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 (2.7.6) (judge verdict: Runtime Error)

N = int(raw_input())
a = []
t = []
for i in range(1,N+1):
        for j in range(1,N+1):
                if i*j == N:
                        a.append(i)
                        a.append(j)
                        a.sort() 
                        if a in t:
                                break       
                        else:
                                t.append(a)
                        a = []
        else:
                continue
        break
ans = []
for i in range(0,len(t)):
        x = t[i][0]
        y = t[i][1]
        if x > y:
                ans.append(len(str(x)))
        else:
                ans.append(len(str(y)))
        
print min(ans)