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
INF = 0x3f3f3f3f
n = int(raw_input())
ns = map(int, raw_input().split())

pre = -INF
pivot = []
for i in xrange(n):
    if ns[i] < pre:
        pivot.append(i - 1)
    pre = ns[i]

# print pivot
if not pivot:
    print 0
elif len(pivot) > 1:
    print -1
else:
    p = pivot[0]
    if ns[-1] <= ns[0] <= pivot:
        print n - pivot[0] - 1
    else:
        print -1