We have an integer sequence A of length N, where A_1 = X, A_{i+1} = A_i + D (1 \leq i < N ) holds. Takahashi will take some (possibly all or none) of the elements in this sequence, and Aoki will take all of the others. Let S and T be the sum of the numbers taken by Takahashi and Aoki, respectively. How many possible values of S - T are there?

-----Constraints-----

• -10^8 \leq X, D \leq 10^8
• 1 \leq N \leq 2 \times 10^5
• All values in input are integers.

-----Input----- Input is given from Standard Input in the following format: N X D

-----Output----- Print the number of possible values of S - T.

-----Sample Input----- 3 4 2

-----Sample Output----- 8

A is (4, 6, 8). There are eight ways for (Takahashi, Aoki) to take the elements: ((), (4, 6, 8)), ((4), (6, 8)), ((6), (4, 8)), ((8), (4, 6))), ((4, 6), (8))), ((4, 8), (6))), ((6, 8), (4))), and ((4, 6, 8), ()). The values of S - T in these ways are -18, -10, -6, -2, 2, 6, 10, and 18, respectively, so there are eight possible values of S - T.