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
#Little Pony and Sort by Shift
a = int(raw_input())
b = map(int,raw_input().split())
c = b
def sort(a,b,c):
    d = True
    for x in xrange(a-1):
        if b[x] <= b[x+1]:
            continue
        else:
#            c = c[:x+1]
            d = False
            break
    for y in xrange(x+1,a-1):
        if b[y] <= b[y+1]: continue
        else:
            return -1
    else:
        if d: return 0
        if b[-1]<= b[0]: return a-x-1
        else: return -1
print sort(a,b,c)

#Little Pony and Expected Maximum
