Problem:
Score : 1000 points

Problem Statement

We will call a string x good if it satisfies the following condition:

Condition: x can be represented as a concatenation of two copies of another string y of length at least 1.

For example, aa and bubobubo are good; an empty string, a, abcabcabc and abba are not good.

Eagle and Owl created a puzzle on good strings.
Find one string s that satisfies the following conditions. It can be proved that such a string always exists under the constraints in this problem.

1 ≤ |s| ≤ 200

Each character of s is one of the 100 characters represented by the integers 1 through 100.

Among the 2^{|s|} subsequences of s, exactly N are good strings.

Constraints

1 ≤ N ≤ 10^{12}

Input

Input is given from Standard Input in the following format:

N

Output

In the first line, print |s|, the length of s.
In the second line, print the elements in s in order, with spaces in between. Any string that satisfies the above conditions will be accepted.

Sample Input 1

7

Sample Output 1

4
1 1 1 1

There are two good strings that appear as subsequences of s: (1,1) and (1,1,1,1). There are six occurrences of (1,1) and one occurrence of (1,1,1,1), for a total of seven.

Sample Input 2

299

Sample Output 2

23
32 11 11 73 45 8 11 83 83 8 45 32 32 10 100 73 32 83 45 73 32 11 10

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Linq.Expressions;
using System.IO;
using System.Text;
using System.Diagnostics;

using static util;
using P = pair<int, int>;

using Binary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.ParameterExpression,
                           System.Linq.Expressions.BinaryExpression>;
using Unary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.UnaryExpression>;

class Program
{
    static StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
    static Scan sc = new Scan();
    const int M = 1000000007;
    const double eps = 1e-11;
    static readonly int[] dd = { 0, 1, 0, -1, 0 };
    static void Main()
    {
        var n = sc.Long;
        var ans = new List<int>();
        int num = 1;
        mymath.Mod = long.MaxValue;
        var combs = mymath.getcombs(50);
        while (n > 0)
        {
            int c = 1;
            while ((1L << c) - 1 <= n)
            {
                ++c;
            }
            n -= (1L << c - 1) - 1;
            if (n > 1) {
                long ma = 0;
                int maid = -1;
                for (int i = 1; i < c; i++)
                {
                    int lim = Math.Min(i, c - i);
                    long ad = 0;
                    for (int j = 0; j <= lim; j++)
                    {
                        if (combs[i][j] * (double)combs[c - i][j] > 1e13) {
                            ad = (long)1e16;
                            break;
                        }
                        ad += combs[i][j] * combs[c - i][j];
                        if (ad > n) break;
                    }
                    if (ad <= n && ma < ad) {
                        ma = ad;
                        maid = i;
                    }
                }
                if (maid != -1) {
                    n -= ma;
                    if (n > 1) {
                        long mma = 0;
                        int mmaid = -1;
                        for (int i = 1; i < c; i++)
                        {
                            int lim = Math.Min(i, c - i);
                            long ad = 0;
                            for (int j = 0; j <= lim; j++)
                            {
                                if (combs[i][j] * (double)combs[c - i][j] > 1e13) {
                                    ad = (long)1e16;
                                    break;
                                }
                                ad += combs[i][j] * combs[c - i][j];
                                if (ad > n) break;
                            }
                            if (ad <= n && mma < ad) {
                                mma = ad;
                                mmaid = i;
                            }
                        }
                        if (mmaid != -1) {
                            n -= mma;

