// KALAM
# include <bits/stdc++.h>

using namespace std;

const int N = 20000 + 77;
int n , W[N] , S[N] , T[N] , P[N];
long long dp[N] , A;
bool CMP(int x , int y){
   return W[x] + S[x] < W[y] + S[y];
}
int main(){
   for(int i = 1;i < N;++ i)
      dp[i] = - 1e18;
   ios::sync_with_stdio(0);cin.tie(0);
   cin >> n;
   for(int i = 1;i <= n;++ i)
      cin >> W[i] >> S[i] >> T[i] , P[i] = i;
   sort(P + 1 , P + 1 + n , CMP);
   for(int i = 1;i <= n;++ i){
      int id = P[i];
      for(int j = S[id] + W[id];j >= W[id];-- j)
         dp[j] = max(dp[j] , dp[j - W[id]] + T[id]);
   }
   for(int i = 1;i < N;++ i)
      A = max(A , dp[i]);
   cout << A;
   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
// KALAM
# include <bits/stdc++.h>

using namespace std;

const int N = 20000 + 77;
int n , W[N] , S[N] , T[N] , P[N];
long long dp[N] , A;
bool CMP(int x , int y){
   return W[x] + S[x] < W[y] + S[y];
}
int main(){
   for(int i = 1;i < N;++ i)
      dp[i] = - 1e18;
   ios::sync_with_stdio(0);cin.tie(0);
   cin >> n;
   for(int i = 1;i <= n;++ i)
      cin >> W[i] >> S[i] >> T[i] , P[i] = i;
   sort(P + 1 , P + 1 + n , CMP);
   for(int i = 1;i <= n;++ i){
      int id = P[i];
      for(int j = S[id] + W[id];j >= W[id];-- j)
         dp[j] = max(dp[j] , dp[j - W[id]] + T[id]);
   }
   for(int i = 1;i < N;++ i)
      A = max(A , dp[i]);
   cout << A;
   return 0;
}

```