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(input())
a = list(map(int,input().split()))
k = 0
c = min(a)
#789456

ind = a.index(c)
p = len(set(a))

while ind == 0 and a[-1] == c and p!=1:
    a.insert(0,a.pop())
    k += 1

if ind!=0:
    a = a[ind::] + a[:ind]
    k += n - ind

if a == sorted(a):
    print(k)
else:
    print('-1')

# 781234566
# 012345678