#include <bits/stdc++.h>
#define maxn 1000
#define maxs 20001
using namespace std;
typedef long long LL;

struct data {
	int w,s,v;
}ar[maxn];

int n;
LL ans;
LL dp[maxs];

bool comp(const data& a, const data& b) {
	if(a.s + a.w == b.s + b.w)
		return a.w > b.w;
	return a.s + a.w < b.s + b.w;
}

int main() {
	scanf("%d",&n);
	for( int i = 0 ; i < n ; i++ )
		scanf("%d%d%d",&ar[i].w,&ar[i].s,&ar[i].v);
	sort( ar , ar+n , comp );
	memset(dp, -1, sizeof(dp));
	dp[0] = 0;
	for( int i = 0 ; i < n ; i++ ) {
		for( int j = ar[i].s ; j >= 0 ; j-- )
			if( dp[j] != -1 && j + ar[i].w < maxs )
				dp[j+ar[i].w] = max( dp[j+ar[i].w] , dp[j] + ar[i].v );
	}
	for( int i = 0 ; i < maxs ; i++ )
		ans = max( ans , dp[i] );
	printf("%lld\n",ans);
	return 0;
}

### Prompt

Your task is to create 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>
#define maxn 1000
#define maxs 20001
using namespace std;
typedef long long LL;

struct data {
	int w,s,v;
}ar[maxn];

int n;
LL ans;
LL dp[maxs];

bool comp(const data& a, const data& b) {
	if(a.s + a.w == b.s + b.w)
		return a.w > b.w;
	return a.s + a.w < b.s + b.w;
}

int main() {
	scanf("%d",&n);
	for( int i = 0 ; i < n ; i++ )
		scanf("%d%d%d",&ar[i].w,&ar[i].s,&ar[i].v);
	sort( ar , ar+n , comp );
	memset(dp, -1, sizeof(dp));
	dp[0] = 0;
	for( int i = 0 ; i < n ; i++ ) {
		for( int j = ar[i].s ; j >= 0 ; j-- )
			if( dp[j] != -1 && j + ar[i].w < maxs )
				dp[j+ar[i].w] = max( dp[j+ar[i].w] , dp[j] + ar[i].v );
	}
	for( int i = 0 ; i < maxs ; i++ )
		ans = max( ans , dp[i] );
	printf("%lld\n",ans);
	return 0;
}

```