//shiawase wa yukkuri hajimaru.

#define  _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES
#define _SILENCE_ALL_CXX17_DEPRECATION_WARNINGS
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma comment (linker, "/STACK:526000000")
#include "bits/stdc++.h"

#ifndef ATCODER_MODINT_HPP
#define ATCODER_MODINT_HPP 1

#ifndef ATCODER_INTERNAL_MATH_HPP
#define ATCODER_INTERNAL_MATH_HPP 1

#include <utility>

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 moduler 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`
			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;
			int vs[3] = { 2,7,61 };
			for (long long a : vs) {
				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

#include <cassert>
#include <numeric>
#include <type_traits>

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

#include <cassert>
#include <numeric>
#include <type_traits>

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

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());
		}
		static_modint(bool 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());
		}
		dynamic_modint(bool 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



#define int ll
using namespace std;
typedef string::const_iterator State;
#define eps 1e-8L
#define MAX_MOD 1000000007LL
#define GYAKU 500000004LL
#define MOD 998244353LL
#define pb push_back
#define mp make_pair
typedef long long ll;
typedef long double ld;
#define REP(a,b) for(long long (a) = 0;(a) < (b);++(a))
#define ALL(x) (x).begin(),(x).end()
unsigned long xor128() {
	static unsigned long x = 123456789, y = 362436069, z = 521288629, w = 88675123;
	unsigned long t = (x ^ (x << 11));
	x = y; y = z; z = w;
	return (w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)));
};
typedef complex<long double> Point;
typedef pair<complex<long double>, complex<long double>> Line;
typedef struct Circle {
	complex<long double> center;
	long double r;
}Circle;
long double dot(Point a, Point b) {
	return (a.real() * b.real() + a.imag() * b.imag());
}
long double cross(Point a, Point b) {
	return (a.real() * b.imag() - a.imag() * b.real());
}
long double Dist_Line_Point(Line a, Point b) {
	if (dot(a.second - a.first, b - a.first) < eps) return abs(b - a.first);
	if (dot(a.first - a.second, b - a.second) < eps) return abs(b - a.second);
	return abs(cross(a.second - a.first, b - a.first)) / abs(a.second - a.first);
}
int is_intersected_ls(Line a, Line b) {
	return (cross(a.second - a.first, b.first - a.first) * cross(a.second - a.first, b.second - a.first) < eps) &&
		(cross(b.second - b.first, a.first - b.first) * cross(b.second - b.first, a.second - b.first) < eps);
}
Point intersection_l(Line a, Line b) {
	Point da = a.second - a.first;
	Point db = b.second - b.first;
	return a.first + da * cross(db, b.first - a.first) / cross(db, da);
}
long double Dist_Line_Line(Line a, Line b) {
	if (is_intersected_ls(a, b) == 1) {
		return 0;
	}
	return min({ Dist_Line_Point(a,b.first), Dist_Line_Point(a,b.second),Dist_Line_Point(b,a.first),Dist_Line_Point(b,a.second) });
}
pair<Point, Point> intersection_Circle_Circle(Circle a, Circle b) {
	long double dist = abs(a.center - b.center);
	assert(dist <= eps + a.r + b.r);
	assert(dist + eps >= abs(a.r - b.r));
	Point target = b.center - a.center;
	long double pointer = target.real() * target.real() + target.imag() * target.imag();
	long double aa = pointer + a.r * a.r - b.r * b.r;
	aa /= 2.0L;
	Point l{ (aa * target.real() + target.imag() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer,
