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())

import sys
def get_ints(): return list(map(int, sys.stdin.readline().strip().split()))
from collections import deque

arr = get_ints()
dicts = {}
flag = 0 
maxnum = max(arr)
items = deque(arr)
flag = 0 
def checkdecreasing(newarr):
    #print(newarr)
    prev = -1 
    for i in newarr:
        if i < prev:
            return False 
        prev = i   
        
    return True 
ansflag = 0 
count = 0 
for i in range(n ):
    if items[-1] == maxnum:
        flag = 1 
        curans = checkdecreasing(items)
        if curans:
            ansflag = 1 
            break 
    
    
    items.rotate(1) 
    count += 1 
if ansflag:
    print(count)
else:
    print(-1)
    
    
    
