/**
 * @file Luogu_P_10061.cpp
 * @author georgeyucjr ([email protected])
 * @brief
 * @version 998244353.1145141919810
 * @date 2024-02-13
 *
 * @copyright Copyright (c) 2024
 *
 */
# include <bits/stdc++.h>

# ifndef ONLINE_JUDGE
# define LOCAL
# endif

# if __cplusplus >= 201100LL
# else
# error Please use C++11 Or Higher CPP version
# endif

using ll = long long;
using ull = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using arr3 = std :: array < int, 3 >;
using arr4 = std :: array < int, 4 >;
using pii = std :: pair < int, int >;

# if __cplusplus >= 201400LL
# define rep(i, f, t, ...) for ( std :: decay < decltype ( f + t ) > :: type i = f, _END_##i = t, ##__VA_ARGS__; i <= _END_##i; ++i )
# define per(i, f, t, ...) for ( std :: decay < decltype ( f + t ) > :: type i = f, _END_##i = t, ##__VA_ARGS__; i >= _END_##i; --i )
# else
# define rep(i, f, t, ...) for ( decltype ( f + t ) i = f, _END_##i = t, ##__VA_ARGS__; i <= _END_##i; ++i )
# define per(i, f, t, ...) for ( decltype ( f + t ) i = f, _END_##i = t, ##__VA_ARGS__; i >= _END_##i; --i )
# endif

# define emb emplace_back
# define pb push_back
# define mkp make_pair
# define FILEIO(filename) freopen(filename ".in", "r", stdin), freopen(filename ".out", "w", stdout)

# ifndef INLINE_V
# if __cplusplus >= 201700LL
# define INLINE_V inline
# else
# define INLINE_V
# endif
# endif

# if __cplusplus >= 201400LL
# define EXPR constexpr
# else
# define EXPR
# endif

# if __cplusplus >= 201400LL
template < class T, class U >
inline constexpr auto ceil ( T && x, U && y ) {
	return ( x > 0 ? ( x + y - 1 ) / y : x / y );
}

template < class T, class U >
inline constexpr auto floor ( T && x, U && y ) {
	return ( x > 0 ? x / y : ( x - y + 1 ) / y );
}

template < class T, class U >
inline constexpr auto divmod ( T && x, U && y ) {
	auto && q = floor ( x, y );
	return std :: make_pair ( q, x - q * y );
}

# else

template < class T, class U >
inline T ceil ( T && x, U && y ) {
	return ( x > 0 ? ( x + y - 1 ) / y : x / y );
}

template < class T, class U >
inline T floor ( T && x, U && y ) {
	return ( x > 0 ? x / y : ( x - y + 1 ) / y );
}

template < class T, class U >
inline pair < T, T > divmod ( T && x, U && y ) {
	T && q = floor ( x, y );
	return std :: pair { q, x - q * y };
}

# endif

# define ALL(vc) std :: begin ( vc ), std :: end ( vc )

# if __cplusplus >= 202000LL

template < class T >
requires ( std :: is_signed_v < T > || std :: is_unsigned_v < T > )
INLINE_V constexpr static T inf = std :: numeric_limits < T > :: max ( ) >> 1;

template <std :: ranges :: forward_range R>
inline constexpr auto Sum ( R && r ) {
	return std :: accumulate ( std :: ranges :: begin ( r ), std :: ranges :: end ( r ), 0 );
}

template < std :: ranges :: forward_range R, typename T >
inline constexpr auto Sum ( R && r, T init) {
	return std :: accumulate ( std :: ranges :: begin ( r ), std :: ranges :: end ( r ), init );
}

template < std :: ranges :: forward_range R >
inline constexpr int SZ ( R && x ) { return std :: size ( x ); }

# else

template < class R >
inline EXPR auto Sum ( R && r ) {
	return std :: accumulate ( ALL ( r ), 0);
}

template < class R, typename T >
inline EXPR auto Sum( R && r, T init ) {
	return std :: accumulate ( ALL ( r ), init );
}

template < class R >
inline EXPR auto Sum ( R f, R t ) {
	return std ::accumulate ( f, t );
}

template < class R, typename T >
inline EXPR auto Sum ( R f, R t, T init ) {
	return std :: accumulate ( f, t, init );
}

template < class T >
inline EXPR int SZ ( T && x ) { return static_cast < int > ( x.size ( ) ) ; }

template < class T >
INLINE_V constexpr static T inf = std :: numeric_limits < T > :: max ( ) >> 1;

# endif

template < class Os, class T >
inline Os & operator << ( Os & os, T & t ) {
	for ( auto ele : t )
		os << ele << " ";
	os << "\n";
	return os;
}

# ifndef __GEORGEYUCJR_READ__
# define __GEORGEYUCJR_READ__

# if __cplusplus >= 202000LL && !defined(MACOS) && defined(__unix__)

# define CHECK_EOF 0
# if CHECK_EOF
# define ECHK0 *ptr ? *ptr++ : -1
# define ECHK1                                                                                                                                        \
  if (ch == -1)                                                                                                                                      \
    return set(false), *this;
# define ECHK2                                                                                                                                        \
  if (!*ptr)                                                                                                                                         \
    return set(false), *this;
# define ECHK3 and ch != -1
# define ECHK4 and*ptr
# else
# define ECHK0 *ptr++
# define ECHK1
# define ECHK2
# define ECHK3
# define ECHK4
# endif

