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: Wrong Answer)

#include<stdio.h>

int max(int a, int b){
  if(a > b) return a;
  else return b;
}

int min(int a, int b){
  if(a < b) return a;
  else return b;
}

int f(int a,int b){

  int 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(){

  int n;
  int minimum = 11;
  scanf("%d",&n);
  for(int a = 1; a <= n ; ++a){
    int b = 0;
    if( n % a == 0 ){
      b = n/a;
      b = f(a,b);
      minimum = min(minimum,b);
    }
  }
  printf("%d",minimum);
  return 0;

}