No Story

Since I got tired to write long problem statements, I decided to make this problem statement short. For given positive integer L, how many pairs of positive integers a, b (a ≤ b) such that LCM(a, b) = L are there? Here, LCM(a, b) stands for the least common multiple of a and b.

Constraints

• 1 ≤ L ≤ 1012

Input

For each dataset, an integer L is given in a line. Input terminates when L = 0.

Output

For each dataset, output the number of pairs of a and b.

Example

Input

12 9 2 0

Output

8 3 2

inputFormat

Input

For each dataset, an integer L is given in a line. Input terminates when L = 0.

outputFormat

Output

For each dataset, output the number of pairs of a and b.

Example

Input

12 9 2 0

Output

8 3 2

样例

12
9
2
0

8
3
2

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