# if !defined(MACOS)
# define USE_MMAP
# include <sys/mman.h>
# include <sys/stat.h>
# endif

# if __cpluspls >= 202000LL && !defined(MACOS)
# define DISABLE_RANGE
# endif

# if CHECK_EOF || !defined(USE_MMAP)
# define EV -1
# else
# define EV 0
# endif

namespace FastIO {
template <typename T> struct make_unsigned : public std :: make_unsigned<T> {};
template <> struct make_unsigned<i128> {
	using type = u128;
};
template <typename T>
concept tupleLike = requires(T t) { std :: tuple_size_v<decltype(std :: tuple_cat(t))>; };

inline constexpr ull pw10(int t) { return t == 0 ? 1 : pw10(t - 1) * 10; }

std :: mt19937 mrand(std :: random_device{}());
std :: mt19937_64 mrand64(std :: random_device{}());

inline constexpr static std :: size_t bufSize = 1 << 20;

class IO;
class In {
	friend class IO;

private:
	FILE *inFile;
	bool status = true;
# ifdef USE_MMAP
	struct stat st;
	char *ptr;
	int fd;
# elif !defined(LOCAL)
	char buf[bufSize], *p1, *p2;
# endif

public:
# ifdef LOCAL
	inline int getch() { return fgetc_unlocked(inFile); }
	inline void input(FILE *f) { inFile = f, set(); }
# elif defined(USE_MMAP)
	inline int getch() { return ECHK0; }
	inline void input(FILE *f) {
		inFile = f;
		if (inFile)
			fd = fileno(inFile), fstat(fd, &st), ptr = (char *)mmap(nullptr, st.st_size, PROT_READ, MAP_PRIVATE, fd, 0), set();
	}
	static constexpr auto n = []() {
		std :: array<uint32_t, 0x10000> n{};
		for (int i = 0; i != 0x10000; ++i)
			n[i] = -1;
		constexpr uint32_t e0 = 0x01, e1 = 0x100;
		int x = 0;
		for (uint32_t i = 0, c0 = 0x3030; i != 10; i++, c0 += e0)
			for (uint32_t j = 0, c1 = c0; j != 10; j++, c1 += e1)
				n[c1] = x++;
		return n;
	}();
# else
	inline int getch() { return (p1 == p2 ? (p2 = (p1 = buf) + fread(buf, 1, bufSize, inFile)) : 0), p1 == p2 ? -1 : *p1++; }
	inline void input(FILE *f) { inFile = f, p1 = p2 = buf, set(); }
# endif
	inline void input(const char *s) { input(fopen(s, "rb")); }
	inline void set(bool s = true) { status = s; }
	inline bool get() const { return status; }
};
class Out {
	friend class IO;

public:
	FILE *outFile;
# ifndef LOCAL
	char pbuf[bufSize], *pp;
# endif

public:
# ifdef LOCAL
	inline void flush() { outFile ? fflush(outFile) : 0; }
	inline void putch(char c) { fputc_unlocked(c, outFile); }
# else
	inline void flush() { (outFile ? fwrite(pbuf, 1, pp - pbuf, outFile), fflush(outFile) : 0), pp = pbuf; }
	inline void putch(char c) { ((pp - pbuf == bufSize) ? fwrite(pbuf, 1, bufSize, outFile), pp = pbuf : 0), *pp++ = c; }
# endif
	inline void output(const char *s) { flush(), outFile = fopen(s, "wb"); }
	inline void output(FILE *f) { flush(), outFile = f; }
};
class IO : public In, public Out {
private:
	std :: size_t precision = 12;

public:
	IO(FILE * = nullptr, FILE * = nullptr);
	~IO() { flush(); }
	static constexpr bool blank(char);
	template <typename... Args>
	requires(sizeof...(Args) > 1)
	IO &read(Args &...);
	template <typename T>
	requires(std :: is_signed_v<T> && std :: is_integral_v<T>) || std :: is_same_v<std :: decay_t<T>, i128>
	IO &read(T &);
	template <typename T>
	requires(std :: is_unsigned_v<T> && std :: is_integral_v<T>) || std :: is_same_v<std :: decay_t<T>, u128>
	IO &read(T &);
	template <typename T>
	requires std :: is_floating_point_v<T>
	IO &read(T &);
	template <typename T> T read();
	IO &read(char &);
	IO &read(char *);
	IO &read(std :: string &);
	IO &readline(char *);
	IO &readline(std :: string &);
	template <tupleLike T> IO &read(T &&);
	template <std :: ranges::input_range R> IO &read(R &&r) { return readArray(std :: forward<R>(r)); }
	void setprecision(std :: size_t n = 6u) { precision = n; }
	template <typename... Args>
	requires(sizeof...(Args) > 1)
	void write(Args &&...);
	inline void write() const {}
	template <typename T>
	requires(std :: is_signed_v<T> && std :: is_integral_v<T>) || std :: is_same_v<std :: decay_t<T>, i128>
	void write(T);
	template <typename T>
	requires(std :: is_unsigned_v<T> && std :: is_integral_v<T>)
	void write(T);
	void write(u128);
	inline void write(char);
	template <typename T>
	requires std :: is_floating_point_v<T>
	void write(T);
	inline void write(bool);
	void write(char *);
	void write(const char *);
	void write(const std :: string &);
	template <typename T> void write(std :: initializer_list<T>);
	template <tupleLike T> void write(T &&);
	template <std :: ranges::input_range R> void write(R &&);
	template <typename... Args> void writeln(Args &&...);
	template <typename T> inline void writespc(T && x);
	operator bool() const { return get(); }
} io(stdin, stdout);
template <typename... Args> inline void writeln(Args &&...x) { io.writeln(std :: forward<Args>(x)...); }
template <typename T> inline void writeln(std :: initializer_list<T> x) { io.writeln(x); }
#pragma endregion

