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 = [int(x) for x in input().split()]
count = 0
i = 1
flag = 0
while i<n:
    if a[i-1]<=a[i] :
        i = i+1
        #print(".")
    else:
        flag = 1
        #print("..")
        break
if flag == 1:
    if a[i-1]>a[i] and a[i]<=a[0]:
        count = count + 1
        i  = i + 1
        #print("*")
    else:
        flag=2
        #print("**")
if flag == 1:
    while i < n:
        if a[i-1]<=a[i] and a[i]<= a[0]:
            count = count + 1
            i = i+1
            #print("***")
        else:
            flag = 2
            #print("****")
            break
if flag == 2:
    print(-1)
else:
    print(count)
            
        