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 = map(int, raw_input().split())

k = -1

for i in xrange(n-1) :
    if a[i] > a[i+1] :
        k = i + 1
        break

if k < 0 :
    print 0
    exit()

a = a[k:] + a[:k]
s = n - k

for i in xrange(n-1) :
    if a[i] > a[i+1] :
        s = -1
        break

print s