# define isdigit(x) ((x) >= '0' && (x) <= '9')
IO::IO(FILE *in, FILE *out) { input(in), output(out); }
constexpr bool IO::blank(char c) { return c == ' ' || c == '\n' || c == '\r'; }
template <typename... Args>
requires(sizeof...(Args) > 1)
IO &IO::read(Args &...args) {
	if constexpr (CHECK_EOF)
		(read(args) && ...);
	else
		(read(args), ...);
	return *this;
}
template <typename T>
requires(std :: is_signed_v<T> && std :: is_integral_v<T>) || std :: is_same_v<std :: decay_t<T>, i128>
IO &IO::read(T &x) {
	x = 0;
	static typename make_unsigned<T>::type t;
	bool sign = false;
# ifndef USE_MMAP
	int ch = getch();
	while (!isdigit(ch) ECHK3)
		sign = (ch == '-'), ch = getch();
	ECHK1
	t = 0;
	while (isdigit(ch))
		t = t * 10 + (ch ^ 48), ch = getch();
# else
	while (!isdigit(*ptr) ECHK4)
		sign = *ptr++ == '-';
	ECHK2
	t = *ptr++ ^ 48;
	while (~n[*reinterpret_cast<std :: uint16_t *&>(ptr)])
		t = t * 100 + n[*reinterpret_cast<std :: uint16_t *&>(ptr)++];
	if (isdigit(*ptr))
		t = t * 10 + (*ptr++ ^ 48);
# endif
	x = sign ? (~t + 1) : t;
	return *this;
}
template <typename T>
requires(std :: is_unsigned_v<T> && std :: is_integral_v<T>) || std :: is_same_v<std :: decay_t<T>, u128>
IO &IO::read(T &x) {
	x = 0;
# ifndef USE_MMAP
	int ch = getch();
	while (!isdigit(ch) ECHK3)
		ch = getch();
	ECHK1
	while (isdigit(ch))
		x = (x << 1) + (x << 3) + (ch ^ 48), ch = getch();
# else
	while (!isdigit(*ptr) ECHK4)
		ptr++;
	ECHK2
	x = *ptr++ ^ 48;
	while (~n[*reinterpret_cast<std :: uint16_t *&>(ptr)])
		x = x * 100 + n[*reinterpret_cast<std :: uint16_t *&>(ptr)++];
	if (isdigit(*ptr))
		x = x * 10 + (*ptr++ ^ 48);
# endif
	return *this;
}
template <typename T>
requires std :: is_floating_point_v<T>
IO &IO::read(T &x) {
	x = 0;
	T t = 1;
	bool sign = false;
	int ch = getch();
	while (!isdigit(ch) ECHK3)
		sign = (ch == '-'), ch = getch();
	ECHK1
	while (isdigit(ch))
		x = x * 10 + (ch ^ 48), ch = getch();
	if (ch == '.')
		for (ch = getch(); isdigit(ch); ch = getch())
			x += (t /= 10) * (ch ^ 48);
	x = sign ? -x : x;
	return *this;
}
template <typename T> T IO::read() {
	static std :: decay_t<T> x;
	return read(x), x;
}
IO &IO::read(char &ch) {
	do
		ch = getch();
	while (blank(ch));
	ECHK1
	return *this;
}
IO &IO::read(char *s) {
	int ch = getch();
	while (blank(ch))
		ch = getch();
	ECHK1
	while (!blank(ch) && ch != EV)
		*s++ = ch, ch = getch();
	*s = 0;
	return *this;
}
IO &IO::read(std :: string &s) {
	int ch = getch();
	while (blank(ch))
		ch = getch();
	ECHK1
	s.erase();
	while (!blank(ch) && ch != EV)
		s.append(1, ch), ch = getch();
	return *this;
}
IO &IO::readline(char *s) {
	char *t = s;
	int ch = getch();
	while (ch != '\n' && ch != EV)
		*s++ = ch, ch = getch();
	*s = 0;
	if (s == t && ch != '\n')
		set(false);
	return *this;
}
IO &IO::readline(std :: string &s) {
	s.erase();
	int ch = getch();
	while (ch != '\n' && ch != EV)
		s.append(1, ch), ch = getch();
	if (s.empty() && ch != '\n')
		set(false);
	return *this;
}
template <tupleLike T> IO &IO::read(T &&t) {
	std :: apply([&](auto & ...t) { (read(t), ...); }, t);
	return *this;
}
template <typename... Args>
requires(sizeof...(Args) > 1)
void IO::write(Args &&...args) {
	(write(std :: forward<Args>(args)), ...);
}
template <typename T>
requires(std :: is_signed_v<T> && std :: is_integral_v<T>) || std :: is_same_v<std :: decay_t<T>, i128>
void IO::write(T x) {
	static typename make_unsigned<T>::type y;
	y = x;
	if (x < 0)
		putch('-'), write(~y + 1);
	else
		write(y);
}
constexpr auto D = []() {
	constexpr uint32_t e0 = 0x1, e1 = 0x100, e2 = 0x10000, e3 = 0x1000000;
	std :: array<uint32_t, 10000> m{};
	int x = 0;
	for (uint32_t i = 0, c0 = 0x30303030; i != 10; i++, c0 += e0)
		for (uint32_t j = 0, c1 = c0; j != 10; j++, c1 += e1)
			for (uint32_t k = 0, c2 = c1; k != 10; k++, c2 += e2)
				for (uint32_t l = 0, c3 = c2; l != 10; l++, c3 += e3)
					m[x++] = c3;
	return m;
}();
template <typename T>
requires(std :: is_unsigned_v<T> && std :: is_integral_v<T>)
void IO::write(T x) {
# ifndef LOCAL
	if (std :: end(pbuf) - pp < 64)
		flush();

	auto L = [&](int x) { return x == 1 ? 0 : pw10(x - 1); };
	auto R = [&](int x) { return pw10(x) - 1; };

