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 9.2.1) (judge verdict: Wrong Answer)

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

unsigned GetDigit(unsigned num){
    return log10(num)+1;
}

int main()
{
    int n,root,div,maxnumber,keep;
    cin >> n;
    root = (int)sqrt(n);
    keep = 11;

    for (int i = 1; i <= root; i++)
    {
        div = n / i;
        if (n % i == 0)
        {
            maxnumber = max(GetDigit(i),GetDigit(div));
            keep = min(keep,maxnumber);
            printf("maxnuber = %d\n",maxnumber);
            printf("keep = %d\n",keep);
        }
    }
    cout << keep << endl;
}