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>
typedef long long ll;

int f(ll a, ll b)
{
  int i = 0, j = 0;
  while(a > 0){
    a /= 10;
    i++;
  }
  while(b > 0){
    b /= 10;
    j++;
  }
  return (i > j ? i : j);
}

int
main(int argc, char *argv[])
{
  ll n;
  scanf("%lld", &n);

  ll k = 1; int ans = 100; int temp;
  while(k * k <= n){
    if(n % k == 0){
      temp = f(k, n / k);
      ans = (ans > temp ? temp : ans);
    }
    k++;
  }
  printf("%d\n", ans);

  return 0;
}