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: Wrong Answer)

#include <iostream>
#include <cmath>

 
using namespace std;
int main() {
 
    int i,j;
    long max_num = 0;
    long min_num,N;
    double sqrtN;
    int counter = 0;
 
    cin >> N;
    sqrtN = sqrt((double)N);
  
    min_num = N;
 
    for(i = 2; i <= (int)sqrtN; i++){
        if(N % i == 0) {
            j = N / i;
            max_num = max(i,j);
            if(min_num >= max_num){
                min_num = max_num;
            }
 
        }
    }

 
    while(min_num > 0){
        min_num /= 10;
        counter++;
    }
 
    cout << counter << endl;
 
    return 0;
}