Waterloo Cup--the seventh session of the final: factorial digits

Number of factorial digits

The factorial of 9 equals: 362880
Its binary representation is: 1011000100110000000
There are 19 digits in this number.

Please calculate that the binary of the factorial of 9999 indicates how many digits there are.

Package the seventh session of the final question;

Import Java.math.BigInteger;
public class factorial number {public
	static void Main (string[] args) {
		BigInteger a=f (9999);
		String n=integer.tobinarystring (A.intvalue ());
		System.out.println (A.bitlength ());
	}
	public static BigInteger F (int n) {
		if (n>1) {return
			biginteger.valueof (n). Multiply (f (n-1));
		else{return
			Biginteger.one
		}}

Note: You need to submit an integer, do not fill in any irrelevant content (such as explanation, etc.)