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())
l=list(map(int,input().split()))
l1=[]
l2=[]
l3=[]
p=-1
k=0
c=0
t=0
for i in range(n-1) :
    if l[i]>l[i+1]:
        p=i
        c=1
        
        l1.append(l[i])
        break
    else :
        l1.append(l[i])
if p!=-1 :
    for j in range(p+1,n) :
        l2.append(l[j])
        k=k+1
else :
    l1.append(l[n-1])
if l2+l1==sorted(l) or k==0 :
    print(k)
else :
    print(-1)
    

    
    
