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 C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<math.h>


typedef long long ll;

int degnum(long long x)
{
	int i;

	for(i=1;x>=10;i++,x/=10)
		;
	return i;
}


int min(int a, int b)
{
	if(a<b) return a;
	return b;
}

int main(void)
{
	ll N, i;
	int result;
	double t;

	while(scanf("%lf", &t)==1)
	{
		N=t;
		t=sqrt(N)+0.1;

		result=50;
		for(i=1;i<t;i++)
		{
			if(N%i==0)
			{
				result=min(result, degnum(N/i));
			}
		}
		printf("%d\n", result);
	}

	return 0;
}