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 figure_count(long long n){
  int cou = 0;
  while(n > 0){
    n /= 10;
    cou++;
  }
  return cou;
}

int main(void)
{
  long long n, i, j;
  int min = 10, a, b, res;
  scanf("%lld", &n);
 
  for(i = 1; i <= sqrt((double)n); i++){
    if(n % i == 0){
      a = figure_count(i);
      b = figure_count(n/i);
      if(a > b) res = a;
      else res = b;
    }
    if(min > res) min = res;
  }

  printf("%d\n", min);
  return 0;
}