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,setrecursionlimit,maxint,exit
#setrecursionlimit(2*10**5)
def listInput():
 return map(long,stdin.readline().split())
def printBS(li):
 for i in xrange(len(li)-1):
  stdout.write("%d "%li[i])
 stdout.write("%d\n"%li[-1])
def sin(): return stdin.readline().rstrip()
n=int(sin())
li=listInput()
b=-1
for i in xrange(n-1):
 if li[i]>li[i+1]:
  if b!=-1: 
   print -1
   exit(0)
  b=i
if b==-1:
 print 0
 exit(0)
if li[n-1]<=li[0]:
 print n-b-1
else: print -1