#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
typedef long long LL;
const LL N = 1000000007;

struct node{
	LL w,s,v;
}b[1005];
bool cmp(node x,node y){
	if(x.s + x.w == y.s + y.w) return x.s < y.s;
	return x.s + x.w < y.s + y.w;
}

LL n,V;
LL dp[1005][30005] = {0};

int main(){
	scanf("%lld",&n);
	for(LL i = 1;i <= n;i ++) scanf("%lld %lld %lld",&b[i].w,&b[i].s,&b[i].v);
	sort(b + 1,b + 1 + n,cmp);
	V = b[n].s + b[n].w;
	for(LL i = 1;i <= n;i ++){
		for(LL v = 0;v <= V;v ++) dp[i][v] = max(dp[i][v],dp[i - 1][v]);
		for(LL v = 0;v <= b[i].s;v ++) dp[i][v + b[i].w] = max(dp[i][v + b[i].w],dp[i - 1][v] + b[i].v);
	}
	LL ans = 0;
	for(LL i = 0;i <= V;i ++) ans = max(ans,dp[n][i]);
	printf("%lld\n",ans);
	return 0;
}
### 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 <cstdio>
#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
typedef long long LL;
const LL N = 1000000007;

struct node{
	LL w,s,v;
}b[1005];
bool cmp(node x,node y){
	if(x.s + x.w == y.s + y.w) return x.s < y.s;
	return x.s + x.w < y.s + y.w;
}

LL n,V;
LL dp[1005][30005] = {0};

int main(){
	scanf("%lld",&n);
	for(LL i = 1;i <= n;i ++) scanf("%lld %lld %lld",&b[i].w,&b[i].s,&b[i].v);
	sort(b + 1,b + 1 + n,cmp);
	V = b[n].s + b[n].w;
	for(LL i = 1;i <= n;i ++){
		for(LL v = 0;v <= V;v ++) dp[i][v] = max(dp[i][v],dp[i - 1][v]);
		for(LL v = 0;v <= b[i].s;v ++) dp[i][v + b[i].w] = max(dp[i][v + b[i].w],dp[i - 1][v] + b[i].v);
	}
	LL ans = 0;
	for(LL i = 0;i <= V;i ++) ans = max(ans,dp[n][i]);
	printf("%lld\n",ans);
	return 0;
}
```