# include "iostream"
# include "cstdio"
# include "algorithm"

using namespace std;

const int maxm=1e3+10;
const int maxn=1e4+10;

int N;
long long DP[maxn<<1];

struct thing{
	int W;
	int S;
	int V;
	# define W(x) Thing[x].W
	# define S(x) Thing[x].S
	# define V(x) Thing[x].V
}Thing[maxm];

inline bool Comp(thing x,thing y){
	return x.S+x.W<y.S+y.W;
}

int main(){
	register int i,j,Max=0;
	register long long Ans=0;
	scanf("%d",&N);
	for(i=1;i<=N;i++) scanf("%d%d%d",&W(i),&S(i),&V(i)),Max=max(Max,S(i)+W(i));
	sort(Thing+1,Thing+1+N,Comp);
	for(i=1;i<=N;i++){
		for(j=S(i);j>=0;j--){
			DP[j+W(i)]=max(DP[j+W(i)],DP[j]+V(i));
		}
	}
	for(i=1;i<=Max;i++) Ans=max(Ans,DP[i]);
	printf("%lld",Ans);
	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
# include "iostream"
# include "cstdio"
# include "algorithm"

using namespace std;

const int maxm=1e3+10;
const int maxn=1e4+10;

int N;
long long DP[maxn<<1];

struct thing{
	int W;
	int S;
	int V;
	# define W(x) Thing[x].W
	# define S(x) Thing[x].S
	# define V(x) Thing[x].V
}Thing[maxm];

inline bool Comp(thing x,thing y){
	return x.S+x.W<y.S+y.W;
}

int main(){
	register int i,j,Max=0;
	register long long Ans=0;
	scanf("%d",&N);
	for(i=1;i<=N;i++) scanf("%d%d%d",&W(i),&S(i),&V(i)),Max=max(Max,S(i)+W(i));
	sort(Thing+1,Thing+1+N,Comp);
	for(i=1;i<=N;i++){
		for(j=S(i);j>=0;j--){
			DP[j+W(i)]=max(DP[j+W(i)],DP[j]+V(i));
		}
	}
	for(i=1;i<=Max;i++) Ans=max(Ans,DP[i]);
	printf("%lld",Ans);
	return 0;
}
```