# define de(t)                                                                                                                                        \
  case L(t)... R(t):                                                                                                                                 \
    *reinterpret_cast<uint32_t *>(pp) = D[x / pw10((t)-4)];                                                                                          \
    pp += 4;                                                                                                                                         \
    x %= pw10((t)-4);

	ull y = x;
	switch (y) {
		de(18);
		de(14);
		de(10);
		de(6);
	case L(2)... R(2):
		*reinterpret_cast<uint32_t *>(pp) = D[x * 100];
		pp += 2;
		break;

		de(17);
		de(13);
		de(9);
		de(5);
	case L(1)... R(1):
		*pp = static_cast<char>('0' + x);
		pp += 1;
		break;

	default:
		*reinterpret_cast<uint32_t *>(pp) = D[x / pw10(16)];
		pp += 4;
		x %= pw10(16);
		de(16);
		de(12);
		de(8);
	case L(4)... R(4):
		*reinterpret_cast<uint32_t *>(pp) = D[x];
		pp += 4;
		break;

		de(19);
		de(15);
		de(11);
		de(7);
	case L(3)... R(3):
		*reinterpret_cast<uint32_t *>(pp) = D[x * 10];
		pp += 3;
		break;
	}
# else
	write(u128(x));
# endif
}
constexpr u128 _pw10(int x) { return x == 0 ? 1 : _pw10(x - 1) * 10; }
void IO::write(u128 x) {
	if (std :: end(pbuf) - pp < 64)
		flush();
	constexpr auto pw10 = _pw10;
	auto L = [&](int x) { return x == 1 ? 0 : pw10(x - 1); };
	auto R = [&](int x) { return pw10(x) - 1; };

# define de(t)                                                                                                                                        \
  case L(t)... R(t):                                                                                                                                 \
    *reinterpret_cast<uint32_t *>(pp) = D[x / pw10((t)-4)];                                                                                          \
    pp += 4;                                                                                                                                         \
    x %= pw10((t)-4);

	switch (x) {
		de(38);
		de(34);
		de(30);
		de(26);
		de(22);
		de(18);
		de(14);
		de(10);
		de(6);
	case L(2)... R(2):
		*reinterpret_cast<uint32_t *>(pp) = D[x * 100];
		pp += 2;
		break;

		de(37);
		de(33);
		de(29);
		de(25);
		de(21);
		de(17);
		de(13);
		de(9);
		de(5);
	case L(1)... R(1):
		*pp = static_cast<char>('0' + x);
		pp += 1;
		break;

		de(36);
		de(32);
		de(28);
		de(24);
		de(20);
		de(16);
		de(12);
		de(8);
	case L(4)... R(4):
		*reinterpret_cast<uint32_t *>(pp) = D[x];
		pp += 4;
		break;

	default:
		*reinterpret_cast<uint32_t *>(pp) = D[x / pw10(35)];
		pp += 4;
		x %= pw10(35);
		de(35);
		de(31);
		de(27);
		de(23);
		de(19);
		de(15);
		de(11);
		de(7);
	case L(3)... R(3):
		*reinterpret_cast<uint32_t *>(pp) = D[x * 10];
		pp += 3;
		break;
	}
}
void IO::write(bool x) { putch(x ^ 48); }
void IO::write(char c) { putch(c); }
template <typename T>
requires std :: is_floating_point_v<T>
void IO::write(T x) {
	static char buf[512];
	*std :: to_chars(buf, buf + 512, x, std :: chars_format::fixed, precision).ptr = 0;
	write(buf);
}
void IO::write(char *s) {
	while (*s)
		putch(*s++);
}
void IO::write(const char *s) {
	while (*s)
		putch(*s++);
}
void IO::write(const std :: string &s) { write(s.data()); }
template <typename T> void IO::write(std :: initializer_list<T> t) {
	auto first = std :: begin(t), last = std :: end(t);
	if (first != last)
		for (write(*first++); first != last; ++first) {
			putch(' ');
			write(*first);
		}
}
template <tupleLike T> void IO::write(T &&t) {
	[&]<std :: size_t... I>(std :: index_sequence<I...>) {
		(..., (I == 0 ? void(0) : putch(' '), write(std :: get<I>(t))));
	}(std :: make_index_sequence<std :: tuple_size_v<std :: remove_reference_t<T>>>());
}
template <std :: ranges::input_range R> void IO::write(R &&r) {
	if constexpr (std :: is_same_v<std :: decay_t<R>, std :: string>)
		return write(r.data());
	auto first = std :: ranges::begin(r), last = std :: ranges::end(r);
	if (first != last)
		for (write(*first++); first != last; ++first) {
			putch(' ');
			write(*first);
		}
}
template <typename... Args> void IO::writeln(Args &&...x) { write(std :: forward<Args>(x)...), putch('\n'); }
template <typename T> inline void IO::writespc(T && x) { write(x), putch('\n'); }
} // namespace FastIO
using namespace FastIO;

# else

# ifndef LUOGU
# define auto_att __attribute__((target("avx2"), optimize(3, "Ofast", "unroll-loops", "inline")))
# else
# define auto_att
# endif

namespace FastIO {
# define endl '\n'
INLINE_V static constexpr size_t buf_size = 1 << 18;
INLINE_V static constexpr size_t integer_size = 20;
INLINE_V static constexpr size_t block_size = 10000;

static char inbuf[buf_size + 1] = {};
static char outbuf[buf_size + 1] = {};
static char block_str[block_size * 4 + 1] = {};

static constexpr uint64_t power10[] = {1,
                                       10,
                                       100,
                                       1000,
                                       10000,
                                       100000,
                                       1000000,
                                       10000000,
                                       100000000,
                                       1000000000,
                                       10000000000,
                                       100000000000,
                                       1000000000000,
                                       10000000000000,
                                       100000000000000,
                                       1000000000000000,
                                       10000000000000000,
                                       100000000000000000,
                                       1000000000000000000,
                                       10000000000000000000u
                                      };

struct Scanner {
# ifndef LOCAL
private:
	size_t pos, end;

	inline void load() {
		end = fread(inbuf, 1, buf_size, stdin);
		inbuf[end] = '\0';
	}
	inline void reload() {
		size_t len = end - pos;
		memmove(inbuf, inbuf + pos, len);
		end = len + fread(inbuf + len, 1, buf_size - len, stdin);
		inbuf[end] = '\0';
		pos = 0;
	}
	inline void skip_space() {
		while (inbuf[pos] <= ' ') {
			if (__builtin_expect(++pos == end, 0))
				reload();
		}
	}
	inline char get_next() { return inbuf[pos++]; }
	inline char get_next_nonspace() {
		skip_space();
		return inbuf[pos++];
	}

