#include <bits/stdc++.h>
#define X first
#define Y second
#define pb push_back
#define pii pair<int, int>
typedef long long ll;
using namespace std;

const int MOD = 1e9 + 7;
const ll INF = 1e18;
const int OFF = (1 << 20);

int n;
pair< pair<int, int>, int> p[1002];

bool cmp(pair< pair<int, int>, int> x, pair< pair<int, int>, int> y) {
	return x.X.X+x.X.Y < y.X.X+y.X.Y;
}

ll dp[20002];

int main () {

	cin >> n;
	for (int i = 0; i < n; i++) cin >> p[i].X.X >> p[i].X.Y >> p[i].Y;
	sort(p, p + n, cmp);
	
	ll maxi = 0;
	for (int i = 0; i < n; i++) {
		for (int j = p[i].X.Y; j >= 0; j--) {
			dp[j+p[i].X.X] = max(dp[j+p[i].X.X], dp[j]+p[i].Y);
		
			maxi = max(maxi, dp[j+p[i].X.X]);
		}
	}
	
	cout << maxi;

	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>
#define X first
#define Y second
#define pb push_back
#define pii pair<int, int>
typedef long long ll;
using namespace std;

const int MOD = 1e9 + 7;
const ll INF = 1e18;
const int OFF = (1 << 20);

int n;
pair< pair<int, int>, int> p[1002];

bool cmp(pair< pair<int, int>, int> x, pair< pair<int, int>, int> y) {
	return x.X.X+x.X.Y < y.X.X+y.X.Y;
}

ll dp[20002];

int main () {

	cin >> n;
	for (int i = 0; i < n; i++) cin >> p[i].X.X >> p[i].X.Y >> p[i].Y;
	sort(p, p + n, cmp);
	
	ll maxi = 0;
	for (int i = 0; i < n; i++) {
		for (int j = p[i].X.Y; j >= 0; j--) {
			dp[j+p[i].X.X] = max(dp[j+p[i].X.X], dp[j]+p[i].Y);
		
			maxi = max(maxi, dp[j+p[i].X.X]);
		}
	}
	
	cout << maxi;

	return 0;
}
```