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()))
f, tp = 0, 0
for i in range(1,n):
    if l[i]<l[i-1]:
        f = 1
        tp = i
        break
if f==0:
    print(0)
else:
    flg = 0
    tn = 0
    for i in range(tp,n):
        if l[i]<=l[0] and l[i]>=tn:
            tn = l[i]
        else:
            flg=1
            break
    if flg==0:
        print(n-tp)
    else:
        print(-1)