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
size = int(input())
inarr = list(map(int , input().split()))
sortarr = sorted(inarr)
n = 0 
if (inarr == sortarr):
    print(0)
    exit()
for i in range (len(inarr)):
    if inarr[i] > inarr[i+1] :
        n = i + 1
        break
if (n == 0):
    print(-1)
elif(inarr[n:] == sortarr[:-n]):
    print(len(inarr) - n)
else:
    print(-1)
# print(inarr)