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: Accepted)

import math

n = int(input())
set = []
i = 1
ans = []

t = n**0.5
if len(str(t)) <=8:
    print(len(str((math.floor(t)))))
else:
    while i*i <= n:
        cc = []
        pre = []
        if n % i == 0:
            pre.append(i)
            cc.append(len(str(i)))
            if i != n // i:
                pre.append(n//i)
                cc.append(len(str(n//i)))
                if cc == []:
                    continue
                else:
                    ans.append(pre)
                    result = abs(cc[0]-cc[1])
                    set.append(result)

        i += 1


    min = set.index(min(set))
    print(len(str((max(ans[min])))))