#include <bits/stdc++.h>

using namespace std;
typedef long long ll;

const int mxN = 1010;
int N;

struct block
{
	int solid, weight, val;
};

block a[mxN];
ll dp[mxN][20005];

bool fun(const block& b1, const block& b2)
{
	return (b1.weight + b1.solid < b2.weight + b2.solid);
}

ll rec(int idx, int wt)
{
	if (idx == N)
	{
		return 0;
	}
	if (dp[idx][wt] != -1)
	{
		return dp[idx][wt];
	}
	dp[idx][wt] = rec(idx + 1, wt);
	if (a[idx].solid >= wt)
	{
		dp[idx][wt] = max(dp[idx][wt], a[idx].val + rec(idx + 1, wt + a[idx].weight));
	}
	return dp[idx][wt];
}

int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);

	cin >> N;
	for (int i = 0; i < N; i++)
	{
		cin >> a[i].weight >> a[i].solid >> a[i].val;
	}
	sort(a, a + N, fun);
	memset(dp, -1, sizeof(dp));
	ll answer = rec(0, 0);
	cout << answer;

	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;
typedef long long ll;

const int mxN = 1010;
int N;

struct block
{
	int solid, weight, val;
};

block a[mxN];
ll dp[mxN][20005];

bool fun(const block& b1, const block& b2)
{
	return (b1.weight + b1.solid < b2.weight + b2.solid);
}

ll rec(int idx, int wt)
{
	if (idx == N)
	{
		return 0;
	}
	if (dp[idx][wt] != -1)
	{
		return dp[idx][wt];
	}
	dp[idx][wt] = rec(idx + 1, wt);
	if (a[idx].solid >= wt)
	{
		dp[idx][wt] = max(dp[idx][wt], a[idx].val + rec(idx + 1, wt + a[idx].weight));
	}
	return dp[idx][wt];
}

int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);

	cin >> N;
	for (int i = 0; i < N; i++)
	{
		cin >> a[i].weight >> a[i].solid >> a[i].val;
	}
	sort(a, a + N, fun);
	memset(dp, -1, sizeof(dp));
	ll answer = rec(0, 0);
	cout << answer;

	return 0;
}

```