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)

def dig(x):
    c=0 
    while x:
        c+=1 
        x//=10 
    return c 
n=int(input())
def div(x):
    if x==1:
        return [1] 
    d=[1,x]
    for i in range(2,int(x**0.5)+1):
        if x%i==0:
            d.append(i)
            if i!=x//i:
                d.append(x//i)
    return d 
d=div(n)
mini=10**9 
for i in d: 
    b=n//i 
    mini=min(mini,max(dig(b),dig(i)))
print(mini)