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
z=int(input())
x=list(map(int,input().split()))

d=sorted(x)
if d==x:
        print(0)
        exit()
w=x.copy()
f=w[-1]
w.pop(-1)
w.insert(0,f)
if w==d:
        print(1)
        exit()
t=True
c=0
e=x.copy()

for i in range(1,z-1):
         if x[i]!=d[i-1]:
                        t=False
                       
                        break

if x[-1]>x[0]:
        t=False
for i in range(1,z):
        if i!=z-1:
                t=False
                if x[i]<=x[0] and x[i-1]!=x[i]:
                        break
        else:
                if x[i]<=x[0]:
                        t=False
                        break
a=x[:i]
b=x[i:]
if b+a==d:
        print(len(b))
else:
        if t:
                print(z-1)
        else:
                print(-1)

