#include <bits/stdc++.h>
using namespace std;

const int N = 1005;
const int W = 20005;

struct block_t {
	int weight, able, value;
	bool operator < (const block_t &b) const {
		return weight + able < b.weight + b.able;
	}
};

int n;
block_t a[N];
long long f[N][W];

int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i) {
		scanf("%d %d %d", &a[i].weight, &a[i].able, &a[i].value);
	}
	sort(a + 1, a + n + 1);
	for (int i = 1; i <= n; ++i) {
		for (int w = 0; w < W; ++w) {
			f[i][w] = max(f[i][w], f[i - 1][w]);
			if (w <= a[i].able && w + a[i].weight < W) {
				f[i][w + a[i].weight] = max(f[i][w + a[i].weight], f[i - 1][w] + a[i].value);
			}
		}
	}
	long long ans = 0;
	for (int i = 0; i < W; ++i) {
		ans = max(ans, f[n][i]);
	}
	printf("%lld\n", ans);
}
### Prompt

Your task is to create 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;

const int N = 1005;
const int W = 20005;

struct block_t {
	int weight, able, value;
	bool operator < (const block_t &b) const {
		return weight + able < b.weight + b.able;
	}
};

int n;
block_t a[N];
long long f[N][W];

int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i) {
		scanf("%d %d %d", &a[i].weight, &a[i].able, &a[i].value);
	}
	sort(a + 1, a + n + 1);
	for (int i = 1; i <= n; ++i) {
		for (int w = 0; w < W; ++w) {
			f[i][w] = max(f[i][w], f[i - 1][w]);
			if (w <= a[i].able && w + a[i].weight < W) {
				f[i][w + a[i].weight] = max(f[i][w + a[i].weight], f[i - 1][w] + a[i].value);
			}
		}
	}
	long long ans = 0;
	for (int i = 0; i < W; ++i) {
		ans = max(ans, f[n][i]);
	}
	printf("%lld\n", ans);
}
```