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
from sys import *
from math import *
from sys import stdin,stdout
from collections import *

int_arr = lambda : list(map(int,stdin.readline().strip().split()))
str_arr = lambda :list(map(str,stdin.readline().split()))
get_str = lambda : map(str,stdin.readline().strip().split())
get_int = lambda: map(int,stdin.readline().strip().split())
get_float = lambda : map(float,stdin.readline().strip().split())


mod = 1000000007
setrecursionlimit(1000)

n = int(input())
arr = int_arr()
mn = min(arr)
lst = arr.copy()
lst.sort()
if arr == lst:
    print(0)
else:
    mx = -1
    for i in range(len(arr)):
        if arr[i] >= mx:
            mx = arr[i]
        else:
            ele = arr[i]
            ind = i
            break
    if ele == mn:
        arr = arr[ind:] + arr[:ind]
        if arr == lst:
            print(n - ind)
        else:
            print(-1)
    else:
        print(-1)

# 121
# 112