#include <bits/stdc++.h>
using namespace std;
const int N = 1005;
int n;
long long dp[100005];

struct Block {
	int w = 0;
	int s = 0;
	long long v = 0;
	
	void read() {
		cin >> w >> s >> v;
	}

	bool operator <(const Block &b) const {
		return w + s < b.w + b.s;
	}
};

Block blocks[N];

int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);

	cin >> n;

	for (int i = 0; i < n; i++) {
		blocks[i].read();
	}

	sort(blocks, blocks + n);

	for (int i = 0; i < n; i++) {
		Block b = blocks[i];
		for (int w = b.s; w >= 0; w--) {
			dp[w + b.w] = max(dp[w + b.w], dp[w] + b.v);
		}
	}

	cout << *max_element(dp, dp + 100000) << '\n';

	return 0;
}

### 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>
using namespace std;
const int N = 1005;
int n;
long long dp[100005];

struct Block {
	int w = 0;
	int s = 0;
	long long v = 0;
	
	void read() {
		cin >> w >> s >> v;
	}

	bool operator <(const Block &b) const {
		return w + s < b.w + b.s;
	}
};

Block blocks[N];

int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);

	cin >> n;

	for (int i = 0; i < n; i++) {
		blocks[i].read();
	}

	sort(blocks, blocks + n);

	for (int i = 0; i < n; i++) {
		Block b = blocks[i];
		for (int w = b.s; w >= 0; w--) {
			dp[w + b.w] = max(dp[w + b.w], dp[w] + b.v);
		}
	}

	cout << *max_element(dp, dp + 100000) << '\n';

	return 0;
}

```