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.