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())
ll = list(map(int,input().split()))
"""
k = ll[0]
t = True
ans = 0
for i in range(1,n):
    if ll[i] < k:
        k = ll[i]
        ans += 1
        for j in range(i+1,n):
            if ll[j] < k:
                t = False
                break
            ans += 1
    else:
        k = ll[i]
if t == True:
    if ll[0] >= ll[-1] and ans > 0:
        print(ans)

    else:
        print(-1)
else:
    print(-1)
"""


def afz(l):
    return all(l[i] >= l[i - 1] for i in range(1, len(l)))

k = -1
for i in range(1, n):
    if ll[i] < ll[i - 1]:
        k = i

if k == -1:
    print(0)
else:
    if (afz(ll[:k]) and afz(ll[k:])) and ll[-1] <= ll[0]:
        print(n - k)
    else:
        print(-1)