#include <bits/stdc++.h>

#define pb push_back
#define mp make_pair
#define sz(x) (int)(x).size()
#define ll long long
#define ld long double
#define ft first
#define sc second
#define pii pair<int, int>
#define pll pair<ll, ll>
#define forn(i, t) for(int i = 0; i < (t); i++)
#define fore(i, f, t) for(int i = (f); i < (t); i++)
#define forr(i, f, t) for(int i = (f) - 1; i >= (t); i--)
#define all(x) (x).begin(), (x).end()
#define ins insert

const int INF = 2147483647;
const int MOD = 1000000007;
const ll INF64 = 9223372036854775807;
const ld EPS = 1e-7;

using namespace std;


void encode(string s){
    int n = sz(s);
    int m = 0;
    while ((1 << m) < m + n + 1)
        m++;
    forn(i, m)
        s.insert((1 << i) - 1, "0");
    n = sz(s);
    forn(i, m){
        int cur = 0;
        forn(j, n)
            if (((j + 1) & (1 << i)) != 0)
                cur ^= (s[j] == '1');
        s[(1 << i) - 1] = ('0' + cur);
    }
    cout << s << "\n";
}


void decode(string s){
    int ans = 0, n = sz(s);
    int m = 0;
    while ((1 << m) < n)
        m++;
    forn(i, m){
        int cur = (s[(1 << i) - 1] == '1');
        forn(j, n)
            if (((j + 1) & (1 << i)) != 0)
                cur ^= (s[j] == '1');
        if (s[(1 << i) - 1] != ('0' + cur))
            ans ^= (1 << i);
    }
    if (ans != 0)
        s[ans - 1] = (s[ans - 1] == '0' ? '1' : '0');
    string t = "";
    forn(i, n)
        if (__builtin_popcount(i + 1) > 1)
            t += s[i];
    cout << ans << " " << t << "\n";
}


int main(){
    string s = "0000000000000";
    // encode(s);
    // decode(s);
    return 0;
}