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 = []
ID = input().split()

for i in range(n):
    a.append(int(ID[i]))

k = 0
while (k < n - 1 and a[k] <= a[k + 1]):
    k += 1
    
i = k + 1
flag = False
while (i < n - 1):
    if (a[i] > a[i + 1]):
        flag = True
    i += 1

if (k < n - 1 and a[n - 1] > a[0]):
    flag = True
    
if flag == True:
    print(-1)
else:
    print(n - 1 - k)
    
