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
from sys import stdin, stdout
nmbr = lambda: int(stdin.readline())
lst = lambda: list(map(int, stdin.readline().split()))
for _ in range(1):#nmbr()):
    n=nmbr()
    a=lst()
    p=-1
    for i in range(1,n):
        if a[i]<a[i-1]:
            p=i
            break
    if p!=-1:new=a[p:]+a[:p]
    if p==-1:print(0)
    elif new==sorted(a):print(n-p)
    else:print(-1)