#include <bits/stdc++.h>
#define int long long
#define f first
#define s second
using namespace std;
int n,dp[1009][10009];
pair <pair<int,int>,int> v[1009];
int f(int i,int c){
	if(i==n)return 0;
	if(dp[i][c]!=-1)
		return dp[i][c];
	dp[i][c]=f(i+1,c);
	if(v[i].f.f<=c)
		dp[i][c]=max(dp[i][c],v[i].s+f(i+1,min(c-v[i].f.f,v[i].f.s)));
	return dp[i][c];
}
int32_t main(){
	// freopen("input.txt", "r", stdin);
	// freopen("output.txt", "w", stdout);
	cin >> n;
	for(int i=0;i<n;i++){
		cin >> v[i].f.f >> v[i].f.s >> v[i].s;
		v[i].f.f+=v[i].f.s;
	}
	sort(v,v+n);
	reverse(v,v+n);
	for(int i=0;i<n;i++)
		v[i].f.f-=v[i].f.s;
	memset(dp,-1,sizeof(dp));
	int m=0;
	for(int i=0;i<n;i++)
		m=max(v[i].s+f(i+1,v[i].f.s),m);
	cout << m << endl;
}

### 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>
#define int long long
#define f first
#define s second
using namespace std;
int n,dp[1009][10009];
pair <pair<int,int>,int> v[1009];
int f(int i,int c){
	if(i==n)return 0;
	if(dp[i][c]!=-1)
		return dp[i][c];
	dp[i][c]=f(i+1,c);
	if(v[i].f.f<=c)
		dp[i][c]=max(dp[i][c],v[i].s+f(i+1,min(c-v[i].f.f,v[i].f.s)));
	return dp[i][c];
}
int32_t main(){
	// freopen("input.txt", "r", stdin);
	// freopen("output.txt", "w", stdout);
	cin >> n;
	for(int i=0;i<n;i++){
		cin >> v[i].f.f >> v[i].f.s >> v[i].s;
		v[i].f.f+=v[i].f.s;
	}
	sort(v,v+n);
	reverse(v,v+n);
	for(int i=0;i<n;i++)
		v[i].f.f-=v[i].f.s;
	memset(dp,-1,sizeof(dp));
	int m=0;
	for(int i=0;i<n;i++)
		m=max(v[i].s+f(i+1,v[i].f.s),m);
	cout << m << endl;
}

```