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>
long long F(long long i, long long j)
{
   long long k,l=1;
    for(k=1;;k++)
        if(i<10)
            break;
        else
            i/=10;
    for(l=1;;l++)
        if(j<10)
            break;
        else
            j/=10;
    return k>l? k:l;

}
main()
{
	long long p=9876543210; 
    long long N,M,i,j=20;
    scanf("%lld",&N);
    M=(long long)sqrt(N);
    for(i=1;i<=M+1;i++)
    {
        if(N%i==0)
        if(F(i,N/i)<j)
        j=F(i,N/i);
    }
    printf("%lld",j);
}