#include <iostream>
#include <algorithm>
#include <vector>
using namespace std;
#define REP(i,n) for (int i=0;i<(n);++i)
typedef long long ll;

int N;
ll dp[21000];

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

int main() {
    cin.tie(0); ios_base::sync_with_stdio(false);
    cin >> N;
    REP(i,N){
        int w,s,v;
        cin >> w >> s >> v;
        blocks.emplace_back(w,s,v);
    }
    sort(blocks.begin(),blocks.end());
    REP(i,N){
        for(int j = blocks[i].s; j>=0; --j){
            if(dp[j+blocks[i].w] < dp[j] + blocks[i].v){
                dp[j+blocks[i].w] = dp[j] + blocks[i].v;
            }
        }
    }
    cout << *(max_element(dp,dp+21000)) << 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 <iostream>
#include <algorithm>
#include <vector>
using namespace std;
#define REP(i,n) for (int i=0;i<(n);++i)
typedef long long ll;

int N;
ll dp[21000];

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

int main() {
    cin.tie(0); ios_base::sync_with_stdio(false);
    cin >> N;
    REP(i,N){
        int w,s,v;
        cin >> w >> s >> v;
        blocks.emplace_back(w,s,v);
    }
    sort(blocks.begin(),blocks.end());
    REP(i,N){
        for(int j = blocks[i].s; j>=0; --j){
            if(dp[j+blocks[i].w] < dp[j] + blocks[i].v){
                dp[j+blocks[i].w] = dp[j] + blocks[i].v;
            }
        }
    }
    cout << *(max_element(dp,dp+21000)) << endl;
    return 0;
}
```