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
from random import randint
from time import time

last=time()

def interval():
    global last
    print time()-last
    last=time()

def readIn():
    return map(lambda x:int(x),sys.stdin.readline().strip("\n").split(" "))


def main():
    n,=readIn()
    a=readIn()
    drop=-1
    for i in xrange(1,n):
        if a[i]<a[i-1]:
            if drop==-1:
                drop=i
            else:
                print -1
                return
    if drop==-1:
        print 0
    else:
        if a[-1]<=a[0]:
            print n-drop
        else:
            print -1



main()
