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()
l=map(int, raw_input().split())
z=sorted(l)
#c=0
#while l[n-1]<l[0]:# and l[n-1]!=l[n-2]:
#   k=l[n-1]
#   del l[n-1]
#   l=[k]+l
#   c+=1
##print l,z
##if l==z:print c
##else:print "-1"
c=0
k=n-1
while k>=0:
    if l[k]>l[(k+1)%n]:break
    else:c+=1
    k-=1
#print k
l=l[k+1:]+l[:k+1]
#print l
f=1
kk=l[0]
for i in l:
    if i!=kk:f=0
if f==1:print 0
elif l==z:print c
else:print "-1"