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()))
if n==2 and l[0] <= l[1]:
    print(0)
    exit(0)

mini = l[0]
inc = 0
dec = 0
ans = 0
sax = 0
for i in range(n-1):
    if l[i] <= l[i+1]:
        if dec == 0:
            mini = min(l[i],l[i-1])
        inc = 1
        if dec == 1:
            ans+=1
    else:
        ans+=1
        dec +=1
    if inc and dec > 1:
        print(-1)
        exit(0)
    if inc and dec==1 and l[i+1] > mini:
        print(-1)
        exit(0)
    if dec > 1:
        print(-1)
        exit(0)
print(ans)