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 <algorithm>
#include <cmath>
#include <string>
#include <array>
#include <vector>
#include <functional>
#include <numeric>
#include <limits>
using namespace std;

int main(void) {
	long long n, i, j, kete, a, b, ma = 0, aa, bb, n2;
	cin >> n;
	n2 = sqrt(n);
	for (i = n2; i>=1; i--) {
		a = i;
		if (n%a == 0) {
			b = n / a;
			aa = log10(a) + 1; bb = log10(b) + 1;
			ma = max(aa, bb);
			break;
		}
	}
	
	cout << ma << endl;
	return 0;
}