#include <bits/stdc++.h>
#define ll long long
#define ld long double
using namespace std;
int n;
pair < pair < int , int > , int > t[1005];
bool cmp( pair < pair < int, int > , int > a , pair < pair < int , int > , int > b )
{
	return b.first.first+b.first.second>a.first.first+a.first.second;
}
ll dp[50005];
int main(){
	cin>>n;
	for(int i=0;n>i;i++)
	{
		cin>>t[i].first.first>>t[i].first.second>>t[i].second;
	}
	sort(t,t+n,cmp);
	fill(dp,dp+20003,-1e18);
	dp[0]=0;
	for(int i=0;n>i;i++)
	{
		int val=t[i].second;
		int waga=t[i].first.first;
		int wyt=t[i].first.second;
		for(int j=wyt;j>=0;j--)
			if(dp[j]>=0)
				dp[j+waga]=max(dp[j+waga],dp[j]+val);
	}
	ll out=0;
	for(int i=0;20005>=i;i++)
		out=max(out,dp[i]);
	cout<<out;
	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>
#define ll long long
#define ld long double
using namespace std;
int n;
pair < pair < int , int > , int > t[1005];
bool cmp( pair < pair < int, int > , int > a , pair < pair < int , int > , int > b )
{
	return b.first.first+b.first.second>a.first.first+a.first.second;
}
ll dp[50005];
int main(){
	cin>>n;
	for(int i=0;n>i;i++)
	{
		cin>>t[i].first.first>>t[i].first.second>>t[i].second;
	}
	sort(t,t+n,cmp);
	fill(dp,dp+20003,-1e18);
	dp[0]=0;
	for(int i=0;n>i;i++)
	{
		int val=t[i].second;
		int waga=t[i].first.first;
		int wyt=t[i].first.second;
		for(int j=wyt;j>=0;j--)
			if(dp[j]>=0)
				dp[j+waga]=max(dp[j+waga],dp[j]+val);
	}
	ll out=0;
	for(int i=0;20005>=i;i++)
		out=max(out,dp[i]);
	cout<<out;
	return 0;
}

```