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 <bits/stdc++.h>
using namespace std;
 
#define MD 1000000007
typedef long long int ll;

int main(){
    ll n;
    cin>>n;
    ll cnt=1,a=0,b=0;
    while(1){
        if(n%cnt==0){
            ll tmpa=cnt,tmpb=n/cnt;
            if(tmpa<=tmpb){
                a=tmpa;b=tmpb;
                 cout<<"a="<<a<<"b="<<b<<endl;
            }else{
                break;
            }
       }
        cnt++;
    }
    cout<<floor(log10(b)+1)<<endl;
    return 0;
}