public:
	Scanner() { load(); }

	auto_att inline void read(char &c) { c = get_next_nonspace(); }
	auto_att inline void read(std :: string &s) {
		skip_space();
		s = "";
		do {
			size_t start = pos;
			while (inbuf[pos] > ' ')
				++pos;
			s += std :: string(inbuf + start, inbuf + pos);
			if (inbuf[pos] != '\0')
				break;
			reload();
		} while (true);
	}

	template <class T> typename std :: enable_if<std :: is_integral<T>::value, void>::type read(T &x) {
		char c = get_next_nonspace();
		if (__builtin_expect(pos + integer_size >= end, 0))
			reload();
		bool neg = false;
		if (c == '-')
			neg = true, x = 0;
		else
			x = c & 15;
		while ((c = get_next()) >= '0')
			x = (x << 3) + (x << 1) + (c & 15);
		if (neg)
			x = -x;
	}
# else
	template <typename _Tp> inline void read(_Tp &x) {
		char ch = getchar();
		int f = 1;
		x = 0;
		for (; ch < '0' || ch > '9'; ch = getchar())
			f = ch == '-' ? -1 : 1;
		for (; ch >= '0' && ch <= '9'; ch = getchar())
			x = (x << 3) + (x << 1) + (ch ^ 48);
		x *= f;
	}
	inline void read(char &c) { c = getchar(); }
	inline void read(char *x) {
		int i = 0;
		char c = ' ';
		for (; c <= ' ';)
			c = getchar();
		for (; c > ' ';)
			x[i++] = c, c = getchar();
		x[i] = 0;
	}
	inline void read(std :: string &x) {
		x.clear();
		char c = ' ';
		for (; c <= ' ';)
			c = getchar();
		for (; c > ' ';)
			x += c, c = getchar();
	}
# endif
	template <class Head, class... Others> void read(Head &head, Others &...others) {
		read(head);
		read(others...);
	}
	template <class T1, class T2> inline void read(std :: pair<T1, T2> &x) { read(x.first), read(x.second); }
} is;

struct Printer {
# ifndef LOCAL
private:
	size_t pos = 0;

	auto_att inline void flush() {
		fwrite(outbuf, 1, pos, stdout);
		pos = 0;
	}

	inline void pre_calc() {
		for (size_t i = 0; i < block_size; ++i) {
			size_t j = 4, k = i;
			while (j--) {
				block_str[i * 4 + j] = k % 10 | 48;
				k /= 10;
			}
		}
	}

	static EXPR size_t get_integer_size(uint64_t n) {
		if (n >= power10[10]) {
			if (n >= power10[19])
				return 20;
			if (n >= power10[18])
				return 19;
			if (n >= power10[17])
				return 18;
			if (n >= power10[16])
				return 17;
			if (n >= power10[15])
				return 16;
			if (n >= power10[14])
				return 15;
			if (n >= power10[13])
				return 14;
			if (n >= power10[12])
				return 13;
			if (n >= power10[11])
				return 12;
			return 11;
		} else {
			if (n >= power10[9])
				return 10;
			if (n >= power10[8])
				return 9;
			if (n >= power10[7])
				return 8;
			if (n >= power10[6])
				return 7;
			if (n >= power10[5])
				return 6;
			if (n >= power10[4])
				return 5;
			if (n >= power10[3])
				return 4;
			if (n >= power10[2])
				return 3;
			if (n >= power10[1])
				return 2;
			return 1;
		}
	}

public:
	Printer() { pre_calc(); }
	~Printer() { flush(); }
	inline void write(char c) {
		outbuf[pos++] = c;
		if (__builtin_expect(pos == buf_size, 0))
			flush();
	}
	inline void write(const char *s) {
		while (*s != 0) {
			outbuf[pos++] = *s++;
			if (__builtin_expect(pos == buf_size, 0))
				flush();
		}
	}
	inline void write(const std :: string &s) {
		for (auto c : s) {
			outbuf[pos++] = c;
			if (__builtin_expect(pos == buf_size, 0))
				flush();
		}
	}

	template <class T> typename std :: enable_if<std :: is_integral<T>::value, void>::type write(T x) {
		if (__builtin_expect(pos + integer_size >= buf_size, 0))
			flush();
		if (x < 0)
			write('-'), x = -x;
		size_t digit = get_integer_size(x);
		size_t len = digit;
		while (len >= 4) {
			len -= 4;
			memcpy(outbuf + pos + len, block_str + ((x % block_size) << 2), 4);
			x /= block_size;
		}
		memcpy(outbuf + pos, block_str + (x << 2) + (4 - len), len);
		pos += digit;
	}
# else
	inline void write(char c) { putchar(c); }
	inline void write(const char *x) {
		for (int i = 0; x[i]; ++i)
			write(x[i]);
	}
	inline void write(std::string s) {
		for (auto c : s)
			write(c);
	}
	template <typename _Tp> inline void write(_Tp x) {
		if (x < 0)
			putchar('-'), x = -x;
		if (x > 9)
			write(x / 10);
		putchar(x % 10 ^ 48);
	}
# endif
	template <class Head, class... Others> void write(const Head &head, const Others &...others) {
		write(head);
		write(' ');
		write(others...);
	}

	template <class... Args> void writeln(const Args &...args) {
		write(args...);
		write('\n');
	}
	template < class T >
	inline void writespc ( const T & x ) {
		write ( x );
		write ( " " );
	}
	template <class T1, class T2> inline void write(const std :: pair<T1, T2> &x) { write(x.first, x.second); }
} os;

struct IO : public Scanner, public Printer {
} io;
}; // namespace FastIO
using namespace FastIO;
# endif
# endif
using namespace std;

