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 <cmath>

using namespace std;

int n_digit(long long x) {
	if (x == 0) {
		return 1;
	}
	int ret = 0;
	while (x > 0) {
		ret++;
		x /= 10;
	}
	return ret;
}

int f(long long a, long long b) {
	return max(n_digit(a), n_digit(b));
}

int main() {
	long long n;
	cin >> n;

	int x = sqrt(n);
	while (x > 0) {
		if (n % x == 0) {
			break;
		}
		x--;
	}

	cout << f(n / x, x) << endl;
	return 0;
}