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
a=int(input())
b=list(map(int,input().split()))
sort=2
for i in range(1,a):
    if b[i]<b[i-1]:
        sort-=1
if b[-1]>b[0]:
    sort-=1
if sort>0:
    x=min(b)
    b=b[::-1]
    while b[-1]==x and len(b)>1:
        b.pop(-1)
    b=b[::-1]
    x=min(b)
    y=b.index(x)
    if b==sorted(b):
        print(0)
    else:
        print(len(b)-y)
else:
    print(-1)
