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
import Queue
from collections import Counter
import math
import bisect
#sys.stdin = open('input.txt', 'r')
#sys.stdout = open('output.txt','w')

N = int(raw_input())
A = map(int, raw_input().split(' '))

res = 0
index = -1
for i in xrange(N-1) :
    if A[i] > A[i+1] :
        index = i
        break
if index == -1 :
    print res
    exit(0)

flag = -1
for i in xrange(index+1,N-1) :
    if A[i] > A[i+1] :
        print -1
        exit(0)
if A[N-1] <= A[0] :
    print N-1-index
else :
    print -1