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
import copy
M=998244353
n=int(input())
a=[int(i) for i in input().split()]
f=[0]*(2*n+1)
p=[0]*(2*n+1)
p[0]=1
b=sorted(copy.copy(a))
qaq=[0]*(n+1)
a=a+a
for i in range(1,2*n+1):
    p[i]=p[i-1]*131%M
    f[i]=(f[i-1]*131+a[i-1])%M
for i in range(1,n+1):
    qaq[i]=(qaq[i-1]*131+b[i-1])%M
ans=-1
for i in range(n+1):
    v1=(f[i+n]-f[i]*p[n]+M)%M
    v2=(qaq[n]-qaq[0]*p[n]+M)%M
    # print(v1,v2)
    if v1==v2:
        ans=n-i
if ans<0:print(ans)
else :print(ans%n)
			    	 	 	     			   	 		 	 	