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

struct Block{
    int w, s, v;
    Block(int w, int s, int v) : w(w), s(s), v(v) {}
};

bool operator<(const Block &a, const Block &b){
    return a.w+a.s < b.w+b.s;
}

int main(){
    int N;
    cin >> N;
    vector<Block> B;
    for(int i = 0; i < N; ++i){
        int w, s, v;
        cin >> w >> s >> v;
        B.emplace_back(w,s,v);
    }
    sort(B.begin(),B.end());
    vector<long long> dp(2e4+1,-1);
    dp[0] = 0;
    for(int i = 0; i < N; ++i){
        for(int j = B[i].s; j >= 0; --j){
            if(j + B[i].w > 2e4) continue;
            dp[j+B[i].w] = max(dp[j+B[i].w],dp[j]+B[i].v);
        }
        for(int j = 1; j <= 2e4; ++j)
            dp[j] = max(dp[j],dp[j-1]);
    }
    cout << dp.back() << endl;
}

### 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 namespace std;

struct Block{
    int w, s, v;
    Block(int w, int s, int v) : w(w), s(s), v(v) {}
};

bool operator<(const Block &a, const Block &b){
    return a.w+a.s < b.w+b.s;
}

int main(){
    int N;
    cin >> N;
    vector<Block> B;
    for(int i = 0; i < N; ++i){
        int w, s, v;
        cin >> w >> s >> v;
        B.emplace_back(w,s,v);
    }
    sort(B.begin(),B.end());
    vector<long long> dp(2e4+1,-1);
    dp[0] = 0;
    for(int i = 0; i < N; ++i){
        for(int j = B[i].s; j >= 0; --j){
            if(j + B[i].w > 2e4) continue;
            dp[j+B[i].w] = max(dp[j+B[i].w],dp[j]+B[i].v);
        }
        for(int j = 1; j <= 2e4; ++j)
            dp[j] = max(dp[j],dp[j-1]);
    }
    cout << dp.back() << endl;
}

```