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: Accepted)

#include <iostream>
#include <math.h>
using namespace std;

// max(Bの桁数)
int calc_keta(long B) {
  int keta = 0;
  while (B > 0) { // n が 0 になるまで
    ++keta;
    B /= 10;
  }
  return keta;
}

int main() {
    long N;
    cin >> N;
 
    int min = calc_keta(N);
    //cout << min <<endl;
    //cout << N << " " << sqrt(N) << endl;
    for (long A = 1; A <= sqrt(N); ++A) { // c: Aピザ購入枚数
       long B = N/A;
       if (A*B==N & calc_keta(B)<min){
       	// cout << "A " << A << " B " << B << endl;
       	min = calc_keta(B);
       } 

    }
    cout << min << endl;
}