# include <bits/stdc++.h>
using namespace std;
# define MOD 1000000007
typedef long long ll;
class box{
public:
    int w, s, v;
};
bool compare(box a, box b){
    return a.s + a.w < b.s + b.w;
}
int main(){
    ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
	int n;
	cin>>n;
	box boxes[n];
	for(int i=0;i<n;i++){
	    cin>>boxes[i].w>>boxes[i].s>>boxes[i].v;
	}
	sort(boxes, boxes + n, compare);
// 	for(int i=0;i<n;i++){
// 	    cout<<boxes[i].w<<" "<<boxes[i].s<<" "<<boxes[i].v<<"\n";
// 	}
    int MAXS = 30001;
	vector<ll> dp(MAXS);
	for(int i=0;i<n;i++){
	    for(int w=min(boxes[i].s, MAXS - boxes[i].w);w>=0;w--){
	        dp[w + boxes[i].w] = max(dp[w + boxes[i].w], dp[w] + boxes[i].v);
	    }
	}
	ll ans = 0;
	for(int i=0;i<MAXS;i++){
	    ans = max(ans, dp[i]);
	}
	cout<<ans;
	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>
using namespace std;
# define MOD 1000000007
typedef long long ll;
class box{
public:
    int w, s, v;
};
bool compare(box a, box b){
    return a.s + a.w < b.s + b.w;
}
int main(){
    ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
	int n;
	cin>>n;
	box boxes[n];
	for(int i=0;i<n;i++){
	    cin>>boxes[i].w>>boxes[i].s>>boxes[i].v;
	}
	sort(boxes, boxes + n, compare);
// 	for(int i=0;i<n;i++){
// 	    cout<<boxes[i].w<<" "<<boxes[i].s<<" "<<boxes[i].v<<"\n";
// 	}
    int MAXS = 30001;
	vector<ll> dp(MAXS);
	for(int i=0;i<n;i++){
	    for(int w=min(boxes[i].s, MAXS - boxes[i].w);w>=0;w--){
	        dp[w + boxes[i].w] = max(dp[w + boxes[i].w], dp[w] + boxes[i].v);
	    }
	}
	ll ans = 0;
	for(int i=0;i<MAXS;i++){
	    ans = max(ans, dp[i]);
	}
	cout<<ans;
	return 0;
}
```