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
import sys
x=input()
h=map(int,raw_input().split())
F=c=0
def r(x,y):
    global F,c
    c+=1
    if x<=y: 
        return y
    else:
        if F==0:
            F=c
        else:
            print -1
            sys.exit(0)
reduce(r,h)
if F==0:
    print 0
else:
    h=h[F:]+h[:F]
    T=len(h)-F
    F=0
    reduce(r,h)
    if F==0:
        print T
    else:
        print -1