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, os.path
from collections import*
from copy import*
import math
mod=10**9+7
if(os.path.exists('input.txt')):
    sys.stdin = open("input.txt","r")
    sys.stdout = open("output.txt","w")

n=int(input())
a=list(map(int,input().split()))
s=deepcopy(a)
s.sort()
c=0
if(a==s):
    print(0)
else:
    res=[]
    cnt=0
    point=0
    for i in range(1,n-1):
        if(a[i]<a[i-1] and a[i]<=a[i+1]):
            point=i
            cnt+=1
            break
    if(cnt==0):
        if(a[n-1]<a[n-2] and a[n-1]<=a[0]):
            k=a.pop()
            a=[k]+a
            if(s==a):
                print(1)
            else:
                print(-1)
        else:
            print(-1)
    else:
        res=[]
        for i in range(point,n):
            res.append(a[i])
        for i in range(point):
            res.append(a[i])

        if(res==s):
            print(n-point)
        else:
            print(-1)
            

   





    
    

