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()
list = raw_input().split()

list[0] = int(list[0])
mark = False
passed = False
flag = False
min = 1000000
pos = 0
for i in range(1, n):
    list[i] = int(list[i])
    if list[i - 1] > list[i]:
        if mark:
            flag = True
            break
        else:
            mark = True
            pos = i
if flag == False and mark:
    if list[n - 1] > list[0]: flag = True

if flag:
    print -1
else:
    if pos == 0: print 0
    else: print n - pos
