#include<bits/stdc++.h>
using namespace std ;
typedef long long ll ;
#define F first 
#define S second
const ll N = 3033 ;
ll n, dp[2][10111], w[N], v[N], s[N], ans;
pair<ll,ll> P[N] ;
int main ()
{
	scanf("%lld", &n) ;
	for(int i = 1 ; i <= n ; i ++){
		scanf("%lld%lld%lld", &w[i], &s[i], &v[i]) ;
		P[i].F = s[i]+w[i] ;
		P[i].S = i ; 
	}
	sort(P+1, P+n+1) ;
	for(int i = w[P[1].S] ; i < 10111 ; i ++)
		dp[0][i] = v[P[1].S] ;
 	ans = v[P[1].S] ;
 	for(int i = 2 ; i <= n ; i ++){
		for(int j = 0 ; j < 10111 ; j ++)
			dp[1][j] = dp[0][j] ; 
		ans= max(ans, dp[0][s[P[i].S]]+v[P[i].S]) ;
		for(int j = w[P[i].S] ; j <= P[i].F ; j ++){
			dp[0][j] = max(dp[0][j], dp[1][j-w[P[i].S]] + v[P[i].S]) ;
		}
		for(int j = 1 ; j < 10111 ; j ++)
			dp[0][j] = max(dp[0][j], dp[0][j-1]) ;
	}
	cout << ans ;
}

### Prompt

Develop a solution in cpp to the problem described below:

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 ;
#define F first 
#define S second
const ll N = 3033 ;
ll n, dp[2][10111], w[N], v[N], s[N], ans;
pair<ll,ll> P[N] ;
int main ()
{
	scanf("%lld", &n) ;
	for(int i = 1 ; i <= n ; i ++){
		scanf("%lld%lld%lld", &w[i], &s[i], &v[i]) ;
		P[i].F = s[i]+w[i] ;
		P[i].S = i ; 
	}
	sort(P+1, P+n+1) ;
	for(int i = w[P[1].S] ; i < 10111 ; i ++)
		dp[0][i] = v[P[1].S] ;
 	ans = v[P[1].S] ;
 	for(int i = 2 ; i <= n ; i ++){
		for(int j = 0 ; j < 10111 ; j ++)
			dp[1][j] = dp[0][j] ; 
		ans= max(ans, dp[0][s[P[i].S]]+v[P[i].S]) ;
		for(int j = w[P[i].S] ; j <= P[i].F ; j ++){
			dp[0][j] = max(dp[0][j], dp[1][j-w[P[i].S]] + v[P[i].S]) ;
		}
		for(int j = 1 ; j < 10111 ; j ++)
			dp[0][j] = max(dp[0][j], dp[0][j-1]) ;
	}
	cout << ans ;
}

```