Problem Statement

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?

Input

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

Output

Print the number of possible values of S - T.

Constraints

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

Sample Input 1

3 4 2

Sample Output 1

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.

Sample Input 2

2 3 -3

Sample Output 2

2

A is (3, 0). There are two possible values of S - T: -3 and 3.

Sample Input 3

100 14 20

Sample Output 3

49805

见题面 Input 部分

见题面 Output 部分