#include <bits/stdc++.h>
using namespace std;
typedef long long ll;


const int MAXS = 30000;

struct huj 
{
	int w, s, v;
	bool operator <(const huj& b) const {
		return w + s < b.w + b.s;
	}
};

int main()
{
	int n;
	cin >> n;
	vector<huj> a(n);
	for (int i = 0; i < n; i++)
	{
		cin >> a[i].w >> a[i].s >> a[i].v;
	}
	
	sort(a.begin(), a.end());
	vector<ll> dp(MAXS);
	for (int i = 0; i < n; i++)
	{
		for (int w = min(a[i].s, MAXS-1 - a[i].w); w >= 0; w--)
		{
			dp[w + a[i].w] = max(dp[w + a[i].w], dp[w] + a[i].v);
		}
	}
	
	ll ans = 0;
	for (int i = 0; i < MAXS; i++)
	{
		ans = max(ans, dp[i]);
	}
	cout << ans;
	
	return 0;
}

### Prompt

Please create a solution in Cpp to 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>
using namespace std;
typedef long long ll;


const int MAXS = 30000;

struct huj 
{
	int w, s, v;
	bool operator <(const huj& b) const {
		return w + s < b.w + b.s;
	}
};

int main()
{
	int n;
	cin >> n;
	vector<huj> a(n);
	for (int i = 0; i < n; i++)
	{
		cin >> a[i].w >> a[i].s >> a[i].v;
	}
	
	sort(a.begin(), a.end());
	vector<ll> dp(MAXS);
	for (int i = 0; i < n; i++)
	{
		for (int w = min(a[i].s, MAXS-1 - a[i].w); w >= 0; w--)
		{
			dp[w + a[i].w] = max(dp[w + a[i].w], dp[w] + a[i].v);
		}
	}
	
	ll ans = 0;
	for (int i = 0; i < MAXS; i++)
	{
		ans = max(ans, dp[i]);
	}
	cout << ans;
	
	return 0;
}

```