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())
x=list(map(int,input().split()))
b=[]
for i in x:
    b.append(i)
b.reverse()

if x==sorted(x):
    print(0)
    exit()
elif (sorted(x)==b) and n!=2 :
    print(-1)
    exit()
elif x[-1]>x[0]:
    print(-1)
    exit()
elif  x[-1]<x[0] or x[-1]==x[0]:
    r=0
    j=-1
    k=0
    while(x[j]<x[k] or x[j]==x[k]):
        r+=1
        j-=1
        k-=1

    if x[:j+1]==sorted(x[:j+1]):
        print(r)
        exit()
    else:
        print(-1)
        exit()
