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>

int main(){
  long int n, a, b;
  scanf("%ld",&n);
  
  double dMedium = sqrt(n*1.0);
  int iMedium = dMedium;
//  printf("%lf %d\n",dMedium,iMedium);
  for(int i=iMedium; i>0; i--){
//    printf("%d\n",i);
    if(n%i==0){
      a = i;
      b = n/a;
//      printf("%ld %ld\n",a,b);
      break;
    }
  }
  
  double dLogb = log10(b*1.0);
  int noDigit = dLogb+1; 
  printf("%d",noDigit);
  
  return 0;
}