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()
{
	long long n;
	long long a,b;
	cin>>n;
	for(int i=1;i<=sqrt(n);i++)
	{
		if(n%i==0)
		{
			a=i;
			b=n/a;
		}
	}
	cout<<a<<" "<<b<<endl;
	//int p,q;
	int count1=1,count2=1;
	while(a!=1)
	{
		count1++;
		a/=10;
	}
	while(b!=1)
	{
		count2++;
		b/=10;
	}
	if(count1>=count2)
	{
		cout<<count1<<endl;
	}
	else
	{
		cout<<count2<<endl;
	}
	return 0;
}