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

void sort_s(vector<int>& w, vector<int>& s, vector<int>& v) {
	int n = w.size();
	vector<tuple<int, int, int>> swv;
	for (int i = 0; i < n; i++) {
		swv.emplace_back(s[i] + w[i], -v[i], w[i]);
	}
	sort(swv.begin(), swv.end());
	for (int i = 0; i < n; i++) {
		tie(s[i], v[i], w[i]) = swv[i];
		v[i] *= -1;
		s[i] -= w[i];
	}
}

const int MAX = 1e4;

int main()
{
	int N;
	cin >> N;
	vector<int> w(N), s(N), v(N);
	for (int i = 0; i < N; i++) {
		cin >> w[i] >> s[i] >> v[i];
	}
	sort_s(w, s, v);
	vector<ll> dp(MAX + 1);
	ll res = 0;
	for (int i = 0; i < N; i++) {
		for (int j = s[i]; j >= 0; j--) {
			res = max(res, dp[j] + v[i]);
			if (j + w[i] <= MAX) dp[j + w[i]] = max(dp[j + w[i]], dp[j] + v[i]);
		}
	}
	cout << res << endl;
	return 0;
}

### Prompt

Please formulate 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;
using ll = long long;

void sort_s(vector<int>& w, vector<int>& s, vector<int>& v) {
	int n = w.size();
	vector<tuple<int, int, int>> swv;
	for (int i = 0; i < n; i++) {
		swv.emplace_back(s[i] + w[i], -v[i], w[i]);
	}
	sort(swv.begin(), swv.end());
	for (int i = 0; i < n; i++) {
		tie(s[i], v[i], w[i]) = swv[i];
		v[i] *= -1;
		s[i] -= w[i];
	}
}

const int MAX = 1e4;

int main()
{
	int N;
	cin >> N;
	vector<int> w(N), s(N), v(N);
	for (int i = 0; i < N; i++) {
		cin >> w[i] >> s[i] >> v[i];
	}
	sort_s(w, s, v);
	vector<ll> dp(MAX + 1);
	ll res = 0;
	for (int i = 0; i < N; i++) {
		for (int j = s[i]; j >= 0; j--) {
			res = max(res, dp[j] + v[i]);
			if (j + w[i] <= MAX) dp[j + w[i]] = max(dp[j + w[i]], dp[j] + v[i]);
		}
	}
	cout << res << endl;
	return 0;
}

```