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 = int(raw_input(""))
a = raw_input("").split(" ")
a = [int(elem) for elem in a]

down = 0
number = 0
for i in range(0,n-1):
    if a[i]>a[i+1]:
        down+=1
        number = i+1
if a[n-1] > a[0]:
    down+=1
    number = n

if down == 0:
    number = n
#print down
#print "***"
#if down == 1:
#    print 0
if down > 1:
    print -1
else:
    print n - number