#include <cstdio>
#include <algorithm>

using namespace std;

const int MAX_N = 1005;
const int MAX_W = 10005;
typedef long long ll;

int n,w[MAX_N],s[MAX_N],v[MAX_N],sm[MAX_N];
ll dp[MAX_N][MAX_W];

int main()
{
	scanf("%d",&n);
	for (int i=1; i<=n; i++)
	{
		scanf("%d %d %d",w+i,s+i,v+i);
		sm[i]=i;
	}
	sort(sm+1,sm+1+n,[](const int &a, const int &b) {
		int d1=min(s[a]-w[b],s[b]);
		int d2=min(s[b]-w[a],s[a]);
		if (d1==d2)
			return a<b;
		return d1<d2;
	});
	for (int i=1; i<=n; i++)
		for (int j=0; j<MAX_W; j++)
		{
			dp[i][j]=dp[i-1][j];
			if (w[sm[i]]<=j)
				dp[i][j]=max(dp[i][j],
					v[sm[i]]+dp[i-1][min(s[sm[i]],j-w[sm[i]])]);
		}
	ll ans=0;
	for (int i=1; i<=n; i++)
		ans=max(ans,v[sm[i]]+dp[i-1][s[sm[i]]]);
	printf("%lld\n",ans);
	return 0;
}

### 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 <cstdio>
#include <algorithm>

using namespace std;

const int MAX_N = 1005;
const int MAX_W = 10005;
typedef long long ll;

int n,w[MAX_N],s[MAX_N],v[MAX_N],sm[MAX_N];
ll dp[MAX_N][MAX_W];

int main()
{
	scanf("%d",&n);
	for (int i=1; i<=n; i++)
	{
		scanf("%d %d %d",w+i,s+i,v+i);
		sm[i]=i;
	}
	sort(sm+1,sm+1+n,[](const int &a, const int &b) {
		int d1=min(s[a]-w[b],s[b]);
		int d2=min(s[b]-w[a],s[a]);
		if (d1==d2)
			return a<b;
		return d1<d2;
	});
	for (int i=1; i<=n; i++)
		for (int j=0; j<MAX_W; j++)
		{
			dp[i][j]=dp[i-1][j];
			if (w[sm[i]]<=j)
				dp[i][j]=max(dp[i][j],
					v[sm[i]]+dp[i-1][min(s[sm[i]],j-w[sm[i]])]);
		}
	ll ans=0;
	for (int i=1; i<=n; i++)
		ans=max(ans,v[sm[i]]+dp[i-1][s[sm[i]]]);
	printf("%lld\n",ans);
	return 0;
}

```