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
#-------------------------------------------------------------------------------
# Name:        Codeforces
# Author:      Gogol
#-------------------------------------------------------------------------------
import sys
from math import *

def solve():
    n = int(input())
    a = list(map(int,input().split()))
    ok = 0
    t = 0
    if (a == sorted(a)):
        print(0)
        return 0
    if (len (a) == 2):
        print(1)
        return 0
    for i in range(n-1):
        if (a[i] <= a[i+1]):
            ok +=1
        else:
            t = i+1
            break
    b = a[t:n]
    if (b == sorted(b)):
        if (b[-1] > a[0]):    
            print(-1)
        else:
            print(n-t)
    else:
        print(-1)
solve()
