#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll mx = 2e4;
int main()
{
	int n;
	cin >> n;
	vector<tuple<ll,ll,ll>> blocks;
	for (int q = 0; q < n; q++)
	{
		ll w,s,v;
		cin >> w >> s >> v;
		blocks.emplace_back(w,s,v);
	}
	sort(blocks.begin(), blocks.end(), [](tuple<ll,ll,ll> a, tuple<ll,ll,ll> b){return (get<0>(a)+get<1>(a)) < (get<0>(b)+get<1>(b));});
	vector<vector<ll>> dp(n+1, vector<ll>(mx+1));
	for (int q = 0; q < n; q++)
	{
		for (int w = 1; w <= mx; w++)
		{
			ll w1 = get<0>(blocks[q]), s1 = get<1>(blocks[q]), v1 = get<2>(blocks[q]);
			dp[q+1][w]=max(dp[q][w], dp[q+1][w-1]);
			if (w >= w1 && s1 >= w-w1)
			{
				dp[q+1][w]=max(dp[q+1][w], dp[q][w-w1]+v1);
			}
		}
	}
	cout << dp[n][mx] << "\n";
	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>
using namespace std;
typedef long long ll;
const ll mx = 2e4;
int main()
{
	int n;
	cin >> n;
	vector<tuple<ll,ll,ll>> blocks;
	for (int q = 0; q < n; q++)
	{
		ll w,s,v;
		cin >> w >> s >> v;
		blocks.emplace_back(w,s,v);
	}
	sort(blocks.begin(), blocks.end(), [](tuple<ll,ll,ll> a, tuple<ll,ll,ll> b){return (get<0>(a)+get<1>(a)) < (get<0>(b)+get<1>(b));});
	vector<vector<ll>> dp(n+1, vector<ll>(mx+1));
	for (int q = 0; q < n; q++)
	{
		for (int w = 1; w <= mx; w++)
		{
			ll w1 = get<0>(blocks[q]), s1 = get<1>(blocks[q]), v1 = get<2>(blocks[q]);
			dp[q+1][w]=max(dp[q][w], dp[q+1][w-1]);
			if (w >= w1 && s1 >= w-w1)
			{
				dp[q+1][w]=max(dp[q+1][w], dp[q][w-w1]+v1);
			}
		}
	}
	cout << dp[n][mx] << "\n";
	return 0;
}

```