There are $N$ blocks, numbered $1,2,\dots ,N$. For each $i$ $(1\le i\le N)$, 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.
• $1\le N\le {10}^3$
• $1\le w_i,s_i\le {10}^4$
• $1\le v_i\le {10}^9$

Input Specification

The first line will contain the integer $N$.

The next $N$ lines will each contain three integers, $w_i,s_i,v_i$.

Output Specification

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

Explanation For Sample 1

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

Explanation For Sample 2

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

Explanation For Sample 3

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

Explanation For Sample 4

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