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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#pragma GCC optimize ("O3")
#pragma GCC target ("avx")
#include "bits/stdc++.h"

using namespace std;
using ll = long long int;

#define debug(v) {printf("L%d %s > ",__LINE__,#v);cout<<(v)<<endl;}
#define debugv(v) {printf("L%d %s > ",__LINE__,#v);for(auto e:(v)){cout<<e<<" ";}cout<<endl;}
#define debuga(m,w) {printf("L%d %s > ",__LINE__,#m);for(int x=0;x<(w);x++){cout<<(m)[x]<<" ";}cout<<endl;}
#define debugaa(m,h,w) {printf("L%d %s >\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){cout<<(m)[y][x]<<" ";}cout<<endl;}}
#define ALL(v) (v).begin(),(v).end()
#define repeat(cnt,l) for(remove_const<decltype(l)>::type cnt=0;(cnt)<(l);++(cnt))
#define rrepeat(cnt,l) for(auto cnt=(l)-1;0<=(cnt);--(cnt))
#define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt))
#define diterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);--(cnt))
const ll MD = 1000000007ll; const long double PI = 3.1415926535897932384626433832795L;
template<typename T1, typename T2> inline void assert_equal(T1 expected, T2 actual) { if (!(expected == actual)) { cerr << "assertion fault: expected=" << expected << " actual=" << actual << endl; abort(); } }
template<typename T1, typename T2> inline void assert_less(T1 actual, T2 threshold) { if (!(actual < threshold)) { cerr << "assertion fault: " << actual << " < (const)" << threshold << endl; abort(); } }
template<typename T1, typename T2> inline void assert_eqless(T1 actual, T2 threshold) { if (!(actual <= threshold)) { cerr << "assertion fault: " << actual << " <= (const)" << threshold << endl; abort(); } }
template<typename T1, typename T2> inline ostream& operator <<(ostream &o, const pair<T1, T2> p) { o << '(' << p.first << ':' << p.second << ')'; return o; }
template<typename Vec> inline ostream& _ostream_vecprint(ostream &o, const Vec& p) { o << '['; for (auto& e : p) o << e << ','; o << ']'; return o; }
template<typename T> inline ostream& operator<<(ostream& o, const vector<T>& v) { return _ostream_vecprint(o, v); }
template<typename T, size_t S> inline ostream& operator<<(ostream& o, const array<T, S>& v) { return _ostream_vecprint(o, v); }
template<typename T> inline T& maxset(T& to, const T& val) { return to = max(to, val); }
template<typename T> inline T& minset(T& to, const T& val) { return to = min(to, val); }
void bye(string s, int code = 0) { cout << s << endl; exit(code); }
mt19937_64 randdev(8901016);
template<typename T> inline T rand(T l, T h) { return uniform_int_distribution<T>(l, h)(randdev); }
template<> inline double rand<double>(double l, double h) { return uniform_real_distribution<double>(l, h)(randdev); }
template<> inline float rand<float>(float l, float h) { return uniform_real_distribution<float>(l, h)(randdev); }

