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 = int(input())
a = list(map(int,input().split()))
b = list()
c = list()
if a == list(sorted(a)):
    print(0)
    exit()
for i in range(1 , n):
    if a[i] < a[i-1]:
        b.append(i)
ans = True
if len(b) == 1:
    for i in range(b[0] , n):
        c.append(a[i])
    for i in range(b[0]):
        c.append(a[i])
    if c != list(sorted(a)):
        ans = False
if len(b) == 1 and ans:
    print(n - b[0])
else:
    print(-1)   