Count of common factors

Given a set of numbers, the program must find the count of the common factors C excluding 1. 

Input Format: 

First line will contain the integer value N representing how many numbers are passed as input. Next N lines will have the numbers. 
Output Format: 

First line will contain the count of common factors C.

Sample Input/Output: 

Example 1: 

Input: 

2 

100 

75 

Output: 

2 

Explanation: The common factors excluding 1 are 5,25. Hence output is 2 

Example 2: 

Input: 

3 

10 

20 

30 

Output: 

3

Explanation: The common factors excluding 1 are 2,5,10. Hence output is 3

Solution:

from fractions import gcd

from math import sqrt

import functools

n = []

for _ in range(int(input())):

    n.append(int(input()))

g = functools.reduce(gcd,n)

c = 0

for i in range(1,int(sqrt(g))+1):

    if g%i == 0:

        if g/i == i:

            c += 1

        else:

            c += 2

print(c-1)