                            if (n > 1) {
                                long mmma = 0;
                                int mmmaid = -1;
                                for (int i = 1; i < c; i++)
                                {
                                    int lim = Math.Min(i, c - i);
                                    long ad = 0;
                                    for (int j = 0; j <= lim; j++)
                                    {
                                        if (combs[i][j] * (double)combs[c - i][j] > 1e13) {
                                            ad = (long)1e16;
                                            break;
                                        }
                                        ad += combs[i][j] * combs[c - i][j];
                                        if (ad > n) break;
                                    }
                                    if (ad <= n && mmma < ad) {
                                        mmma = ad;
                                        mmmaid = i;
                                    }
                                }
                                if (mmmaid != -1) {
                                    n -= mmma;
                                    for (int i = 0; i < mmmaid; i++)
                                    {
                                        ans.Add(num);
                                    }
                                    ans.Add(num + 3);
                                    for (int i = mmmaid; i < mmaid; i++)
                                    {
                                        ans.Add(num);
                                    }
                                    ans.Add(num + 2);
                                    for (int i = mmaid; i < maid; i++)
                                    {
                                        ans.Add(num);
                                    }
                                    ans.Add(num + 1);
                                    for (int i = maid; i < c; i++)
                                    {
                                        ans.Add(num);
                                    }
                                    ans.Add(num + 1);
                                    ans.Add(num + 2);
                                    ans.Add(num + 3);
                                    num += 4;
                                }
                                else {
                                    for (int i = 0; i < mmaid; i++)
                                    {
                                        ans.Add(num);
                                    }
                                    ans.Add(num + 2);
                                    for (int i = mmaid; i < maid; i++)
                                    {
                                        ans.Add(num);
                                    }
                                    ans.Add(num + 1);
                                    for (int i = maid; i < c; i++)
                                    {
                                        ans.Add(num);
                                    }
                                    ans.Add(num + 1);
                                    ans.Add(num + 2);
                                    num += 3;
                                }
                            }
                            else {
                                for (int i = 0; i < mmaid; i++)
                                {
                                    ans.Add(num);
                                }
                                ans.Add(num + 2);
                                for (int i = mmaid; i < maid; i++)
                                {
                                    ans.Add(num);
                                }
                                ans.Add(num + 1);
                                for (int i = maid; i < c; i++)
                                {
                                    ans.Add(num);
                                }
                                ans.Add(num + 1);
                                ans.Add(num + 2);
                                num += 3;
                            }
                        }
                        else {
                            for (int i = 0; i < maid; i++)
                            {
                                ans.Add(num);
                            }
                            ans.Add(num + 1);
                            for (int i = 0; i < c - maid; i++)
                            {
                                ans.Add(num);
                            }
                            ans.Add(num + 1);
                            num += 2;
                        }
                    }
                    else {
                        for (int i = 0; i < maid; i++)
                        {
                            ans.Add(num);
                        }
                        ans.Add(num + 1);
                        for (int i = 0; i < c - maid; i++)
                        {
                            ans.Add(num);
                        }
                        ans.Add(num + 1);
                        num += 2;
                    }
                }
                else {
                    for (int i = 0; i < c; i++)
                    {
                        ans.Add(num);
                    }
                    ++num;
                }
            }
            else {
                for (int i = 0; i < c; i++)
                {
                    ans.Add(num);
                }
                ++num;
            }
        }
        Prt(ans.Count);
        Prt(ans);
        sw.Flush();
    }
    static void DBG(string a) { Console.WriteLine(a); }
    static void DBG<T>(IEnumerable<T> a) { DBG(string.Join(" ", a)); }
    static void DBG(params object[] a) { DBG(string.Join(" ", a)); }
    static void Prt(string a) { sw.WriteLine(a); }
    static void Prt<T>(IEnumerable<T> a) { Prt(string.Join(" ", a)); }
    static void Prt(params object[] a) { Prt(string.Join(" ", a)); }

    // for AOJ
    // static string Join<T>(string sep, IEnumerable<T> a) { return string.Join(sep, a.Select(x => x.ToString()).ToArray()); }
    // static void DBG<T>(IEnumerable<T> a) { DBG(Join(" ", a)); }
    // static void DBG(params object[] a) { DBG(Join(" ", a)); }
    // static void Prt<T>(IEnumerable<T> a) { Prt(Join(" ", a)); }
    // static void Prt(params object[] a) { Prt(Join(" ", a)); }
}
class pair<T, U> : IComparable<pair<T, U>> where T : IComparable<T> where U : IComparable<U>
{
    public T v1;
    public U v2;
    public pair(T v1, U v2) {
        this.v1 = v1;
        this.v2 = v2;
    }
    public int CompareTo(pair<T, U> a) {
        return v1.CompareTo(a.v1) != 0 ? v1.CompareTo(a.v1) : v2.CompareTo(a.v2);
    }
    public override string ToString() {
        return "(" + v1 + "," + v2 + ")";
    }
}
static class util
{
    public static pair<T, U> make_pair<T, U>(T v1, U v2) where T : IComparable<T> where U : IComparable<U> {
        return new pair<T, U>(v1, v2);
    }
    public static T sqr<T>(T a) { return Operator<T>.Multiply(a, a); }
    public static T Max<T>(params T[] a) { return a.Max(); }
    public static T Min<T>(params T[] a) { return a.Min(); }
    public static void swap<T>(ref T a, ref T b) { var t = a; a = b; b = t; }
    public static void swap<T>(this IList<T> a, int i, int j) { var t = a[i]; a[i] = a[j]; a[j] = t; }
    public static T[] copy<T>(this IList<T> a) {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
}
static class Operator<T>
{
    static readonly ParameterExpression x = Expression.Parameter(typeof(T), "x");
    static readonly ParameterExpression y = Expression.Parameter(typeof(T), "y");
    public static readonly Func<T, T, T> Add = Lambda(Expression.Add);
    public static readonly Func<T, T, T> Subtract = Lambda(Expression.Subtract);
    public static readonly Func<T, T, T> Multiply = Lambda(Expression.Multiply);
    public static readonly Func<T, T, T> Divide = Lambda(Expression.Divide);
    public static readonly Func<T, T> Plus = Lambda(Expression.UnaryPlus);
    public static readonly Func<T, T> Negate = Lambda(Expression.Negate);
    public static Func<T, T, T> Lambda(Binary op) { return Expression.Lambda<Func<T, T, T>>(op(x, y), x, y).Compile(); }
    public static Func<T, T> Lambda(Unary op) { return Expression.Lambda<Func<T, T>>(op(x), x).Compile(); }
}

