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 PyPy2 (5.6.0) (judge verdict: Wrong Answer)

import math
n=int(raw_input())
sq=math.sqrt(n)
ans=None



if str(sq)[-2]=='.':
    print len(str(sq))-2
else:
    nu=[]
    while sq>1:
        sq=int(sq)
        if n%sq==0:
            nu.append(str(sq))
            nu.append(str(n/sq))
            sq-=1
            break
        else:
            sq-=1
    if len(nu)!=0:
        nu.sort()
        print len((nu[1]))
    else:
        print len(str(n))