#include<bits/stdc++.h>   
using namespace std;
long long n,a,b,i,j,ans,m;
int main() {
cin>>n;
for(i=1;i*i<=n;i++)
{
if(n%i!=0) 
{continue;}
a=i;
b=n/i;
m=max(a,b);
j=0;
while(m!=0){
m=m/10; j++;} 
m=j;}
cout<<m;
return 0;
}  	

### Prompt

Please provide a CPP coded solution to the problem described below:

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.

Examples

Input

10000


Output

3


Input

1000003


Output

7


Input

9876543210


Output

6

### Response

```cpp
#include<bits/stdc++.h>   
using namespace std;
long long n,a,b,i,j,ans,m;
int main() {
cin>>n;
for(i=1;i*i<=n;i++)
{
if(n%i!=0) 
{continue;}
a=i;
b=n/i;
m=max(a,b);
j=0;
while(m!=0){
m=m/10; j++;} 
m=j;}
cout<<m;
return 0;
}  	

```