Polycarp loves geometric progressions — he collects them. However, as such progressions occur very rarely, he also loves the sequences of numbers where it is enough to delete a single element to get a geometric progression.

In this task we shall define geometric progressions as finite sequences of numbers a1, a2, ..., ak, where ai = c·bi - 1 for some real numbers c and b. For example, the sequences [2, -4, 8], [0, 0, 0, 0], [199] are geometric progressions and [0, 1, 2, 3] is not.

Recently Polycarp has found a sequence and he can't classify it. Help him to do it. Determine whether it is a geometric progression. If it is not, check if it can become a geometric progression if an element is deleted from it.

Input

The first line contains an integer n (1 ≤ n ≤ 105) — the number of elements in the given sequence. The second line contains the given sequence. The numbers are space-separated. All the elements of the given sequence are integers and their absolute value does not exceed 104.

Output

Print 0, if the given sequence is a geometric progression. Otherwise, check if it is possible to make the sequence a geometric progression by deleting a single element. If it is possible, print 1. If it is impossible, print 2.

Examples

Input

4
3 6 12 24


Output

0


Input

4
-8 -16 24 -32


Output

1


Input

4
0 1 2 3


Output

2
import java.io.File;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws IOException {
		InputStream fin = System.in;
		// fin = new FileInputStream(new File("in.txt"));
		Scanner cin = new Scanner(fin);

		while (cin.hasNextInt()) {
			int n = cin.nextInt();
			int[] a = new int[n];

			for (int i = 0; i < n; i++)
				a[i] = cin.nextInt();

			if (n == 1) {
				System.out.println(0);
				continue;
			}

			int cnt = 0;
			for (int i = 0; i < n; i++) {
				if (a[i] == 0)
					cnt++;
			}

			if (cnt == n || cnt == n - 1 && a[0] != 0)
				System.out.println(0);
			else if (cnt != 0 && (cnt == n - 1 || cnt == n - 2 && a[0] != 0))
				System.out.println(1);
			else {
				if (isGeo(a)) {
					System.out.println(0);
				} else if (Delete0(a)) {
					System.out.println(1);
				} else {
					System.out.println(2);
				}
			}
		}
	}

	private static boolean Delete0(int[] a) {
		int n = a.length;
		boolean[] fd = new boolean[n];
		int cnt = 0;

		if (n == 2)
			return true;

		for (int i = 0; i < n; i++)
			if (a[i] == 0)
				cnt++;
		if (cnt > 1)
			return false;
		cnt = 0;

		for (int i = 1; i < n - 1; i++) {
			if (a[i] * a[i] != a[i - 1] * a[i + 1]) {
				fd[i] = false;
				cnt++;
			} else {
				fd[i] = true;
			}
		}

		for (int i = 0; i < n; i++) {
			if (i == 0) {
				if (cnt == 1 && fd[1] == false)
					return true;
			} else if (i == n - 1) {
				if (cnt == 1 && fd[n - 2] == false)
					return true;
			} else {
				int tmp = 0;
				if (fd[i] == false)
					tmp++;
				if (i - 1 > 0 && a[i - 1] * a[i - 1] != a[i - 2] * a[i + 1])
					continue;
				if (i - 1 > 0 && fd[i - 1] == false) {
					tmp++;
				}
				if (i + 1 < n - 1 && a[i + 1] * a[i + 1] != a[i + 2] * a[i - 1])
					continue;
				if (i + 1 < n - 1 && fd[i + 1] == false) {
					tmp++;
				}
				if (cnt == tmp) {
					return true;
				}
			}
		}

		return false;
	}

	private static boolean isGeo(int[] a) {
		int n = a.length;
		if (a[0] == 0 || a[n - 1] == 0)
			return false;
		if (n <= 2)
			return true;
		for (int i = 1; i < n - 1; i++) {
			if (a[i] == 0)
				return false;
			if (a[i] * a[i] != a[i - 1] * a[i + 1])
				return false;
		}
		return true;
	}
}
