You are given integer $n$. You have to arrange numbers from $1$ to $2n$, using each of them exactly once, on the circle, so that the following condition would be satisfied:

For every $n$ consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard $2n$ numbers differ not more than by $1$.

For example, choose $n = 3$. On the left you can see an example of a valid arrangement: $1 + 4 + 5 = 10$, $4 + 5 + 2 = 11$, $5 + 2 + 3 = 10$, $2 + 3 + 6 = 11$, $3 + 6 + 1 = 10$, $6 + 1 + 4 = 11$, any two numbers differ by at most $1$. On the right you can see an invalid arrangement: for example, $5 + 1 + 6 = 12$, and $3 + 2 + 4 = 9$, $9$ and $12$ differ more than by $1$.

 [Image] 


-----Input-----

The first and the only line contain one integer $n$ ($1 \le n \le 10^5$).


-----Output-----

If there is no solution, output "NO" in the first line. 

If there is a solution, output "YES" in the first line. In the second line output $2n$ numbers — numbers from $1$ to $2n$ in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.


-----Examples-----
Input
3

Output
YES
1 4 5 2 3 6 
Input
4

Output
NO


-----Note-----

Example from the statement is shown for the first example. 

It can be proved that there is no solution in the second example.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "'''\ndef sdvig():\n    tmp=A[2*n-1]\n    for i in range(2*n-3,0,-2):\n        A[i+2]=A[i]\n    A[1]=tmp\n\ndef check():\n    tmp=0\n    for i in range(n):\n        tmp+=A[i]\n    low,high=tmp,tmp\n    for i in range(2*n):\n        tmp-=A[i]\n        tmp+=A[(i+n)%(2*n)]\n        if(tmp<low):\n            low=tmp\n        if(tmp>high):\n            high=tmp\n        if(high-low>1):\n            return False\n    else:\n        return True\nfor kek in range(100):\n    n=int(input())\n    A=[int(i) for i in range(1,2*n+1)]\n    for i in range(n):\n        sdvig()\n        if(check()):\n            print('YES')\n            for i in A:\n                print(i,end=' ')\n            quit()\n    else:\n        print('NO')\n        quit()\n'''\ndef sdvig():\n    tmp=A[2*(n//2)+1]\n    for i in range(2*(n//2)+2,2*n,2):\n        tArr.append(A[i+1])\n    for i in range(1,2*n-2*(n//2),2):\n        A[i+2*(n//2)]=A[i]\n    A[2*n-1]=tmp\n    for i in range(len(tArr)):\n        A[i*2+1]=tArr[i]\n\n\nn=int(input())\nA=[int(i) for i in range(1,2*n+1)]\ntArr=[]\nif(n%2):\n    sdvig()\n    print('YES')\n    for i in A:\n        print(i,end=' ')\nelse:\n    print('NO')\n    "
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13097