/*  _              _     _                                             _       __      __      __   
   / \     _   _  | |_  | |__     ___    _ __   _    ___   _ __ ___   | | __  / /_    / /_    / /_  
  / _ \   | | | | | __| | '_ \   / _ \  | '__| (_)  / __| | '_ ` _ \  | |/ / | '_ \  | '_ \  | '_ \ 
 / ___ \  | |_| | | |_  | | | | | (_) | | |     _  | (__  | | | | | | |   <  | (_) | | (_) | | (_) |
/_/   \_\  \__,_|  \__| |_| |_|  \___/  |_|    (_)  \___| |_| |_| |_| |_|\_\  \___/   \___/   \___/ 
[Created Time:       2024-09-04 09:20:17]
[Last Modified Time: 2024-09-04 09:45:18] */
#pragma GCC optimize("Ofast", "unroll-loops")
#include<bits/stdc++.h>
#ifdef LOCAL
#include"debug.h"
#else
#define D(...) ((void)0)
#endif
using namespace std; using ll = long long;
#define For(i, j, k) for ( int i = (j) ; i <= (k) ; i++ )
#define Fol(i, j, k) for ( int i = (j) ; i >= (k) ; i-- )
/*namespace FastIO
{
// ------------------------------
// #define DISABLE_MMAP
// ------------------------------
#if ( defined(LOCAL) || defined(_WIN32) ) && !defined(DISABLE_MMAP)
#define DISABLE_MMAP
#endif
#ifdef LOCAL
	inline char gc() { return getchar(); }
	inline void pc(char c) { putchar(c); }
#else
#ifdef DISABLE_MMAP
	inline constexpr int _READ_SIZE = 1 << 18;
	inline static char _read_buffer[_READ_SIZE], *_read_ptr = nullptr, *_read_ptr_end = nullptr;
	inline char gc()
	{
		if ( __builtin_expect(_read_ptr == _read_ptr_end, false) )
		{
			_read_ptr = _read_buffer, _read_ptr_end = _read_buffer + fread(_read_buffer, 1, _READ_SIZE, stdin);
			if ( __builtin_expect(_read_ptr == _read_ptr_end, false) ) return EOF;
		}
		return *_read_ptr++;
	}
#else
#include<sys/mman.h>
	inline static const char *_read_ptr = (const char *)mmap(nullptr, 0x7fffffff, 1, 2, 0, 0);
	inline char gc() { return *_read_ptr++; }
#endif
	inline constexpr int _WRITE_SIZE = 1 << 18;
	inline static char _write_buffer[_WRITE_SIZE], *_write_ptr = _write_buffer;
	inline void pc(char c)
	{
		*_write_ptr++ = c;
		if ( __builtin_expect(_write_buffer + _WRITE_SIZE == _write_ptr, false) )
			fwrite(_write_buffer, 1, _write_ptr - _write_buffer, stdout), _write_ptr = _write_buffer;
	}
	inline struct _auto_flush
	{
		inline ~_auto_flush() { fwrite(_write_buffer, 1, _write_ptr - _write_buffer, stdout); }
	}	_auto_flush;
#endif
#define println println_ // don't use C++23 std::println
	template < class T > inline constexpr bool _is_signed = numeric_limits < T >::is_signed;
	template < class T > inline constexpr bool _is_unsigned = numeric_limits < T >::is_integer && !_is_signed < T >;
#if __SIZEOF_LONG__ == 64
	template <> inline constexpr bool _is_signed < __int128 > = true;
	template <> inline constexpr bool _is_unsigned < __uint128_t > = true;
#endif
	inline void read(char &c) { do c = gc(); while ( !isgraph(c) ); }
	inline void read_cstr(char *s)
	{
		char c = gc(); while ( !isgraph(c) ) c = gc();
		while ( isgraph(c) ) *s++ = c, c = gc(); *s = 0;
	}
	inline void read(string &s)
	{
		char c = gc(); s.clear(); while ( !isgraph(c) ) c = gc();
		while ( isgraph(c) ) s.push_back(c), c = gc();
	}
	template < class T, enable_if_t < _is_signed < T >, int > = 0 >
	inline void read(T &x)
	{
		char c = gc(); bool f = true; x = 0;
		while ( !isdigit(c) ) { if ( c == 45 ) f = false; c = gc(); }
		if ( f ) while ( isdigit(c) ) x = x * 10 + ( c & 15 ), c = gc();
		else     while ( isdigit(c) ) x = x * 10 - ( c & 15 ), c = gc();
	}
	template < class T, enable_if_t < _is_unsigned < T >, int > = 0 >
	inline void read(T &x)
	{
		char c = gc(); while ( !isdigit(c) ) c = gc();
		x = 0; while ( isdigit(c) ) x = x * 10 + ( c & 15 ), c = gc();
	}
	inline void write(char c) { pc(c); }
	inline void write_cstr(const char *s) { while ( *s ) pc(*s++); }
	inline void write(const string &s) { for ( char c : s ) pc(c); }
	template < class T, enable_if_t < _is_signed < T >, int > = 0 >
	inline void write(T x)
	{