#if defined(_WIN32) || defined(_WIN64)
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#elif defined(__GNUC__)
#else
#define getchar_unlocked getchar
#define putchar_unlocked putchar
#endif
namespace {
#define isvisiblechar(c) (0x21<=(c)&&(c)<=0x7E)
    class MaiScanner {
    public:
        template<typename T> void input_integer(T& var) {
            var = 0; T sign = 1;
            int cc = getchar_unlocked();
            for (; cc<'0' || '9'<cc; cc = getchar_unlocked())
                if (cc == '-') sign = -1;
            for (; '0' <= cc && cc <= '9'; cc = getchar_unlocked())
                var = (var << 3) + (var << 1) + cc - '0';
            var = var * sign;
        }
        inline int c() { return getchar_unlocked(); }
        inline MaiScanner& operator>>(int& var) { input_integer<int>(var); return *this; }
        inline MaiScanner& operator>>(long long& var) { input_integer<long long>(var); return *this; }
        inline MaiScanner& operator>>(string& var) {
            int cc = getchar_unlocked();
            for (; !isvisiblechar(cc); cc = getchar_unlocked());
            for (; isvisiblechar(cc); cc = getchar_unlocked())
                var.push_back(cc);
            return *this;
        }
        template<typename IT> void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; }
    };
    class MaiPrinter {
    public:
        template<typename T>
        void output_integer(T var) {
            if (var == 0) { putchar_unlocked('0'); return; }
            if (var < 0)
                putchar_unlocked('-'),
                var = -var;
            char stack[32]; int stack_p = 0;
            while (var)
                stack[stack_p++] = '0' + (var % 10),
                var /= 10;
            while (stack_p)
                putchar_unlocked(stack[--stack_p]);
        }
        inline MaiPrinter& operator<<(char c) { putchar_unlocked(c); return *this; }
        inline MaiPrinter& operator<<(int var) { output_integer<int>(var); return *this; }
        inline MaiPrinter& operator<<(long long var) { output_integer<long long>(var); return *this; }
        inline MaiPrinter& operator<<(char* str_p) { while (*str_p) putchar_unlocked(*(str_p++)); return *this; }
        inline MaiPrinter& operator<<(const string& str) {
            const char* p = str.c_str();
            const char* l = p + str.size();
            while (p < l) putchar_unlocked(*p++);
            return *this;
        }
        template<typename IT> void join(IT begin, IT end, char sep = '\n') { for (auto it = begin; it != end; ++it) *this << *it << sep; }
    };
}
MaiScanner scanner;
MaiPrinter printer;



template<typename T> inline T gcd(T a, T b) { while (b) { T t = a % b; a = b; b = t; }return a; }
template<typename T> inline T lcm(T a, T b) { return a * b / gcd(a, b); }


// MEMO : 逆元...pow_md(n,MOD-2,MOD)
template<typename T> T pow_md(T x, T p, T mod = MD) {
    T y = 1; x = x % mod;
    while (0<p) {
        if (p & 1)
            y = (y*x) % mod;
        x = (x*x) % mod;
        p >>= 1;
    }
    return y;
}
template<typename T> T fact_md(T n, T mod = MD) {
    T p = 1; for (; 1<n; p = (p*n--) % mod); return p;
}
template<typename T> T nPr_md(T n, T r, T mod = MD) {
    T p = 1; for (r = n - r; r<n; p = (p*n--) % mod); return p;
}
template<typename T> T nCr_md(T n, T r, T mod = MD) {
    if (n / 2 < r) return nCr_md(n, n - r);
    T p = 1; for (; 0<r; r--)
        p = (((p*(n - r + 1)) % mod)*pow_md(r, mod - 2)) % mod;
    return p;
}
template<typename T> T nHr_md(T n, T r, T mod = MD) {
    return nCr_md(n - 1 + r, n - 1, mod);
}

template<typename T> T nCr(T n, T r) {
    if (n / 2 < r) return nCr(n, n - r);
    T p = 1; for (T t=1; t<=r; ++t) p = p*(n - t + 1) / t;
    return p;
}


ll N, M, K;
int str[222];



ll seq(ll size) {
    ll cnt = 0;
    for (ll i = 2; i <= size; i += 2) {
        cnt += nCr(size, i);
    }
    return cnt;
}


int main() {
    scanner >> N;
    
    vector<int> aa;
    int asum = 0;
    
    ll n = N;

    while (0 < n) {
        ll x, t;
        repeat(_x, 200) {
            ll _t = seq(_x);
            if (n < _t) {
                x = _x - 1;
                break;
            }
            t = _t;
        }
        aa.push_back(x);
        asum += x;
        n -= t;
    }
    
    int z = 1;
    printer << asum << '\n';
    for (int a : aa) {
        repeat(_, a) printer << z << ' ';
        ++z;
    }
    cout << endl;

    return 0;
}