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

struct block {
    int w, s, v;
};
// 比較関数
bool comp(block a, block b) { return a.w + a.s < b.w + b.s; }

int N;
block B[1009];
long long dp[1009][20009];

int main() {
    cin >> N;
    for(int i = 0; i < N; i++) {
        int w, s, v;
        cin >> w >> s >> v;
        B[i] = block{w, s, v};
    }

    sort(B, B + N, comp);

    for(int i = 0; i < N; i++) {
        for(int j = 0; j <= 20000; j++) {
            dp[i + 1][j] = dp[i][j];
            if(j >= 1) dp[i + 1][j] = max(dp[i + 1][j], dp[i + 1][j - 1]);
            if(j >= B[i].w && j - B[i].w <= B[i].s)
                dp[i + 1][j] = max(dp[i + 1][j], dp[i][j - B[i].w] + B[i].v);
        }
    }

    cout << dp[N][20000] << endl;

    return 0;
}
### Prompt

Develop a solution in CPP 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 <algorithm>
#include <iostream>
using namespace std;

struct block {
    int w, s, v;
};
// 比較関数
bool comp(block a, block b) { return a.w + a.s < b.w + b.s; }

int N;
block B[1009];
long long dp[1009][20009];

int main() {
    cin >> N;
    for(int i = 0; i < N; i++) {
        int w, s, v;
        cin >> w >> s >> v;
        B[i] = block{w, s, v};
    }

    sort(B, B + N, comp);

    for(int i = 0; i < N; i++) {
        for(int j = 0; j <= 20000; j++) {
            dp[i + 1][j] = dp[i][j];
            if(j >= 1) dp[i + 1][j] = max(dp[i + 1][j], dp[i + 1][j - 1]);
            if(j >= B[i].w && j - B[i].w <= B[i].s)
                dp[i + 1][j] = max(dp[i + 1][j], dp[i][j - B[i].w] + B[i].v);
        }
    }

    cout << dp[N][20000] << endl;

    return 0;
}
```