		char buffer[numeric_limits < T >::digits10 + 1]; int digits = 0;
		if ( x >= 0 )  do buffer[digits++] =  ( x % 10 ) | 48, x /= 10; while ( x );
		else { pc(45); do buffer[digits++] = -( x % 10 ) | 48, x /= 10; while ( x ); }
		while ( digits ) pc(buffer[--digits]);
	}
	template < class T, enable_if_t < _is_unsigned < T >, int > = 0 >
	inline void write(T x)
	{
		char buffer[numeric_limits < T >::digits10]; int digits = 0;
		do buffer[digits++] = ( x % 10 ) | 48, x /= 10; while ( x );
		while ( digits ) pc(buffer[--digits]);
	}
	template < int N > struct _tuple_io_helper
	{
		template < class ...T > static inline void _read(tuple < T... > &x) { _tuple_io_helper < N - 1 >::_read(x), read(get<N - 1>(x)); }
		template < class ...T > static inline void _write(const tuple < T... > &x) { _tuple_io_helper < N - 1 >::_write(x), pc(32), write(get<N - 1>(x)); }
	};
	template <> struct _tuple_io_helper < 1 >
	{
		template < class ...T > static inline void _read(tuple < T... > &x) { read(get<0>(x)); }
		template < class ...T > static inline void _write(const tuple < T... > &x) { write(get<0>(x)); }
	};
	template < class ...T > inline void read(tuple < T... > &x) { _tuple_io_helper < sizeof...(T) >::_read(x); }
	template < class ...T > inline void write(const tuple < T... > &x) { _tuple_io_helper < sizeof...(T) >::_write(x); }
	template < class T1, class T2 > inline void read(pair < T1, T2 > &x) { read(x.first), read(x.second); }
	template < class T1, class T2 > inline void write(const pair < T1, T2 > &x) { write(x.first), pc(32), write(x.second); }
	template < class T1, class ...T2 > inline void read(T1 &x, T2 &...y) { read(x), read(y...); }
	template < class ...T > inline void read_cstr(char *x, T *...y) { read_cstr(x), read_cstr(y...); }
	template < class T1, class ...T2 > inline void write(const T1 &x, const T2 &...y) { write(x), write(y...); }
	template < class ...T > inline void write_cstr(const char *x, const T *...y) { write_cstr(x), write_cstr(y...); }
	template < class T > inline void print(const T &x) { write(x); }
	inline void print_cstr(const char *x) { write_cstr(x); }
	template < class T1, class ...T2 > inline void print(const T1 &x, const T2 &...y) { write(x), pc(32), print(y...); }
	template < class ...T > inline void print_cstr(const char *x, const T *...y) { write_cstr(x), pc(32), print_cstr(y...); }
	inline void println() { pc(10); } inline void println_cstr() { pc(10); }
	template < class ...T > inline void println(const T &...x) { print(x...), pc(10); }
	template < class ...T > inline void println_cstr(const T *...x) { print_cstr(x...), pc(10); }
}	using FastIO::read, FastIO::read_cstr, FastIO::write, FastIO::write_cstr, FastIO::println, FastIO::println_cstr;*/
#include"message.h"
void send_message(vector < bool > m, vector < bool > c)
{
	int d[31] = {}, x = 0, y = -1; bool a[66][31] = {};
	For(i, 0, 30) if ( !c[i] )
	{
		for ( int j = i == 30 ? 0 : i + 1 ; c[j] ; j = j == 30 ? 0 : j + 1 ) d[i]++;
		a[d[i]][i] = 1;
	}
	For(i, 0, 1024)
	{
		do y = y == 30 ? x++, 0 : y + 1; while ( c[y] || x <= d[y] );
		a[x][y] = i < (int)m.size() ? m[i] : i != (int)m.size();
	}
	For(i, 0, 65) send_packet(vector(a[i], a[i] + 31));
}
vector < bool > receive_message(vector < vector < bool > > r)
{
	int d[31] = {}, to[31], x = 0, y = -1; bool ok[31] = {}; vector < bool > m;
	For(i, 0, 30)
	{
		to[i] = i == 30 ? 0 : i + 1;
		while ( d[i] < 66 && !r[d[i]][i] ) d[i]++, to[i] = to[i] == 30 ? 0 : to[i] + 1;
	}
	For(i, 0, 30)
	{
		int o = i; For(_, 0, 14) if ( ( o = to[o] ) == i ) { o = -1; break; }
		if ( ~o && ( o = to[o] ) == i ) { For(_, 0, 15) ok[o = to[o]] = true; break; }
	}
	For(i, 0, 1024)
	{
		do y = y == 30 ? x++, 0 : y + 1; while ( !ok[y] || x <= d[y] );
		m.push_back(r[x][y]);
	}
	while ( m.back() ) m.pop_back();
	return m.pop_back(), m;
}
#ifdef LOCAL
#include"grader.cpp"
#endif
// 想上GM捏 想上GM捏 想上GM捏 想上GM捏 想上GM捏
// 伊娜可爱捏 伊娜贴贴捏