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 getPrimeFactorsList(num):
  pn = 2 #素数は2から
  pflist = [] #素因数のリスト
  while pn * pn <= num: #√numまで調べる
    while num % pn == 0: #現在の素数で割り切れる範囲でループ
      num = num / pn
      pflist.append(pn)
    pn += 1 #割り切れなくなったら次の素数へ
  if num > 1:
    pflist.append(int(num))
    
  return pflist

n = int(input())

pf = getPrimeFactorsList(n)
pf_r = reversed(pf)

a = 1
b = 1
for i in pf_r:
  if a > b:
    b *= i
  else:
    a *= i

print(max([len(list(str(int(a)))), len(list(str(int(b))))]))