#include <bits/stdc++.h>
#define ll long long
#define pb push_back
#define mp make_pair
using namespace std;
const int maxn = 20100;

class block {
public:
	ll w, s, v;
};

class comparator {
public:
	bool operator()(block a, block b) {
		return a.w + a.s < b.w + b.s;
	}
};

block a[maxn];
int n;

ll dp[1010][maxn];

int main() {
	cin>>n;

	ll w, s, v;
	for(int i=1;i<=n;i++) {
		cin>>w>>s>>v;
		a[i] = {w, s, v};
	}

	sort(a+1, a+n+1, comparator());

	ll result = 0LL;
	for(int i=1;i<=n;i++) {
		for(int j=0;j<maxn;j++) {
			dp[i][j] = dp[i-1][j];
			if(j - a[i].w >= 0 && a[i].s >= j - a[i].w) {
				dp[i][j] = max(dp[i][j], dp[i-1][j-a[i].w] + a[i].v);
			}
			result = max(result, dp[i][j]);
		}
	}
	cout<<result;
}
### Prompt

Please create a solution in cpp 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>
#define ll long long
#define pb push_back
#define mp make_pair
using namespace std;
const int maxn = 20100;

class block {
public:
	ll w, s, v;
};

class comparator {
public:
	bool operator()(block a, block b) {
		return a.w + a.s < b.w + b.s;
	}
};

block a[maxn];
int n;

ll dp[1010][maxn];

int main() {
	cin>>n;

	ll w, s, v;
	for(int i=1;i<=n;i++) {
		cin>>w>>s>>v;
		a[i] = {w, s, v};
	}

	sort(a+1, a+n+1, comparator());

	ll result = 0LL;
	for(int i=1;i<=n;i++) {
		for(int j=0;j<maxn;j++) {
			dp[i][j] = dp[i-1][j];
			if(j - a[i].w >= 0 && a[i].s >= j - a[i].w) {
				dp[i][j] = max(dp[i][j], dp[i-1][j-a[i].w] + a[i].v);
			}
			result = max(result, dp[i][j]);
		}
	}
	cout<<result;
}
```