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 main():
    num = input()
    arr = input().split(' ')


    arr_ = [int(i) for i in arr]
    if len(arr_) == 0:
        return -1
    breakpoint = 0
    sol = 0

    for i in range(len(arr_)-1):
        if arr_[i+1] >= arr_[i]:
            breakpoint += 1
        else:
            break
    if arr_[-1] > arr_[0] and breakpoint != len(arr)-1:
        print(-1)
        return

    for i in range(breakpoint+1, len(arr_)-1):
        sol += 1
        if arr_[i+1] < arr_[i]:
            print(-1)
            return
    print(len(arr_)-1 - breakpoint)

if __name__ == '__main__':
    main()
		   	   		 			  					 	 		 	