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
def is_sorted(arr, n):
    for i in range(n-1):
        if arr[i] > arr[i+1]:
            return False
    return True


def main():
    n = input()
    arr = map(int, raw_input().split())

    if is_sorted(arr, n):
        print 0
    else:
        ind = -1
        cnt = 0
        for i in range(n-1):
            if arr[i] > arr[i+1]:
                cnt += 1
                ind = i
                if cnt > 1:
                    print -1
                    return
        if is_sorted(arr[ind+1:]+arr[0:ind+1], n):
            print n-ind-1
        else:
            print -1


if __name__ == "__main__":
    main()
