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: Time Limit Exceeded)

#include<stdio.h>
 
long max(long a,long b){
	if(a>b){
    	return a;
    }else{
    	return b;
    }
}
 
long min(long a,long b){
	if(a<b){
    	return a;
    }else{
    	return b;
    }
}
 
int f(long a,long b){
  long c=max(a,b);
  int keta=1;
  for(int i=0;i<10;i++){
  	if(c/10>0){
    	keta++;
      	c/=10;
    }
  }
  return keta;
}
 
 
 
int main(void){
  
  long N;
  int minnum=11;
  scanf("%ld",&N);
  
  for(long a=1;a<=N;a++){
  	if(N%a == 0){
      long b=N/a;
      int res=f(a,b);
      minnum=min(minnum,res);
    }
  }
  
  printf("%ld",minnum);
  
 
return 0;
}