#include <bits/stdc++.h>
#define ll long long
#define max_weight 20002 

using namespace std;
 
//ordened by weight and solidness
bool cmp(vector<ll> &a, vector<ll> &b)
{
	return a[0] + a[1] < b[0] + b[1];
}

	
int main()
{
 
	int n;
	cin >> n;

	vector<vector<ll>> a(n, vector<ll>(3));
	//ll a[n][3];

	for (int i = 0; i < n; ++i)
	{
		cin >> a[i][0] >> a[i][1] >> a[i][2];
	}

	sort(a.begin(), a.end(), cmp);

	vector<ll> dp(max_weight);

	
	for (int i = 0; i < n; ++i)
	{
		for (ll aguenta = a[i][1]; aguenta >= 0; aguenta--)
		{
			dp[aguenta + a[i][0]] = max(dp[aguenta + a[i][0]], dp[aguenta] + a[i][2]);
		}


	}

	ll resp = -1;
	for (int i = 0; i < max_weight; ++i)
	{	
		resp = max(resp, dp[i]);
	}


	cout << resp << endl;

 
 
    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>
#define ll long long
#define max_weight 20002 

using namespace std;
 
//ordened by weight and solidness
bool cmp(vector<ll> &a, vector<ll> &b)
{
	return a[0] + a[1] < b[0] + b[1];
}

	
int main()
{
 
	int n;
	cin >> n;

	vector<vector<ll>> a(n, vector<ll>(3));
	//ll a[n][3];

	for (int i = 0; i < n; ++i)
	{
		cin >> a[i][0] >> a[i][1] >> a[i][2];
	}

	sort(a.begin(), a.end(), cmp);

	vector<ll> dp(max_weight);

	
	for (int i = 0; i < n; ++i)
	{
		for (ll aguenta = a[i][1]; aguenta >= 0; aguenta--)
		{
			dp[aguenta + a[i][0]] = max(dp[aguenta + a[i][0]], dp[aguenta] + a[i][2]);
		}


	}

	ll resp = -1;
	for (int i = 0; i < max_weight; ++i)
	{	
		resp = max(resp, dp[i]);
	}


	cout << resp << endl;

 
 
    return 0;
}
```