#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define fill(name, val) memset(name, val, sizeof(name));
#define vll vector<ll>
#define vvll vector<vll>

/*	Author: 🆉🅴🅽🅾🅻🆄🆂	*/

ll n, dp[1001][10001];	vvll a(1001, vll(3));
bool cmp(vll& a, vll& b){
	return a[0] + a[1] < b[0] + b[1];
}
ll calc(ll i, ll w){
	if(i == n || w > 10000)	return 0;
	if(dp[i][w] != -1)	return dp[i][w];
	dp[i][w] = calc(i+1, w);
	if(a[i][1] >= w)	dp[i][w] = max(dp[i][w], a[i][2] + calc(i+1, w + a[i][0]));
	return dp[i][w];
}
int main(){
	cin>>n;	fill(dp, -1);
	for(ll i = 0; i < n; i++)	cin>>a[i][0]>>a[i][1]>>a[i][2];
	sort(a.begin(), a.begin() + n, cmp);
	cout<<calc(0, 0);
}

// Time: O()
### 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;
#define ll long long
#define fill(name, val) memset(name, val, sizeof(name));
#define vll vector<ll>
#define vvll vector<vll>

/*	Author: 🆉🅴🅽🅾🅻🆄🆂	*/

ll n, dp[1001][10001];	vvll a(1001, vll(3));
bool cmp(vll& a, vll& b){
	return a[0] + a[1] < b[0] + b[1];
}
ll calc(ll i, ll w){
	if(i == n || w > 10000)	return 0;
	if(dp[i][w] != -1)	return dp[i][w];
	dp[i][w] = calc(i+1, w);
	if(a[i][1] >= w)	dp[i][w] = max(dp[i][w], a[i][2] + calc(i+1, w + a[i][0]));
	return dp[i][w];
}
int main(){
	cin>>n;	fill(dp, -1);
	for(ll i = 0; i < n; i++)	cin>>a[i][0]>>a[i][1]>>a[i][2];
	sort(a.begin(), a.begin() + n, cmp);
	cout<<calc(0, 0);
}

// Time: O()
```