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=int(input())
A=[int(i) for i in input().split()]
B=A[::]
B.sort()
Neg=0
c=True
D=[]
index=-1
if B==A:
    print(0)
else:
    for i in range(1,n):
        if i==n-1:
            d=A[i]-A[i-1]
            if d<0 :
                Neg+=1
                index=i
            if A[0]-A[i]<0:
                Neg+=1
              
            
            
                
        else:
            d=A[i]-A[i-1]
            if d<0:
                Neg+=1
                index=i
            if d>=0:
             D.append(d)
    if c==True and Neg<=1:
       
        print(n-index)
    else:
        print(-1)