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 5.4.1) (judge verdict: Accepted)

/* Coached by rainboy */
#include <stdio.h>

int length(long long n) {
	return n == 0 ? 0 : length(n / 10) + 1;
}

int max(int a, int b) {
	return a > b ? a : b;
}

int main() {
	long long n, a, a_;

	scanf("%lld", &n);
	a_ = 1;
	for (a = 1; a <= n / a; a++)
		if (n % a == 0 && a_ < a)
			a_ = a;
	printf("%d\n", max(length(a_), length(n / a_)));
	return 0;
}