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

int n;
int w[1055], s[1055];
int v[1055];

long long dp[20055];

int main() {
	cin >> n;
	
	for (int i = 0; i < n; i++) {
		cin >> w[i] >> s[i] >> v[i];
	}
	
	vector<int> vs(n);
	
	for (int i = 0; i < n; i++) {
		vs[i] = i;
	}
	
	// sum(w[1..i - 1]) <= s[i]
	
	sort(vs.begin(), vs.end(), [&] (int v, int u) {
		return s[v] - w[u] < s[u] - w[v];
	});
	
	for (int i = 0; i < n; i++) {
		int u = vs[i];
		
		for (int j = s[u]; j >= 0; j--) {
			dp[j + w[u]] = max(dp[j + w[u]], dp[j] + v[u]);
		}
	}
	
	cout << *max_element(dp, dp + (int)2e4 + 1);
}

### 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;

int n;
int w[1055], s[1055];
int v[1055];

long long dp[20055];

int main() {
	cin >> n;
	
	for (int i = 0; i < n; i++) {
		cin >> w[i] >> s[i] >> v[i];
	}
	
	vector<int> vs(n);
	
	for (int i = 0; i < n; i++) {
		vs[i] = i;
	}
	
	// sum(w[1..i - 1]) <= s[i]
	
	sort(vs.begin(), vs.end(), [&] (int v, int u) {
		return s[v] - w[u] < s[u] - w[v];
	});
	
	for (int i = 0; i < n; i++) {
		int u = vs[i];
		
		for (int j = s[u]; j >= 0; j--) {
			dp[j + w[u]] = max(dp[j + w[u]], dp[j] + v[u]);
		}
	}
	
	cout << *max_element(dp, dp + (int)2e4 + 1);
}

```