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
import math
def findCol(a, n):
    mn = 1234567890
    id = 0
    k = []
    for i in range(1, n):
        if a[i] <= a[id] and a[i] != a[i - 1]:
            id = i
    for i in range(id, n):
        k.append(a[i])
    for i in range (id):
        k.append(a[i])
    a.sort()
    if a != k:
        return -1
    elif id == 0:
        return 0
    else:
        return n - id
n = int(input())
a = list(map(int, input().split()))
print(findCol(a, n))
