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()
A = map(int, raw_input().split())
c, d = 0, 0
clash = False
possible = True
for i in xrange(n):
    if c > A[i]:
        if clash:
            possible = False
            break
        else:
            clash = True
            d = n - i
    c = A[i]
    
if not clash:
    print 0
else:
    if possible and A[-1] <= A[0]:
        print d
    else:
        print -1
