Given is a positive integer N.
We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K.
- Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K.
In how many choices of K will N become 1 in the end?

-----Constraints-----
- $2 \leq N \leq 10^{12}$
- N is an integer.

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

-----Output-----
Print the number of choices of K in which N becomes 1 in the end.

-----Sample Input-----
6

-----Sample Output-----
3

There are three choices of K in which N becomes 1 in the end: 2, 5, and 6.
In each of these choices, N will change as follows:
- When K=2: $6 \to$ $3 \to$ 1
- When K=5: $6 \to$ 1
- When K=6: $6 \to$ 1

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