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 (3.4.3) (judge verdict: Accepted)

# -*- coding: utf-8 -*-
"""
Created on Sun May 31 17:19:32 2020

@author: NEC-PCuser
"""

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            while temp%i==0:
                temp //= i
                arr.append(i)

    if temp!=1:
        arr.append(temp)

    if arr==[]:
        arr.append(n)

    return arr

def multiplication(n):
    ans = len(str(n))
    for i in range(2, int(-(-n**0.5//1))+1):
        if (n % i == 0):
            ans = max([len(str(i)), len(str(n // i))])
    return ans
        

if __name__ == "__main__":
    N = int(input())
    """
    l = factorization(N)
    """
    print(multiplication(N))
    """
    minimu = 10 ** 10
    ans = 0
    for i in range(0, 2**len(l)):
        a = 1
        b = 1
        for j in range(0, len(l)):
            if ((i >> j) & 1):
                a *= l[j]
            else:
                b *= l[j]
        if (abs(a - b) < minimu):
            minimu = abs(a - b)
            ans = max([len(str(a)), len(str(b))])
    print(ans)
    """