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.util.*;

public class C48D {
    public static void main(String args[]){
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        double nums[]=new double[n];
        int z=0;
        for(int i=0;i<n;i++){
            nums[i]=sc.nextDouble();
            if(nums[i]==0)
                z++;
        }
        int x=0;
        double c1=0;
        double c2=0;
        double c3=0;
        double c4=0;
        double cc=0;
        int count=-1;
        int res=0;

	if(z==nums.length)
		res=0;
        else{
            if(z>1){
		if (z==nums.length-1){
                    if( nums[0]!=0)
            		res=0;
                    else 
                        res=1;
                }
		else if(z==nums.length-2 && nums[0]!=0)
	  		res=1;
                else
                    res=2;
            }
            else if(n<=3){
                if(z == 1){
                    if(n==2){
			if(nums[1]==0)
				res=0;
			else
				res=1;
                    }
                    if(n==3)
			res=1;

                }

                else if(z == 0 && n == 2)
                    res=0;

                else if(n == 3){

                    if(nums[2]/nums[1]==nums[1]/nums[0])
                        res=0;
                    else
                        res=1;
                }
            }
            else if(n>4){
            
            c1=nums[1]/nums[0];
            c2=nums[2]/nums[1];
            c3=nums[3]/nums[2];
            c4=nums[4]/nums[3];

            if(c1==c2)
                cc=c1;
            else if(c1==c3)
                cc=c1;
            else if(c1==c4)
                cc=c1;
            else if(c2==c3)
                cc=c2;
            else if(c2==c4)
                cc=c2;
            else if(c3==c4)
                cc=c3;
            else
                res=2;

            //System.out.println(cc);
            if(res!=2){

            for(int i=0;i<nums.length-1;i++){

                if(cc!=nums[i+1]/nums[i]){
                    x++;
                    count=i+1;
                   
                }
            }


            if(x>2){
                res=2;
            }
            else if(count!=-1){
                if(count!=nums.length-1 && count!= 1 ){
                    if(cc==(double)nums[count]/nums[count-2])
                        res=1;
                    else
                        res=2;
                }
                else{
                    res=1;
                }
            }
            else{
                res=0;
            }
        }
        }
        else if(n == 4){
            
            c1=nums[1]/nums[0];
            c2=nums[2]/nums[1];
            c3=nums[3]/nums[2];

            if(c1==c2){
                if(c1!=c3)
                    res=1;
                else
                    res=0;
            }
            else if(c1==c3){
                if(c1!=c2)
                    res=1;
                else
                    res=0;
            }
            else if(c2==c3){
                res=1;
            }
            else{

                if(nums[3]/nums[1]==nums[1]/nums[0])
                    res=1;
                else if(nums[2] / nums[0] == nums[3] / nums[2])
                    res=1;
                else
                    res=2;

            }



        }
        }
        System.out.println(res);
    }//main
}//class
