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
n=int(input())
inp=input().split(' ')
inp=list(map(int,inp))
num=0
pos=-1
for i in range(0,len(inp)-1):
    if(inp[i]>inp[i+1] and num==0):
        num=num+1
        pos=i
    elif(inp[i]>inp[i+1]):
        num=num+1
if(num==0):
    print('0')
elif(num>1):
    print('-1')
elif(num==1):
    if(inp[len(inp)-1]<=inp[0]):
        print(len(inp)-pos-1)
    else:
        print('-1')