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)

uses math;
var n:int64;
    ans,i,t:longint;
function tryit(x:int64):longint;
var ans:longint;
    now:int64;
begin
  now:=x;ans:=0;
  while (now<>0) do
  begin
    inc(ans);now:=now div 10;
  end;
  exit(ans);
end;
begin
  readln(n);
  ans:=20;
  for i:=1 to trunc(sqrt(n)) do
    if (n mod i=0) then
    begin
	  t:=max(tryit(i),tryit(n div i));
	  if (t<ans) then ans:=t;
	end;
  writeln(ans);
end.