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.*;
import java.util.*;

public class Main 
{
    public static void main(String[] args) throws IOException
    {
//      Scanner in = new Scanner(System.in);
        FastScanner sc = new FastScanner(new BufferedReader(new InputStreamReader(System.in)));
        int n = sc.nextInt();
        double[] seq = new double[n];
        int zeroCounter = 0;
        for (int i = 0; i < n; ++i)
        {
            seq[i] = sc.nextDouble();
            if (seq[i] == 0)
                ++zeroCounter;
        }
        // sequence has zeroes
        if (zeroCounter > 0)
        {
            if (n == 1)
                System.out.print(0);
            else if (n == 2)
                if (zeroCounter == 2 || zeroCounter == 1 && seq[0] != 0)
                    System.out.print(0);
                else
                    System.out.print(1);
            else if (zeroCounter == 1)
                {
                    int pos = 0;
                    while (seq[pos] != 0)
                        ++pos;
                    for (int i = pos; i + 1 < n; ++i)
                        seq[i] = seq[i + 1];
                    double q = seq[1] / seq[0];
                    boolean success = true;
                    for (int i = 2; i + 1 < n; ++i)
                        if (seq[i] / seq[i - 1] != q)
                        {
                            success = false;
                            break;
                        }
                    if (success)
                        System.out.print(1);
                    else
                        System.out.print(2);
                }
            else if (zeroCounter == n)
                System.out.print(0);
            else if (zeroCounter == n - 1)
                    if (seq[0] != 0)
                        System.out.print(0);
                    else
                        System.out.print(1);
            else 
                if (zeroCounter == n - 2 && seq[0] != 0)
                    System.out.print(1);
                else
                    System.out.print(2);
            System.out.close();
            return;
        }
        // sequence hasn't any zeroes
        if (n < 3)
        {
            System.out.print(0);
            System.out.close();
            return;
        }
        double q;
        boolean success;
        // check all sequence
        q = seq[1] / seq[0];
        success = true;
        for (int i = 2; i < n; ++i)
            if (seq[i] / seq[i - 1] != q)
            {
                success = false;
                break;
            }
        if (success)
        {
            System.out.print(0);
            System.out.close();
            return;
        }
        // delete first element
        q = seq[2] / seq[1];
        success = true;
        for (int i = 3; i < n; ++i)
            if (seq[i] / seq[i - 1] != q)
            {
                success = false;
                break;
            }
        if (success)
        {
            System.out.print(1);
            System.out.close();
            return;
        }
        // delete second element
        q = seq[2] / seq[0];
        success = true;
        for (int i = 3; i < n; ++i)
            if (seq[i] / seq[i - 1] != q)
            {
                success = false;
                break;
            }
        if (success)
        {
            System.out.print(1);
            System.out.close();
            return;
        }
        // delete element with index more than 1
        q = seq[1] / seq[0];
        success = true;
        int cnt = 0;
        double prev = seq[1];
        for (int i = 2; i < n; ++i)
            if (seq[i] / prev != q)
                ++cnt;
            else
                prev = seq[i];
        if (cnt == 1)
            System.out.print(1);
        else
            System.out.print(2);
        System.out.close();
    }
}

class FastScanner
{
    private BufferedReader Reader;
    private StringTokenizer Tokenizer;
    public FastScanner (BufferedReader Reader)
    {
        this.Reader = Reader;
    }
    public String nextToken() throws IOException
    {
        while (Tokenizer == null || !Tokenizer.hasMoreTokens())
            Tokenizer = new StringTokenizer(Reader.readLine());
        return Tokenizer.nextToken();
    }
    public int nextInt() throws NumberFormatException, IOException
    {
        return Integer.parseInt(nextToken());
    }
    public long nextLong() throws NumberFormatException, IOException
    {
        return Long.parseLong(nextToken());
    }
    public double nextDouble() throws NumberFormatException, IOException
    {
        return Double.parseDouble(nextToken());
    }
}



