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

typedef tuple<int,int,int> trinca;
typedef long long ll;

const int MAXW = 2*1e4 + 10;

vector<trinca> guloso;
ll dp[MAXW];
int N;

int main(){

	cin >> N;
	for(int i = 1;i<=N;i++){
		int w,s,v;
		cin >> w >> s >> v;
		guloso.push_back(make_tuple(s+w,w,v));
	}

	sort(guloso.begin(),guloso.end());

	ll best=0;
	for(trinca davez : guloso){
		int solid = get<0>(davez), w = get<1>(davez);
		ll v = get<2>(davez);
		for(int i =solid-w;i>=0;i--){

				dp[i+w] = max(dp[i+w],dp[i] + v);

				best=max(best,dp[i+w]);

		}
	}


	cout << best << endl;

	return 0;

}

### Prompt

Generate a CPP solution 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 tuple<int,int,int> trinca;
typedef long long ll;

const int MAXW = 2*1e4 + 10;

vector<trinca> guloso;
ll dp[MAXW];
int N;

int main(){

	cin >> N;
	for(int i = 1;i<=N;i++){
		int w,s,v;
		cin >> w >> s >> v;
		guloso.push_back(make_tuple(s+w,w,v));
	}

	sort(guloso.begin(),guloso.end());

	ll best=0;
	for(trinca davez : guloso){
		int solid = get<0>(davez), w = get<1>(davez);
		ll v = get<2>(davez);
		for(int i =solid-w;i>=0;i--){

				dp[i+w] = max(dp[i+w],dp[i] + v);

				best=max(best,dp[i+w]);

		}
	}


	cout << best << endl;

	return 0;

}

```