#include <bits/stdc++.h>
using namespace std;
#define modulo 1000000007
#define mod(mod_x) ((((long long)mod_x+modulo))%modulo)
#define Inf 1000000000000000001


int main(){
	
	int N;
	cin>>N;
	
	vector<vector<int>> V(N);
	for(int i=0;i<N;i++){
		int w,s,v;
		cin>>w>>s>>v;
		
		V[i] = {w+s,w,s,v};
	}
	
	sort(V.begin(),V.end());
	
	vector<vector<long long>> dp(N+1,vector<long long>(20001,-Inf));
	dp[0][0] = 0;
	
	for(int i=0;i<N;i++){
		for(int j=0;j<=20000;j++){
			if(dp[i][j]==-Inf)continue;
			dp[i+1][j] = max(dp[i+1][j],dp[i][j]);
			if(j>V[i][2])continue;
			int to = j + V[i][1];
			if(to<=20000)dp[i+1][to] = max(dp[i+1][to],dp[i][j]+V[i][3]);
		}
	}
	
	long long ans = 0;
	for(int i=0;i<dp.back().size();i++)ans = max(ans,dp.back()[i]);
	
	cout<<ans<<endl;
		
	return 0;
}

### Prompt

Your challenge is to write 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;
#define modulo 1000000007
#define mod(mod_x) ((((long long)mod_x+modulo))%modulo)
#define Inf 1000000000000000001


int main(){
	
	int N;
	cin>>N;
	
	vector<vector<int>> V(N);
	for(int i=0;i<N;i++){
		int w,s,v;
		cin>>w>>s>>v;
		
		V[i] = {w+s,w,s,v};
	}
	
	sort(V.begin(),V.end());
	
	vector<vector<long long>> dp(N+1,vector<long long>(20001,-Inf));
	dp[0][0] = 0;
	
	for(int i=0;i<N;i++){
		for(int j=0;j<=20000;j++){
			if(dp[i][j]==-Inf)continue;
			dp[i+1][j] = max(dp[i+1][j],dp[i][j]);
			if(j>V[i][2])continue;
			int to = j + V[i][1];
			if(to<=20000)dp[i+1][to] = max(dp[i+1][to],dp[i][j]+V[i][3]);
		}
	}
	
	long long ans = 0;
	for(int i=0;i<dp.back().size();i++)ans = max(ans,dp.back()[i]);
	
	cout<<ans<<endl;
		
	return 0;
}

```