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 Python (3.8.2) (judge verdict: Runtime Error)

n=int(input())

for i in range(1,n//2+1):
    a=i
    if n%a==0:
        b=n//a
        sa=str(a)
        sb=str(b)
        
        #print(a,b,len(sa),len(sb))
        if len(sb)-len(sa)==0:
            ans=len(sb)
            break
        elif len(sb)-len(sa)>=1:
             ans=len(sb)
        else:
            #print(b,sb,len(sa),len(sb))
            break

print(ans)