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: Wrong Answer)

#include <stdio.h>

int max(unsigned long a, unsigned long b) {
	if (a > b) return a;
	else return b;
}

int main(void) {
	unsigned long N;
	unsigned long a, b, pre, ans;
	int i = 2, digits = 1, x = 10;

	/*int x = 10;
	digits = 1;
	scanf("%d", &N);
	while (N > x) {
		x *= 10;
		digits++;
	}
	printf("%d\n", digits);*/

	scanf("%d", &N);
	a = 1;
	b = N;
	ans = N;
	//printf("%d\n", ans);
	while (a < b) {
		if (N%i == 0) {
			a = i;
			b = N / i;
			pre = max(a, b);
			if (ans > pre) ans = pre;
		}
		i++;
	}

	while (ans >= x) {
		x *= 10;
		digits++;
	}
	//printf("ans:%d\n", ans);
	printf("%d\n", digits);

	return 0;
}