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 = input().split(' ')
pre = int(a[0])
pos = n
for i in range(1,n):
    x = int(a[i])
    if x<pre:
        pre = x
        pos = i
        break
    pre = x
if pos==n:
    print(0)
else:
    ans = 0
    for j in range(pos,n):
        x = int(a[j])
        if x<pre:
            ans = -1
            break
        pre = x
    if ans==-1:
        print(-1)
    elif int(a[n-1])>int(a[0]):
        print(-1)
    else:
        print (n-pos)