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;
using ll = long long;
#define rep(i,n) for(ll i=0;i<(ll)n;++i)

//引数の整数の約数が入った配列を返す関数
vector<ll> func( ll n ){
  vector<ll> a;
  for(ll i=1;i*i<=n;++i){
    if( n%i == 0 ) a.push_back(i);
  }
  return a;
}

ll keta( ll n ){
  if( n == 0 ) return 0;
  return 1 + keta(n/10);
}


int main() {
  ll n;cin >> n;
  vector<ll> a = func(n);
  
  // rep(i,a.size()) cout << a.at(i) << " ";
  // cout << endl;

  ll ans = 9999999999;
  for(ll i=0;i<a.size();++i){
    ll an = a.at(i);
    ll bn = n/an;
    ans = min(ans,max(keta(an),keta(bn)));
  }
  cout << ans << endl;
  return 0;
}