# warning Do not use debug.hpp.

#ifndef ATCODER_MODINT_HPP
#define ATCODER_MODINT_HPP 1

#include <type_traits>

#ifdef _MSC_VER
#include <intrin.h>
#endif

#ifndef ATCODER_INTERNAL_MATH_HPP
#define ATCODER_INTERNAL_MATH_HPP 1

#include <utility>

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
  x %= m;
  if (x < 0)
    x += m;
  return x;
}

// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
  unsigned int _m;
  unsigned long long im;

  // @param m `1 <= m < 2^31`
  barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

  // @return m
  unsigned int umod() const { return _m; }

  // @param a `0 <= a < m`
  // @param b `0 <= b < m`
  // @return `a * b % m`
  unsigned int mul(unsigned int a, unsigned int b) const {
    // [1] m = 1
    // a = b = im = 0, so okay

    // [2] m >= 2
    // im = ceil(2^64 / m)
    // -> im * m = 2^64 + r (0 <= r < m)
    // let z = a*b = c*m + d (0 <= c, d < m)
    // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
    // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) <
    // 2^64 * 2
    // ((ab * im) >> 64) == c or c + 1
    unsigned long long z = a;
    z *= b;
#ifdef _MSC_VER
    unsigned long long x;
    _umul128(z, im, &x);
#else
    unsigned long long x =
        (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
    unsigned int v = (unsigned int)(z - x * _m);
    if (_m <= v)
      v += _m;
    return v;
  }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
  if (m == 1)
    return 0;
  unsigned int _m = (unsigned int)(m);
  unsigned long long r = 1;
  unsigned long long y = safe_mod(x, m);
  while (n) {
    if (n & 1)
      r = (r * y) % _m;
    y = (y * y) % _m;
    n >>= 1;
  }
  return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
  if (n <= 1)
    return false;
  if (n == 2 || n == 7 || n == 61)
    return true;
  if (n % 2 == 0)
    return false;
  long long d = n - 1;
  while (d % 2 == 0)
    d /= 2;
  constexpr long long bases[3] = {2, 7, 61};
  for (long long a : bases) {
    long long t = d;
    long long y = pow_mod_constexpr(a, t, n);
    while (t != n - 1 && y != 1 && y != n - 1) {
      y = y * y % n;
      t <<= 1;
    }
    if (y != n - 1 && t % 2 == 0) {
      return false;
    }
  }
  return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
  a = safe_mod(a, b);
  if (a == 0)
    return {b, 0};

  // Contracts:
  // [1] s - m0 * a = 0 (mod b)
  // [2] t - m1 * a = 0 (mod b)
  // [3] s * |m1| + t * |m0| <= b
  long long s = b, t = a;
  long long m0 = 0, m1 = 1;

  while (t) {
    long long u = s / t;
    s -= t * u;
    m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b

    // [3]:
    // (s - t * u) * |m1| + t * |m0 - m1 * u|
    // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
    // = s * |m1| + t * |m0| <= b

    auto tmp = s;
    s = t;
    t = tmp;
    tmp = m0;
    m0 = m1;
    m1 = tmp;
  }
  // by [3]: |m0| <= b/g
  // by g != b: |m0| < b/g
  if (m0 < 0)
    m0 += b / s;
  return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
  if (m == 2)
    return 1;
  if (m == 167772161)
    return 3;
  if (m == 469762049)
    return 3;
  if (m == 754974721)
    return 11;
  if (m == 998244353)
    return 3;
  int divs[20] = {};
  divs[0] = 2;
  int cnt = 1;
  int x = (m - 1) / 2;
  while (x % 2 == 0)
    x /= 2;
  for (int i = 3; (long long)(i)*i <= x; i += 2) {
    if (x % i == 0) {
      divs[cnt++] = i;
      while (x % i == 0) {
        x /= i;
      }
    }
  }
  if (x > 1) {
    divs[cnt++] = x;
  }
  for (int g = 2;; g++) {
    bool ok = true;
    for (int i = 0; i < cnt; i++) {
      if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
        ok = false;
        break;
      }
    }
    if (ok)
      return g;
  }
}
template <int m>
constexpr int primitive_root = primitive_root_constexpr(m);

}  // namespace internal

}  // namespace atcoder

#endif  // ATCODER_INTERNAL_MATH_HPP

#ifndef ATCODER_INTERNAL_TYPE_TRAITS_HPP
#define ATCODER_INTERNAL_TYPE_TRAITS_HPP 1

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T>
using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T>
using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder

#endif  // ATCODER_INTERNAL_TYPE_TRAITS_HPP

namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T>
using is_modint = std::is_base_of<modint_base, T>;
template <class T>
using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
  using mint = static_modint;

 public:
  static constexpr int mod() { return m; }
  static mint raw(int v) {
    mint x;
    x._v = v;
    return x;
  }

  static_modint() : _v(0) {}
  template <class T, internal::is_signed_int_t<T>* = nullptr>
  static_modint(T v) {
    long long x = (long long)(v % (long long)(umod()));
    if (x < 0)
      x += umod();
    _v = (unsigned int)(x);
  }
  template <class T, internal::is_unsigned_int_t<T>* = nullptr>
  static_modint(T v) {
    _v = (unsigned int)(v % umod());
  }

  unsigned int val() const { return _v; }

  mint& operator++() {
    _v++;
    if (_v == umod())
      _v = 0;
    return *this;
  }
  mint& operator--() {
    if (_v == 0)
      _v = umod();
    _v--;
    return *this;
  }
  mint operator++(int) {
    mint result = *this;
    ++*this;
    return result;
  }
  mint operator--(int) {
    mint result = *this;
    --*this;
    return result;
  }

  mint& operator+=(const mint& rhs) {
    _v += rhs._v;
    if (_v >= umod())
      _v -= umod();
    return *this;
  }
  mint& operator-=(const mint& rhs) {
    _v -= rhs._v;
    if (_v >= umod())
      _v += umod();
    return *this;
  }
  mint& operator*=(const mint& rhs) {
    unsigned long long z = _v;
    z *= rhs._v;
    _v = (unsigned int)(z % umod());
    return *this;
  }
  mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

