One day, Twilight Sparkle is interested in how to sort a sequence of integers a1, a2, ..., an in non-decreasing order. Being a young unicorn, the only operation she can perform is a unit shift. That is, she can move the last element of the sequence to its beginning:

a1, a2, ..., an → an, a1, a2, ..., an - 1.

Help Twilight Sparkle to calculate: what is the minimum number of operations that she needs to sort the sequence?

Input

The first line contains an integer n (2 ≤ n ≤ 105). The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 105).

Output

If it's impossible to sort the sequence output -1. Otherwise output the minimum number of operations Twilight Sparkle needs to sort it.

Examples

Input

2
2 1


Output

1


Input

3
1 3 2


Output

-1


Input

2
1 2


Output

0
n = input()
b = [int(i) for i in raw_input().split()]
#compare = ''.join(i for i in sorted(series))

#s = series + series

#a = s.find(compare)

#if a == 0 or a == -1:
#    print a
#else:
#    print n-a

ascending = True
drop_index = 0
drop_count = 0

for i in xrange(n):
    if b[i] > b[(i+1)%n]:
        #print i, (i+1)%n
        drop_count += 1
        drop_index = i

if drop_count == 0:
    print 0
elif drop_count > 1:
    print -1
else:
    print (n-1-drop_index)
