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 collections import *
from bisect import *
from math import *
from heapq import *
from fractions import *
import sys
input=sys.stdin.readline
t=1
def r(a):
    return ((a*(a-1))//2)
while(t):
    t-=1
    n=int(input())
    a=list(map(int,input().split()))
    b=a[:]
    b.sort()
    s=0
    pos=-1
    for i in range(n-1):
        if(a[i]>a[i+1]):
            pos=i
            break
    a=a[pos+1:]+a[:pos+1]
    if(pos==-1):
        print(0)
        exit(0)
    if(b==a):
        print(n-pos-1)
    else:
        print(-1)
    
