#include <bits/stdc++.h>
using namespace std;
 
#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define endl "\n"
#define int long long

const int N=1005;

struct data
{
	int w, s, v;
};

int n;
int cache[N][20005];
data a[N];

bool comp(data &d1, data &d2)
{
	return (d1.w+d1.s)<(d2.w+d2.s);
}

int dp(int idx, int wt)
{
	if(idx==n+1)
		return 0;
	int &ans=cache[idx][wt];
	if(ans!=-1)
		return ans;
	ans=dp(idx+1, wt);
	if(a[idx].s>=wt)
		ans=max(ans, a[idx].v + dp(idx+1, wt+a[idx].w));
	return ans;
}

int32_t main()
{
	IOS;
	memset(cache, -1, sizeof(cache));
	cin>>n;
	for(int i=1;i<=n;i++)
		cin>>a[i].w>>a[i].s>>a[i].v;
	sort(a+1, a+n+1, comp);
	int ans=dp(1, 0);
	cout<<ans;
	return 0;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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>
using namespace std;
 
#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define endl "\n"
#define int long long

const int N=1005;

struct data
{
	int w, s, v;
};

int n;
int cache[N][20005];
data a[N];

bool comp(data &d1, data &d2)
{
	return (d1.w+d1.s)<(d2.w+d2.s);
}

int dp(int idx, int wt)
{
	if(idx==n+1)
		return 0;
	int &ans=cache[idx][wt];
	if(ans!=-1)
		return ans;
	ans=dp(idx+1, wt);
	if(a[idx].s>=wt)
		ans=max(ans, a[idx].v + dp(idx+1, wt+a[idx].w));
	return ans;
}

int32_t main()
{
	IOS;
	memset(cache, -1, sizeof(cache));
	cin>>n;
	for(int i=1;i<=n;i++)
		cin>>a[i].w>>a[i].s>>a[i].v;
	sort(a+1, a+n+1, comp);
	int ans=dp(1, 0);
	cout<<ans;
	return 0;
}
```