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 = list(map(int,input().split()))

sub = []
for i in range(1,n):
    x = a[i] - a[i-1]
    sub.append(x)
sub.append(a[0]-a[-1])

c =  0
for i in range(n):
    if sub[i] < 0:
        c += 1
        pos = i
#print(sub)
if c == 0 :
    print(0)
elif c > 1:
    print(-1)
else:
    print(n - pos - 1)
        
