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()))

maxu = max(A)
ind = A.index(maxu)

while ind < n - 1 and A[ind + 1] == A[ind]:
    ind += 1

flag = 1

for i in range(n - 1):
    # print(A[(i + ind + 2) % n], A[(i + ind + 1) % n])
    if A[(i + ind + 2) % n] >= A[(i + ind + 1) % n]:
        continue
    else:
        print(-1)
        flag = 0
        break

"""for i in range(a,n-1):
    if A[a+1] == A[a]:
        a += 1"""

if flag:
    print(n - ind - 1)

"""4
4 4 4 4"""
