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())
l = list(map(int, input().rstrip().split(" ")))
if n == 1:
    print(0)
elif n == 2:
    if l[0] > l[1]:
        print(1)
    else:
        print(0)
else:
    going_down = False
    la = l[0]
    c = 0
    for i in range(1,n):
        if not going_down:
            if l[i]<l[i-1]:
                going_down=True
                if l[i]>la:
                    c = -1
                    break
                else:
                    c=c+1
        else:
            if l[i]<l[i-1] or l[i]>la:
                c = -1
                break
            c+=1
    print(c)
