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
#!/usr/bin/python

import sys

def Ni(): return tuple(map(int, sys.stdin.readline().split()))
def Nil(): return map(int, sys.stdin.readline().split())
def Ns(): return tuple(map(int, sys.stdin.readline().split()))

n = Ni()[0]
a = Nil()

i = 0

def sayno():
    print "-1"
    sys.exit(0)

while i < n - 1:
    if a[i] > a[i+1]:
        dropAt = i
        i += 1
        while i < n - 1 and a[i] <= a[i+1]:
            i += 1

        if i != n - 1:
            sayno()

        if a[-1] > a[0]:
            sayno()

        print n - dropAt - 1
        sys.exit(0)
            
    i += 1

print 0

