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>

int keta(long A,long B);

int main(){
  int i,ans,x;
  long N,A,B;
  scanf("%ld",&N);
  ans = 11;
  for(A=1;A*A<=N;A++){
      if(N%A == 0){
        B = N/A;
        x = keta(A,B);
           if(ans>x){
             ans = x;    
           }
         }
      } 
  printf("%ld ",ans);
  return 0;
}
    
int keta(long A,long B){
  int ketaA,ketaB;
  ketaA = 1;
  ketaB = 1;
  if(A>B){
  while(A/10 > 0){
    A /=10;
    ketaA++;
  }
    return ketaA;
  }
  else{
  while(B/10 > 0){
    B /=10;
    ketaB++;
  }
    return ketaB;
  } 
}