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 PyPy3 (2.4.0) (judge verdict: Accepted)

# ABC057 C - Digits in Multiplication
from itertools import combinations
def factorize(n):
    retlist = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            while temp%i==0:
                temp //= i
                retlist.append(i)
    if temp!=1:
        retlist.append(temp)

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

    return retlist

N = int(input())

ans = 10000000
L = []
L = factorize(N)
# print(L)

for i in range(1,len(L)+1):
    C = []
    C = list(combinations(L,i))
    # print(C)
    for c in C:
        a,b = 1,0
        for j in range(len(c)):
            a *= c[j]
        b = N//a
        a = str(a)
        b = str(b)
        # print('a:',a,'b:',b)
        ans = min(ans,max(len(a),len(b)))

print(ans)