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<cmath>
#define ll long long
using namespace std;

int main(){
	ll n; cin >> n;
	ll flag = static_cast<int>(sqrt(n));
	for(;;++flag){
		bool jud = 0;
		if(!(n % flag)){
			jud = 1;
			for(int i = 0;; ++i){
				if(pow(10, i) == flag){
					cout << i + 1 << endl;
					break;
				}else if(pow(10, i) > flag){
					cout << i << endl;
					break;
				}
			}
		}
		if(jud) break;
	}
	return 0;
}