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

const int mxN = 1010, mxW = 2e4 + 5;
int N;

struct block {
	int weight, solid, value;
};

block a[mxN];
ll dp[mxN][mxW];

bool comp(const block& b1, const block& b2) {
	return (b1.weight + b1.solid < b2.weight + b2.solid);
}

ll rec(int b, int w) {
	if (b == N) {
		return 0;
	}
	ll& ret = dp[b][w];
	if (ret != -1) {
		return ret;
	}
	ret = rec(b + 1, w);
	if (a[b].solid >= w) {
		ret = max(ret, a[b].value + rec(b + 1, w + a[b].weight));
	}
	return ret;
}

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	
	cin >> N;
	for (int i = 0; i < N; i++) {
		cin >> a[i].weight >> a[i].solid >> a[i].value;
	}
	sort(a, a + N, comp);
	memset(dp, -1, sizeof(dp));
	ll ans = rec(0, 0);
	cout << ans;
	
	return 0;
}

### Prompt

In cpp, your task is to solve 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;
typedef long long ll;

const int mxN = 1010, mxW = 2e4 + 5;
int N;

struct block {
	int weight, solid, value;
};

block a[mxN];
ll dp[mxN][mxW];

bool comp(const block& b1, const block& b2) {
	return (b1.weight + b1.solid < b2.weight + b2.solid);
}

ll rec(int b, int w) {
	if (b == N) {
		return 0;
	}
	ll& ret = dp[b][w];
	if (ret != -1) {
		return ret;
	}
	ret = rec(b + 1, w);
	if (a[b].solid >= w) {
		ret = max(ret, a[b].value + rec(b + 1, w + a[b].weight));
	}
	return ret;
}

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	
	cin >> N;
	for (int i = 0; i < N; i++) {
		cin >> a[i].weight >> a[i].solid >> a[i].value;
	}
	sort(a, a + N, comp);
	memset(dp, -1, sizeof(dp));
	ll ans = rec(0, 0);
	cout << ans;
	
	return 0;
}

```