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: Runtime Error)

from itertools import combinations
from functools import reduce
from operator import mul
def prime_dec(n):
  i = 2
  table = []
  while i * i <= n:
    while n % i == 0:
      n /= i
      table.append(int(i))
    i += 1
  if n > 1:
    table.append(n)
  return table

n = int(input())
ps = prime_dec(n)
ps_com = []
for i in range(len(ps)):    
    ps_com += set(combinations(ps, i))
divs = [reduce(mul, k) for k in ps_com if not len(k) == 0]
divs_twin = [(k, int(n/k)) for k in divs]
divs_twin = set(divs_twin)
divs_twin_len = [max(len(str(k[0])) ,len(str(k[1])))  for k in divs_twin]

print(min(divs_twin_len))