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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#include <math.h>
using namespace std;

int main(){
   long int n;
   cin >>n;
   long int b;
   int min=10000;
   int s=0;
   int t=0;
   long int ax;
   long int bx;
   for(long int a=1;a<=sqrt(n);a++){
      b=n/a;
      if(a*b==n){
            ax=a;
            bx=b;
            s=0;
            t=0;
            while(ax>=1){
               ax/=10;
               s++;
            }
            while(bx>=1){
               bx/=10;
               t++;
            }
            if(min>max(s,t))min=max(s,t);
         }
   }
   cout <<min <<endl;
}