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
#!/usr/bin/env python
import sys

if __name__ == '__main__':
    n = int(sys.stdin.readline())
    a = map(int, sys.stdin.readline().split())
    if n == 1:
        print 0
        sys.exit()
    elif n == 2 and a[0] != 0:
        print 0
        sys.exit()
    elif n == 2 and a[0] == 0 and a[1] == 0:
        print 0
        sys.exit()
    elif n == 2:
        print 1
        sys.exit()
    c = a[0]
    if c == 0:
        b = 0
    else:
        b = a[1] / float(c)
    p = a[0] * b
    q = 0
    for x in a[1:]:
        if x != p:
            q += 1
        else:
            p *= b
    if q == 0:
        print 0
        sys.exit()
    elif q == 1:
        print 1
        sys.exit()

    c = a[1]
    if c == 0:
        b = 0
    else:
        b = a[2] / float(c)
    p = a[1] * b
    q = 0
    for x in a[2:]:
        if x != p:
            q += 1
        else:
            p *= b
    if q == 0:
        print 1
        sys.exit()

    c = a[0]
    if c == 0:
        b = 0
    else:
        b = a[2] / float(c)
    p = a[0] * b
    q = 0
    for x in a[2:]:
        if x != p:
            q += 1
        else:
            p *= b
    if q == 0:
        print 1
        sys.exit()

    print 2
