#include <cstdio>
#include <algorithm>

const int64_t INF=1e15;

void setmax(int64_t& x,int64_t y){
  x=std::max(x,y);
}

struct Block{
  int w,s,v;
  bool operator<(struct Block b)const{
    return s+w<b.s+b.w;
  }   
}blocks[1005];

int64_t dp[20001];

int main(){
  int N;
  scanf("%d",&N);
  for(int i=0;i<N;i++){
    scanf("%d %d %d",&blocks[i].w,&blocks[i].s,&blocks[i].v);
  }
  std::sort(blocks,blocks+N);
  std::fill(dp+1,dp+20001,-INF);
  for(int i=0;i<N;i++){
    for(int w=blocks[i].s;w>=0;w--){
      setmax(dp[w+blocks[i].w],dp[w]+blocks[i].v);
    }
  }
  printf("%ld\n",*std::max_element(dp,dp+20001));
  return 0;
}

### Prompt

Please provide a CPP coded solution 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 <cstdio>
#include <algorithm>

const int64_t INF=1e15;

void setmax(int64_t& x,int64_t y){
  x=std::max(x,y);
}

struct Block{
  int w,s,v;
  bool operator<(struct Block b)const{
    return s+w<b.s+b.w;
  }   
}blocks[1005];

int64_t dp[20001];

int main(){
  int N;
  scanf("%d",&N);
  for(int i=0;i<N;i++){
    scanf("%d %d %d",&blocks[i].w,&blocks[i].s,&blocks[i].v);
  }
  std::sort(blocks,blocks+N);
  std::fill(dp+1,dp+20001,-INF);
  for(int i=0;i<N;i++){
    for(int w=blocks[i].s;w>=0;w--){
      setmax(dp[w+blocks[i].w],dp[w]+blocks[i].v);
    }
  }
  printf("%ld\n",*std::max_element(dp,dp+20001));
  return 0;
}

```