
    }
    std::cout << *std::max_element(dp.begin(), dp.end()) << std::endl;
    return 0;
}

### 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
#include <iostream>
#include <vector>
#include <algorithm>
using ll = long long;
struct Block
{
    int w, s;
    ll v;
    bool operator<(const Block& b) const { return w + s < b.w + b.s; };
};
int main()
{
    int N;
    std::cin >> N;
    std::vector<Block> b(N);
    for (int i = 0; i < N; i++) { std::cin >> b[i].w >> b[i].s >> b[i].v; }
    std::sort(b.begin(), b.end());
    std::vector<ll> dp(20001, -(1LL << 60));
    dp[0] = 0;
    for (int i = 0; i < N; i++) {
        for (int j = std::min(b[i].s, 20000 - b[i].w); j >= 0; j--) { dp[j + b[i].w] = std::max(dp[j + b[i].w], dp[j] + b[i].v); }
    }
    std::cout << *std::max_element(dp.begin(), dp.end()) << std::endl;
    return 0;
}

```