#include<bits/stdc++.h>
#define F first
#define S second
#define node pair<pair<ll,ll>,ll>
using namespace std;
typedef long long ll;
ll read(){
	ll a=0,b=getchar(),c=1;
	while(!isdigit(b))c=b=='-'?-1:1,b=getchar();
	while(isdigit(b))a=a*10+b-'0',b=getchar();
	return a*c;
}
node a[1005];
ll n,dp[20005];
bool cmp(node x,node y){
	return x.F.F+x.F.S>y.F.F+y.F.S;
}
int main(){
	n=read();
	for(int i=1;i<=n;i++)
		a[i].F.F=read(),a[i].F.S=read(),a[i].S=read();
	sort(a+1,a+n+1,cmp);
	for(int i=1;i<=n;i++)
		for(int j=a[i].F.F;j<=a[i].F.F+a[i].F.S;j++)
			dp[j-a[i].F.F]=max(dp[j-a[i].F.F],dp[j]+a[i].S);
	printf("%lld",dp[0]);
	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<bits/stdc++.h>
#define F first
#define S second
#define node pair<pair<ll,ll>,ll>
using namespace std;
typedef long long ll;
ll read(){
	ll a=0,b=getchar(),c=1;
	while(!isdigit(b))c=b=='-'?-1:1,b=getchar();
	while(isdigit(b))a=a*10+b-'0',b=getchar();
	return a*c;
}
node a[1005];
ll n,dp[20005];
bool cmp(node x,node y){
	return x.F.F+x.F.S>y.F.F+y.F.S;
}
int main(){
	n=read();
	for(int i=1;i<=n;i++)
		a[i].F.F=read(),a[i].F.S=read(),a[i].S=read();
	sort(a+1,a+n+1,cmp);
	for(int i=1;i<=n;i++)
		for(int j=a[i].F.F;j<=a[i].F.F+a[i].F.S;j++)
			dp[j-a[i].F.F]=max(dp[j-a[i].F.F],dp[j]+a[i].S);
	printf("%lld",dp[0]);
	return 0;
}
```