Problem:
Score : 300 points

Problem Statement

You are given an integer N.

For two positive integers A and B, we will define F(A,B) as the larger of the following: the number of digits in the decimal notation of A, and the number of digits in the decimal notation of B.

For example, F(3,11) = 2 since 3 has one digit and 11 has two digits.

Find the minimum value of F(A,B) as (A,B) ranges over all pairs of positive integers such that N = A \times B.

Constraints

1 \leq N \leq 10^{10}

N is an integer.

Input

The input is given from Standard Input in the following format:

N

Output

Print the minimum value of F(A,B) as (A,B) ranges over all pairs of positive integers such that N = A \times B.

Sample Input 1

10000

Sample Output 1

3

F(A,B) has a minimum value of 3 at (A,B)=(100,100).

Sample Input 2

1000003

Sample Output 2

7

There are two pairs (A,B) that satisfy the condition: (1,1000003) and (1000003,1). For these pairs, F(1,1000003)=F(1000003,1)=7.

Sample Input 3

9876543210

Sample Output 3

6

Solution in Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
        i,min,s:longint;
        n,l:int64;
begin
        readln(n);
        min:=maxlongint;
        for i:=trunc(sqrt(n)) downto 1 do
            if n mod i=0 then
            begin
                s:=11;
                l:=10000000000;
                while n div i div l=0 do
                begin
                    l:=l div 10;
                    dec(s);
                end;
                if s<min then min:=s;
            end;
        writeln(min);
end.