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
def mi():return map(int,input().split())
def li():return list(mi())
def ii():return int(input())
n=ii()
a=li()
f1=0
f2=0
c=0
x=a[0]
for i in range(n-1,-1,-1):
    if(a[i]<=x):
        c+=1
        x=a[i]
    else:
        break
i+=1
a=a[i:]+a[:i]
for i in range(1,n):
    if(a[i]>a[i-1]):
        f2=1
    if(a[i]<a[i-1]):
        f1=1
        break

if(f1):
    print('-1')
elif(f2==0):
    print('0')
else:
    print(c)