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
# s = input()
# # print(s)
# p = []
# for i in range(1,len(s)+1):
#
#     if not(s[i-1] == '{' or s[i-1]==',' or s[i-1]==' ' or s[i-1]=='}'):
#         p.append(s[i-1])
#
# x = len(set(p))
# print(x)
n = int(input())
s = list(map(int, input().split()))[:n]

t = s
s0 = sorted(s)
c = 0
for i in range(n):
    if t[i-1]>t[i]:
        p = i
        c+=1

# print(c)

if t==s0:
    print(0)

else:
    if c>1:
        print(-1)
    else:
        print(n-p)
