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: Time Limit Exceeded)

#include<iostream>
#include<algorithm>
#include<string>
#include<cstdlib>
#include<map>
#include<iomanip>
#include<sstream>
using namespace std;

int keta(long long int a){
    int cou=0;
    while(a!=0){
        a/=10;
        cou++;
    }
    return cou;
}

int main(void){
    const long long int mod=1000000007;
    long long int n,m=0,a[200005],plsum=0,misum=0,pl=0,mi=0;
    cin>>n;
    for(int i=0;i*i<=n;i++){
        m=i;
    }
     for(int i=m;i>=0;i--){
        if(n%i==0){cout<<keta(n/i);return 0;}
    }
    
}