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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
int a,b;
#define For(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n) For(i,0,n)

#define F first
#define S second
typedef double db;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

const ll INF=1e17;


ll gcd(ll x,ll y){
return y? gcd(y,x%y):x;
}


int main(){
  ll n,a;
  cin>>n;
  for(int i=pow(n,0.5);i>0;i--){
  if(n%i==0){a=i;break;}
  }
  cout<<to_string(n/a).length()<<endl;
return 0;
}