#include <bits/stdc++.h>
#define mp make_pair
#define pb push_back
#define pii pair<ll, ll>
#define to second
#define cost first
typedef long long ll;
typedef long double ld;
using namespace std;

struct block {
	ll w, s, v;
	void read() {scanf("%lld%lld%lld", &w, &s, &v);}
};
bool cmp(block a, block b) {
	return a.s + a.w <= b.s + b.w;
}

int main()
{	
	ll i, j, k;
	ll n, mx = 20132;

	cin >> n;
	vector<block> v(n);
	for(int i = 0; i < n; i++) v[i].read();

	sort(v.begin(), v.end(), cmp);

	vector<ll> dp(mx+1, 0);

	for(block X : v) {
		for(int i = min(mx-X.w, X.s); i >= 0; i--) {
			dp[i+X.w] = max(dp[i+X.w], dp[i]+X.v);
		}
	}
	ll answer = 0;
	for(i = 0; i < dp.size(); i++) answer = max(answer, dp[i]);

	cout << answer << endl;

    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>
#define mp make_pair
#define pb push_back
#define pii pair<ll, ll>
#define to second
#define cost first
typedef long long ll;
typedef long double ld;
using namespace std;

struct block {
	ll w, s, v;
	void read() {scanf("%lld%lld%lld", &w, &s, &v);}
};
bool cmp(block a, block b) {
	return a.s + a.w <= b.s + b.w;
}

int main()
{	
	ll i, j, k;
	ll n, mx = 20132;

	cin >> n;
	vector<block> v(n);
	for(int i = 0; i < n; i++) v[i].read();

	sort(v.begin(), v.end(), cmp);

	vector<ll> dp(mx+1, 0);

	for(block X : v) {
		for(int i = min(mx-X.w, X.s); i >= 0; i--) {
			dp[i+X.w] = max(dp[i+X.w], dp[i]+X.v);
		}
	}
	ll answer = 0;
	for(i = 0; i < dp.size(); i++) answer = max(answer, dp[i]);

	cout << answer << endl;

    return 0;
}
```