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)

# _*_ coding:utf-8 _*_

import sys

N = sys.stdin.readline().replace('\n','')
N = int(N)

def Func(a,b):
	if a > b:
		return digit(a)
	else: return digit(b)
		
def digit(num):
	d = len(str(num))
	return d

ans = 10

for i in range(1,N+1):
	if i*i > N: break
	if N % i == 0:
		dum = Func(N//i,i)
		if ans > dum:
			ans = dum

print(ans)