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=input()
temp1=raw_input().strip().split()
temp2=map(int,temp1)
l=map(int,temp1)
l.sort()
count=0
'''
for i in range(0,n):
    if(temp2 is l):
        print count
        break
    else:
        shift=temp2[0]
        temp2.remove(shift)
        temp2.append(shift)
        count+=1
if(count==n):
    print -1
'''

for i in range(0,n-1):
    if(temp2[i]>temp2[i+1]):
        count+=1
        var=i
if(temp2[n-1]>temp2[0] and count!=0):
    count+=1
if(count>1):
    print -1
elif(count==0):
    print count
else:
    print n-1-var
    
        
