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>
int main(void){

  int N=0,A=0,B=0,remA=0,remB=0,ketaA=0,ketaB=0;
  int res=0,ans=0;
  int min=10;
  scanf("%d",&N);
  
  for(long long int i=1;i<=10000000000;i++){
  	A=i;
    if(N%A == 0){
    	B=N/A;
      while(A!=1){
      	remA = A%10;
        A = (A-remA)/10;
        ketaA++;
      }
      while(B!=1){
      	remB = A%10;
        B = (A-remB)/10;
        ketaB++;
      }
      if(ketaA>ketaB){
      	res=ketaA;
      }else{
      	res=ketaB;
      }
      if(min>res){
      	ans=res;
      }
    }
  }
  
  printf("%d",ans);


return 0;
}