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 = [int(x) for x in input().split()]
violate = pos = 0
for i in range(1, n):
    if a[i] < a[i - 1] and violate == 0:
        violate = 1
        pos = i
    elif a[i] < a[i - 1]:
        violate = 2
        break
if violate == 0:
    print(0)
elif violate == 1 and a[n - 1] <= a[0]:
    print(n - pos)
else:
    print(-1)