  mint operator+() const { return *this; }
  mint operator-() const { return mint() - *this; }

  mint pow(long long n) const {
    assert(0 <= n);
    mint x = *this, r = 1;
    while (n) {
      if (n & 1)
        r *= x;
      x *= x;
      n >>= 1;
    }
    return r;
  }
  mint inv() const {
    if (prime) {
      assert(_v);
      return pow(umod() - 2);
    } else {
      auto eg = internal::inv_gcd(_v, m);
      assert(eg.first == 1);
      return eg.second;
    }
  }

  friend mint operator+(const mint& lhs, const mint& rhs) {
    return mint(lhs) += rhs;
  }
  friend mint operator-(const mint& lhs, const mint& rhs) {
    return mint(lhs) -= rhs;
  }
  friend mint operator*(const mint& lhs, const mint& rhs) {
    return mint(lhs) *= rhs;
  }
  friend mint operator/(const mint& lhs, const mint& rhs) {
    return mint(lhs) /= rhs;
  }
  friend bool operator==(const mint& lhs, const mint& rhs) {
    return lhs._v == rhs._v;
  }
  friend bool operator!=(const mint& lhs, const mint& rhs) {
    return lhs._v != rhs._v;
  }

 private:
  unsigned int _v;
  static constexpr unsigned int umod() { return m; }
  static constexpr bool prime = internal::is_prime<m>;
};

template <int id>
struct dynamic_modint : internal::modint_base {
  using mint = dynamic_modint;

 public:
  static int mod() { return (int)(bt.umod()); }
  static void set_mod(int m) {
    assert(1 <= m);
    bt = internal::barrett(m);
  }
  static mint raw(int v) {
    mint x;
    x._v = v;
    return x;
  }

  dynamic_modint() : _v(0) {}
  template <class T, internal::is_signed_int_t<T>* = nullptr>
  dynamic_modint(T v) {
    long long x = (long long)(v % (long long)(mod()));
    if (x < 0)
      x += mod();
    _v = (unsigned int)(x);
  }
  template <class T, internal::is_unsigned_int_t<T>* = nullptr>
  dynamic_modint(T v) {
    _v = (unsigned int)(v % mod());
  }

  unsigned int val() const { return _v; }

  mint& operator++() {
    _v++;
    if (_v == umod())
      _v = 0;
    return *this;
  }
  mint& operator--() {
    if (_v == 0)
      _v = umod();
    _v--;
    return *this;
  }
  mint operator++(int) {
    mint result = *this;
    ++*this;
    return result;
  }
  mint operator--(int) {
    mint result = *this;
    --*this;
    return result;
  }

  mint& operator+=(const mint& rhs) {
    _v += rhs._v;
    if (_v >= umod())
      _v -= umod();
    return *this;
  }
  mint& operator-=(const mint& rhs) {
    _v += mod() - rhs._v;
    if (_v >= umod())
      _v -= umod();
    return *this;
  }
  mint& operator*=(const mint& rhs) {
    _v = bt.mul(_v, rhs._v);
    return *this;
  }
  mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

  mint operator+() const { return *this; }
  mint operator-() const { return mint() - *this; }

  mint pow(long long n) const {
    assert(0 <= n);
    mint x = *this, r = 1;
    while (n) {
      if (n & 1)
        r *= x;
      x *= x;
      n >>= 1;
    }
    return r;
  }
  mint inv() const {
    auto eg = internal::inv_gcd(_v, mod());
    assert(eg.first == 1);
    return eg.second;
  }

  friend mint operator+(const mint& lhs, const mint& rhs) {
    return mint(lhs) += rhs;
  }
  friend mint operator-(const mint& lhs, const mint& rhs) {
    return mint(lhs) -= rhs;
  }
  friend mint operator*(const mint& lhs, const mint& rhs) {
    return mint(lhs) *= rhs;
  }
  friend mint operator/(const mint& lhs, const mint& rhs) {
    return mint(lhs) /= rhs;
  }
  friend bool operator==(const mint& lhs, const mint& rhs) {
    return lhs._v == rhs._v;
  }
  friend bool operator!=(const mint& lhs, const mint& rhs) {
    return lhs._v != rhs._v;
  }

 private:
  unsigned int _v;
  static internal::barrett bt;
  static unsigned int umod() { return bt.umod(); }
};
template <int id>
internal::barrett dynamic_modint<id>::bt = 998244353;

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class>
struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal

}  // namespace atcoder

#endif  // ATCODER_MODINT_HPP

using mint = atcoder :: modint1000000007;

# define x1 Daniel1234
# define y1 AK_IOI

INLINE_V constexpr static int N = 3e3 + 5;
INLINE_V constexpr static int B = 55;

int n, q;
mint a[2][N][N];
struct Query {
	int opt, x1, y1, x2, y2; mint d;
	inline void rd() { io.read(opt, x1, y1, x2, y2); if (opt == 2) { int x; io.read(x); d = x; } }
} que[N];

struct Trans {
	short xx = 1, xy = 0, xB = 0, yx = 0, yy = 1, yB = 0;
	mint sm = 0;
	inline void rtt(const Query & qry) {
    // cerr << xx << " " << xy << " " << yx << " " << yy << "\n";
		int _xx = xx, _xy = xy, _xB = xB;
		xx = -yx, xy = -yy, xB = qry.x2 + qry.y1 - yB;
		yx = _xx, yy = _xy, yB = qry.y1 - qry.x1 + _xB;
    // cerr << xx << " " << xy << " " << yx << " " << yy << " " << xB << " " << yB << "\n";
    // cerr << qry.x1 << " " << qry.y1 << " " << qry.x2 << " " << qry.y2 << " " << xB <<  " " << yB << " " << xx << " " << xy << " " << yx << " " << yy << "\n";
	}
	inline void add(const Query & qry) { sm += qry.d; }
	inline void cfg(int &x, int &y) {
		int _x = x; x = xx * x + xy * y + xB, y = yx * _x + yy * y + yB;
    // cerr << "cfg : " << x << " " << y << "\n";
	}
  inline void wrk(short &x, short &y) {
    // cerr << "x = " << x << ", y = " << y << ", xx = " << xx << ", yy = " << yy << "\n";
		if (!xy && !yx) x = (x - xB) / xx, y = (y - yB) / yy;
		else if (!xx && !yy) { int _x = x; x = (y - yB) / yx, y = (_x - xB) / xy; }
		else assert(false);
    // cerr << "wrk : " << x << " " << y << "\n";
	}
  // inline void dbg() {
  //   cerr << "xx = " << xx << ", xy = " << xy << ", yx = " << yx << ", yy = " << yy << "\n";
  // }
};

