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
N = input()
mas = map(int, raw_input().split())

c = mas[0]
if N == 1:
    print 0
    exit(0)

b = mas[1]
if N == 2:
    if c == 0:
        if b == 0:
            print 0
        else:
            print 1
    else:
        print 0
    exit(0)
if c == 0:
    b = 0
else:
    b = mas[1] / float(c)
nextel = c * b
q = 0
for el in mas[1:]:
    if q > 1:
        break
    if el == nextel:
        nextel *= b
    else:
        q += 1
if q == 0:
    print 0
    exit(0)
if q == 1:
    print 1
    exit(0)

if c != 0:
    b = mas[2] / float(c)

nextel = c * b
q = 0   
for el in mas[2:]:
    if el == nextel:
        nextel *= b
    else:
        q += 1
        break    
if q == 0:
    print 1
    exit(0)
    
c = mas[1]
if c == 0:
    b = 0
else:
    b = mas[2] / float(c)

nextel = c * b   
for el in mas[2:]:
    if el == nextel:
        nextel *= b
    else:
        print 2
        exit(0)
        
print 1