Petya has n integers: 1, 2, 3, ..., n. He wants to split these integers in two non-empty groups in such a way that the absolute difference of sums of integers in each group is as small as possible. 

Help Petya to split the integers. Each of n integers should be exactly in one group.

Input

The first line contains a single integer n (2 ≤ n ≤ 60 000) — the number of integers Petya has.

Output

Print the smallest possible absolute difference in the first line.

In the second line print the size of the first group, followed by the integers in that group. You can print these integers in arbitrary order. If there are multiple answers, print any of them.

Examples

Input

4


Output

0
2 1 4 


Input

2


Output

1
1 1 

Note

In the first example you have to put integers 1 and 4 in the first group, and 2 and 3 in the second. This way the sum in each group is 5, and the absolute difference is 0.

In the second example there are only two integers, and since both groups should be non-empty, you have to put one integer in the first group and one in the second. This way the absolute difference of sums of integers in each group is 1.
import sys
# sys.setrecursionlimit(300000)
# Get out of main functoin
def main():
    pass
# decimal to binary
def binary(n):
    return (bin(n).replace("0b", ""))
# binary to decimal
def decimal(s):
    return (int(s, 2))
# power of a number base 2
def pow2(n):
    p = 0
    while n > 1:
        n //= 2
        p += 1
    return (p)
# if  number is prime in √n time
def isPrime(n):
    if (n == 1):
        return (False)
    else:
        root = int(n ** 0.5)
        root += 1
        for i in range(2, root):
            if (n % i == 0):
                return (False)
        return (True)
# list to string ,no spaces
def lts(l):
    s = ''.join(map(str, l))
    return s
# String to list
def stl(s):
    # for each character in string to list with no spaces -->
    l = list(s)
    # for space in string  -->
    # l=list(s.split(" "))
    return l
# Returns list of numbers with a particular sum
def sq(a, target, arr=[]):
    s = sum(arr)
    if (s == target):
        return arr
    if (s >= target):
        return
    for i in range(len(a)):
        n = a[i]
        remaining = a[i + 1:]
        ans = sq(remaining, target, arr + [n])
        if (ans):
            return ans
# Sieve for prime numbers in a range
def SieveOfEratosthenes(n):
    cnt = 0
    prime = [True for i in range(n + 1)]
    p = 2
    while (p * p <= n):
        if (prime[p] == True):
            for i in range(p * p, n + 1, p):
                prime[i] = False
        p += 1
    for p in range(2, n + 1):
        if prime[p]:
            cnt += 1
            # print(p)
    return (cnt)
# for positive integerse only
def nCr(n, r):
    f = math.factorial
    return f(n) // f(r) // f(n - r)
# 1000000007
mod = int(1e9) + 7
def ssinp(): return sys.stdin.readline().strip()
# s=input()
def iinp(): return int(input())
# n=int(input())
def nninp(): return map(int, sys.stdin.readline().strip().split())
# n, m, a=[int(x) for x in input().split()]
def llinp(): return list(map(int, sys.stdin.readline().strip().split()))
# a=list(map(int,input().split()))
def p(xyz): print(xyz)
def p2(a, b): print(a, b)
import math
########################list.sort(key=lambda x:x[1]) for sorting a list according to second element in sublist
#d1.setdefault(key, []).append(value)
###################ASCII of A-Z= 65-90
##########################ASCII of a-z= 97-122
#import random
#######################from collections import OrderedDict
#from fractions import Fraction
#=#####################===========Speed: STRING < LIST < SET,DICTIONARY==========================
#######################from collections import deque
#for __ in range(iinp()):
n=iinp()
s=(n*(n+1)//2)
if(s%2==0):
    print(0)
    ans=[]
    s1=0
    for i in range(n,0,-1):
        if(s1+i<=s//2):
            ans.append(i)
            s1=s1+i
            if(s1==s//2):
                break
    print(len(ans),*ans)
else:
    print(1)
    ans=[]
    s1=0
    for i in range(n,0,-1):
        if(s1+i<=s//2+1):
            ans.append((i))
            s1+=i
            if (s1 == s // 2 + 1):
                break
    print(len(ans),*ans)



""" Stuff you should look for
    int overflow, array bounds
    special cases (n=1?)
    do something instead of nothing and stay organized
    WRITE STUFF DOWN
	DON'T GET STUCK ON ONE APPROACH"""