struct BLK {
	short xl, xr, yl, yr;
	template < class T >
	requires ( std :: is_signed_v < T > || std :: is_unsigned_v < T > )
	BLK (T _xl, T _xr, T _yl, T _yr) : xl(_xl), xr(_xr), yl(_yl), yr(_yr) {}
  // inline void dbg() {
  //   cerr << "xl = " << xl << ", xr = " << xr << ", yl = " << yl << ", yr = " << yr << "\n";
  // }
};

vector<pair<BLK, Trans>>vc[2];

signed main() {
	io.read(n, q);
	rep(i, 1, n) rep(j, 1, n, t = 1) a[0][i][j] = t = 1ll * t * (i + 1) % 998244353;
  // rep(i, 1, n) rep(j, 1, n) cerr << a[0][i][j].val() << (j == n ? "\n" : " ");
  rep(i, 1, q)que[i].rd();
	for (int bll = 1, blr; bll <= q; bll += B) {
		blr = min (bll + B - 1, q);
		vc[0].emb(BLK(1, n, 1, n), Trans());
		rep(i, bll, blr) {
			for (auto [blk, trs] : vc[0]) {
				vector<pair<short, short>> vx, vy;
				if (que[i].x2 < blk.xl || blk.xr < que[i].x1 || (que[i].x1 <= blk.xl && blk.xr <= que[i].x2))
					vx.emb(blk.xl, blk.xr);
				else if (que[i].x1 <= blk.xl && que[i].x2 < blk.xr)
					vx.emb(blk.xl, que[i].x2), vx.emb(que[i].x2 + 1, blk.xr);
				else if (blk.xl < que[i].x1 && blk.xr <= que[i].x2)
					vx.emb(blk.xl, que[i].x1 - 1), vx.emb(que[i].x1, blk.xr);
				else vx.emb(que[i].x1, que[i].x2),
					     vx.emb(blk.xl, que[i].x1 - 1), vx.emb(que[i].x2 + 1, blk.xr);
				if (que[i].y2 < blk.yl || blk.yr < que[i].y1 || (que[i].y1 <= blk.yl && blk.yr <= que[i].y2))
					vy.emb(blk.yl, blk.yr);
				else if (que[i].y1 <= blk.yl && que[i].y2 < blk.yr)
					vy.emb(blk.yl, que[i].y2), vy.emb(que[i].y2 + 1, blk.yr);
				else if (blk.yl < que[i].y1 && blk.yr <= que[i].y2)
					vy.emb(blk.yl, que[i].y1 - 1), vy.emb(que[i].y1, blk.yr);
				else vy.emb(que[i].y1, que[i].y2),
					     vy.emb(blk.yl, que[i].y1 - 1), vy.emb(que[i].y2 + 1, blk.yr);
				for (auto xi : vx) for (auto yi : vy) {
						BLK _blk = BLK(xi.first, xi.second, yi.first, yi.second);
						Trans _trs = trs;
						if (que[i].x1 <= _blk.xl && _blk.xr <= que[i].x2 &&
						    que[i].y1 <= _blk.yl && _blk.yr <= que[i].y2) {
							if (que[i].opt == 1) {
								_trs.rtt(que[i]);
								_blk.xl = que[i].x2 + que[i].y1 - _blk.yr, _blk.xr = que[i].x2 + que[i].y1 - _blk.yl;
								_blk.yl = que[i].y1 - que[i].x1 + xi.first, _blk.yr = que[i].y1 - que[i].x1 + xi.second;
							} else _trs.add(que[i]);
						}
						vc[1].emb(_blk, _trs);
					}
			}
			vc[0].clear(), swap(vc[0], vc[1]);
		}
    // for (auto [blk, trs] : vc[0])
    //   blk.dbg();
    //  trs.dbg();
		for (auto [blk, trs] : vc[0]) {
      // cerr << blk.xl << " " << blk.xr << " " << blk.yl << " " << blk.yr << "\n";
			trs.wrk(blk.xl, blk.yl), trs.wrk(blk.xr, blk.yr);
			if (blk.xl > blk.xr) swap(blk.xl, blk.xr);
			if (blk.yl > blk.yr) swap(blk.yl, blk.yr);
      // cerr << blk.xl << " " << blk.xr << " " << blk.yl << " " << blk.yr << "\n";
			rep(i, blk.xl, blk.xr)rep(j, blk.yl, blk.yr) {
				int x = i, y = j; trs.cfg(x, y); a[1][x][y] = a[0][i][j] + trs.sm;
        // cerr << x << " " << y << " " << i << " " << j << "\n";
			}
		}
		vc[0].clear(), swap(a[0], a[1]);
	}
	mint ans = 0, t = 1;
  // rep(i, 1, n) rep(j, 1, n) cerr << a[0][i][j].val() << (j == n ? "\n" : " ");
  rep (i, 1, n) rep (j, 1, n) ans += a[0][i][j] * (t *= 12345);
	io.writeln(ans.val());

# if defined(LOCAL) && !defined(CPH)
	cerr << "Spend time : " << clock ( ) * 1. / CLOCKS_PER_SEC * 1000. << "ms\n";
# endif
	return 0;
}