class Scan
{
    public int Int { get { return int.Parse(Str); } }
    public long Long { get { return long.Parse(Str); } }
    public double Double { get { return double.Parse(Str); } }
    public string Str { get { return Console.ReadLine().Trim(); } }
    public int[] IntArr { get { return StrArr.Select(int.Parse).ToArray(); } }
    public long[] LongArr { get { return StrArr.Select(long.Parse).ToArray(); } }
    public double[] DoubleArr { get { return StrArr.Select(double.Parse).ToArray(); } }
    public string[] StrArr { get { return Str.Split(new []{' '}, System.StringSplitOptions.RemoveEmptyEntries); } }
    bool eq<T, U>() { return typeof(T).Equals(typeof(U)); }
    T ct<T, U>(U a) { return (T)Convert.ChangeType(a, typeof(T)); }
    T cv<T>(string s) { return eq<T, int>()    ? ct<T, int>(int.Parse(s))
                             : eq<T, long>()   ? ct<T, long>(long.Parse(s))
                             : eq<T, double>() ? ct<T, double>(double.Parse(s))
                             : eq<T, char>()   ? ct<T, char>(s[0])
                                               : ct<T, string>(s); }
    public void Multi<T>(out T a) { a = cv<T>(Str); }
    public void Multi<T, U>(out T a, out U b)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); }
    public void Multi<T, U, V>(out T a, out U b, out V c)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); }
    public void Multi<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]); }
}
static class mymath
{
    public static long Mod = 1000000007;
    public static bool isprime(long a) {
        if (a < 2) return false;
        for (long i = 2; i * i <= a; i++) if (a % i == 0) return false;
        return true;
    }
    public static bool[] sieve(int n) {
        var p = new bool[n + 1];
        for (int i = 2; i <= n; i++) p[i] = true;
        for (int i = 2; i * i <= n; i++) if (p[i]) for (int j = i * i; j <= n; j += i) p[j] = false;
        return p;
    }
    public static List<int> getprimes(int n) {
        var prs = new List<int>();
        var p = sieve(n);
        for (int i = 2; i <= n; i++) if (p[i]) prs.Add(i);
        return prs;
    }
    public static long[][] E(int n) {
        var ret = new long[n][];
        for (int i = 0; i < n; i++) { ret[i] = new long[n]; ret[i][i] = 1; }
        return ret;
    }
    public static double[][] dE(int n) {
        var ret = new double[n][];
        for (int i = 0; i < n; i++) { ret[i] = new double[n]; ret[i][i] = 1; }
        return ret;
    }
    public static long[][] pow(long[][] A, long n) {
        if (n == 0) return E(A.Length);
        var t = pow(A, n / 2);
        if ((n & 1) == 0) return mul(t, t);
        return mul(mul(t, t), A);
    }
    public static double[][] pow(double[][] A, long n) {
        if (n == 0) return dE(A.Length);
        var t = pow(A, n / 2);
        if ((n & 1) == 0) return mul(t, t);
        return mul(mul(t, t), A);
    }
    public static double dot(double[] x, double[] y) {
        int n = x.Length;
        double ret = 0;
        for (int i = 0; i < n; i++) ret += x[i] * y[i];
        return ret;
    }
    public static double _dot(double[] x, double[] y) {
        int n = x.Length;
        double ret = 0, r = 0;
        for (int i = 0; i < n; i++) {
            double s = ret + (x[i] * y[i] + r);
            r = (x[i] * y[i] + r) - (s - ret);
            ret = s;
        }
        return ret;
    }
    public static long dot(long[] x, long[] y) {
        int n = x.Length;
        long ret = 0;
        for (int i = 0; i < n; i++) ret = (ret + x[i] * y[i]) % Mod;
        return ret;
    }
    public static T[][] trans<T>(T[][] A) {
        int n = A[0].Length, m = A.Length;
        var ret = new T[n][];
        for (int i = 0; i < n; i++) { ret[i] = new T[m]; for (int j = 0; j < m; j++) ret[i][j] = A[j][i]; }
        return ret;
    }
    public static double[] mul(double[][] A, double[] x) {
        int n = A.Length;
        var ret = new double[n];
        for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
        return ret;
    }
    public static long[] mul(long[][] A, long[] x) {
        int n = A.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
        return ret;
    }
    public static long[][] mul(long[][] A, long[][] B) {
        int n = A.Length;
        var Bt = trans(B);
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]);
        return ret;
    }
    public static double[][] mul(double[][] A, double[][] B) {
        int n = A.Length;
        var Bt = trans(B);
        var ret = new double[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]);
        return ret;
    }
    public static long[] add(long[] x, long[] y) {
        int n = x.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = (x[i] + y[i]) % Mod;
        return ret;
    }
    public static long[][] add(long[][] A, long[][] B) {
        int n = A.Length;
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = add(A[i], B[i]);
        return ret;
    }
    public static long pow(long a, long b) {
        if (a >= Mod) return pow(a % Mod, b);
        if (a == 0) return 0;
        if (b == 0) return 1;
        var t = pow(a, b / 2);
        if ((b & 1) == 0) return t * t % Mod;
        return t * t % Mod * a % Mod;
    }
    public static long inv(long a) { return pow(a, Mod - 2); }
    public static long gcd(long a, long b) {
        while (b > 0) { var t = a % b; a = b; b = t; } return a;
    }
    // a x + b y = gcd(a, b)
    public static long extgcd(long a, long b, out long x, out long y) {
        long g = a; x = 1; y = 0;
        if (b > 0) { g = extgcd(b, a % b, out y, out x); y -= a / b * x; }
        return g;
    }
    public static long lcm(long a, long b) { return a / gcd(a, b) * b; }

