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: Wrong Answer)

def comp_digit(x,y):
  x = str(x)
  y = str(y)
  return max(len(x),len(y))

def factorize(n):
    b = 2
    fct = []
    sosu = 1
    keta = 10**9
    while b * b <= n:
        while n % b == 0:
            n //= b
            sosu *= b
            digit = comp_digit(n,sosu)
            if keta > digit:
              keta = digit
            #fct.append(b)
        b = b + 1
    if n > 1:
        keta = len(str(n))
    return keta

n = int(input())
print(factorize(n))