A permutation *p* of size *n* is the sequence *p*<sub class="lower-index">1</sub>, *p*<sub class="lower-index">2</sub>, ..., *p*<sub class="lower-index">*n*</sub>, consisting of *n* distinct integers, each of them is from 1 to *n* (1 ≤ *p*<sub class="lower-index">*i*</sub> ≤ *n*).

A lucky permutation is such permutation *p*, that any integer *i* (1 ≤ *i* ≤ *n*) meets this condition *p*<sub class="lower-index">*p*<sub class="lower-index">*i*</sub></sub> = *n* - *i* + 1.

You have integer *n*. Find some lucky permutation *p* of size *n*.
The first line contains integer *n* (1 ≤ *n* ≤ 10<sup class="upper-index">5</sup>) — the required permutation size.
import sys
from collections import deque
n = int(input())
if n % 4 == 2 or n % 4 == 3:
    print('-1')
    sys.exit(0)

arr = [None] * (n + 1)
qt = deque([i for i in range(1, n + 1)])
mark = set()
while qt:
    while qt and qt[0] in mark:
        qt.popleft()
    if not qt:
        break
    a = qt.popleft()
    while qt and qt[0] in mark:
        qt.popleft()
    if not qt:
        break
    b = qt.popleft()
    for i in range(4):
        mark.add(a) 
        mark.add(b)
        arr[a] = b
        arr[b] = n - a + 1
        a = b
        b = arr[b]

for i in range(1, n + 1):
    if not arr[i]:
        arr[i] = a
        break