    static long[] facts;
    public static long[] setfacts(int n) {
        facts = new long[n + 1];
        facts[0] = 1;
        for (int i = 0; i < n; i++) facts[i + 1] = facts[i] * (i + 1) % Mod;
        return facts;
    }
    public static long comb(int n, int r) {
        if (n < 0 || r < 0 || r > n) return 0;
        if (n - r < r) r = n - r;
        if (r == 0) return 1;
        if (r == 1) return n;
        if (facts != null && facts.Length > n) return facts[n] * inv(facts[r]) % Mod * inv(facts[n - r]) % Mod;
        int[] numer = new int[r], denom = new int[r];
        for (int k = 0; k < r; k++) { numer[k] = n - r + k + 1; denom[k] = k + 1; }
        for (int p = 2; p <= r; p++) {
            int piv = denom[p - 1];
            if (piv > 1) {
                int ofst = (n - r) % p;
                for (int k = p - 1; k < r; k += p) { numer[k - ofst] /= piv; denom[k] /= piv; }
            }
        }
        long ret = 1;
        for (int k = 0; k < r; k++) if (numer[k] > 1) ret = ret * numer[k] % Mod;
        return ret;
    }
    public static long[][] getcombs(int n) {
        var ret = new long[n + 1][];
        for (int i = 0; i <= n; i++) {
            ret[i] = new long[i + 1];
            ret[i][0] = ret[i][i] = 1;
            for (int j = 1; j < i; j++) ret[i][j] = (ret[i - 1][j - 1] + ret[i - 1][j]) % Mod;
        }
        return ret;
    }
    // nC0, nC2, ..., nCn
    public static long[] getcomb(int n) {
        var ret = new long[n + 1];
        ret[0] = 1;
        for (int i = 0; i < n; i++) ret[i + 1] = ret[i] * (n - i) % Mod * inv(i + 1) % Mod;
        return ret;
    }
}