Factorial (function)

Determine if the factorial of a number, N!, is divisible by N^2.

The factorial, N!, is the product of all integers from 1 to N, expressed as N! = 1 * 2 * 3 * ... * N.

Implement the following function:

• Pascal: function Factorial(N: type): type;

• C++, C#, JAVA: type Factorial(type x)

• Python: def Factorial(x)

This function should accept an integer N (1 ≤ N ≤ 10^9) and return true if N! is divisible by N^2, otherwise return false.

type refers to the appropriate data type based on the language's requirements.

Examples:

• For N = 3, 3! = 6, which is not divisible by 9. Therefore, the function should return false.

• For N = 6, 6! = 720, which is divisible by 36. Thus, the function should return true.

Examples