Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

3
2 2 20
2 1 30
3 1 40

Sample Output 1

50

If Blocks 2, 1 are stacked in this order from top to bottom, this tower will satisfy the condition, with the total value of 30 + 20 = 50.

Sample Input 2

4
1 2 10
3 1 10
2 4 10
1 6 10

Sample Output 2

40

Blocks 1, 2, 3, 4 should be stacked in this order from top to bottom.

Sample Input 3

5
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000

Sample Output 3

5000000000

The answer may not fit into a 32-bit integer type.

Sample Input 4

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

Sample Output 4

22

We should, for example, stack Blocks 5, 6, 8, 4 in this order from top to bottom.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
#define ll long long
const int N = 1e3+7, M = 1e4+7;
ll f[N][M];
struct node
{
	int w;
	int s;
	int v;
}q[N];
bool cmp(node a, node b)
{
	if(a.s==b.s)
	{
		return a.w < b.w;
	}
	return a.s > b.s;
}
ll calc(int n, int m)
{
	ll ans = 0;
	memset(f, 0xcf, sizeof(f));
    for(int i = 1; i <= n; i++)
    {
    	for(int j = q[i].w; j <= m; j++)
    	{
    		int p = min(j-q[i].w, q[i].s);
    		f[i][p] = max(f[i][p], f[i-1][j]+q[i].v);
    	}
    	f[i][q[i].s] = max(f[i][q[i].s], (ll)q[i].v);
    }
    for(int i = 1; i <= n; i++)
    {
    	for(int j = 0; j <= m; j++)
    	{
    		ans = max(ans, f[i][j]);
    	}
    }
    return ans;
}
int main()
{
    ll ans = 0;
    int n, m = 0;
    srand(time(0));
    scanf("%d", &n);
    for(int i = 1; i <= n; i++)
    {
    	scanf("%d%d%d", &q[i].w, &q[i].s, &q[i].v);
    	m = max(m, q[i].s);
    }
    sort(q+1, q+1+n, cmp);
    ans = max(ans, calc(n, m));
    for(int i = 1; i <= 100; i++)
    {
    	random_shuffle(q+1, q+1+n);
    	ans = max(ans, calc(n, m));
    }
    printf("%lld\n", ans);
    return 0;
}