			(aa * target.imag() - target.real() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer };
	Point r{ (aa * target.real() - target.imag() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer,
		(aa * target.imag() + target.real() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer };
	r = r + a.center;
	l = l + a.center;
	return mp(l, r);
}
ll gcd(ll a, ll b) {
	if (b == 0) return a;
	return gcd(b, a % b);
}
template<typename A>
A pows(A val, ll b) {
	assert(b >= 1);
	A ans = val;
	b--;
	while (b) {
		if (b % 2) {
			ans *= val;
		}
		val *= val;
		b /= 2LL;
	}
	return ans;
}
template<typename A>
class Compressor {
public:
	bool is_zipped = false;
	map<A, ll> zipper;
	map<ll, A> unzipper;
	queue<A> fetcher;
	Compressor() {
		is_zipped = false;
		zipper.clear();
		unzipper.clear();
	}
	void add(A now) {
		assert(is_zipped == false);
		zipper[now] = 1;
		fetcher.push(now);
	}
	void exec() {
		assert(is_zipped == false);
		int cnt = 0;
		for (auto i = zipper.begin(); i != zipper.end(); ++i) {
			i->second = cnt;
			unzipper[cnt] = i->first;
			cnt++;
		}
		is_zipped = true;
	}
	ll fetch() {
		assert(is_zipped == true);
		A hoge = fetcher.front();
		fetcher.pop();
		return zipper[hoge];
	}
	ll zip(A now) {
		assert(is_zipped == true);
		assert(zipper.find(now) != zipper.end());
		return zipper[now];
	}
	A unzip(ll a) {
		assert(is_zipped == true);
		assert(a < unzipper.size());
		return unzipper[a];
	}
	ll next(A now) {
		auto x = zipper.upper_bound(now);
		if (x == zipper.end()) return zipper.size();
		return (ll)((*x).second);
	}
	ll back(A now) {
		auto x = zipper.lower_bound(now);
		if (x == zipper.begin()) return -1;
		x--;
		return (ll)((*x).second);
	}
};
template<typename A>
class Matrix {
public:
	vector<vector<A>> data;
	Matrix(vector<vector<A>> a) :data(a) {
	}
	Matrix operator + (const Matrix obj) {
		vector<vector<A>> ans;
		assert(obj.data.size() == this->data.size());
		assert(obj.data[0].size() == this->data[0].size());
		REP(i, obj.data.size()) {
			ans.push_back(vector<A>());
			REP(q, obj.data[i].size()) {
				A hoge = obj.data[i][q] + (this->data[i][q]);
				ans.back().push_back(hoge);
			}
		}
		return Matrix(ans);
	}
	Matrix operator - (const Matrix obj) {
		vector<vector<A>> ans;
		assert(obj.data.size() == this->data.size());
		assert(obj.data[0].size() == this->data[0].size());
		REP(i, obj.data.size()) {
			ans.push_back(vector<A>());
			REP(q, obj.data[i].size()) {
				A hoge = this->data[i][q] - obj.data[i][q];
				ans.back().push_back(hoge);
			}
		}
		return Matrix(ans);
	}
	Matrix operator * (const Matrix obj) {
		vector<vector<A>> ans;
		assert(obj.data.size() == this->data[0].size());
		REP(i, this -> data.size()) {
			ans.push_back(vector<A>());
			REP(q, obj.data[0].size()) {
				A hoge = ((this->data[i][0]) * (obj.data[0][q]));
				for (int t = 1; t < obj.data.size(); ++t) {
					hoge += ((this->data[i][t]) * obj.data[t][q]);
				}
				ans.back().push_back(hoge);
			}
		}
		return Matrix(ans);
	}
	Matrix& operator *= (const Matrix obj) {
		*this = (*this * obj);
		return *this;
	}
	Matrix& operator += (const Matrix obj) {
		*this = (*this + obj);
		return *this;
	}
	Matrix& operator -= (const Matrix obj) {
		*this = (*this - obj);
		return *this;
	}
};
struct Fraction {
	ll a;
	ll b;
	Fraction() :a(0LL), b(1LL) {
	}
	Fraction(ll c, ll d) {
		int hoge = gcd(llabs(c), llabs(d));
		if (hoge != 0) {
			c /= hoge;
			d /= hoge;
			if (d < 0 or (d == 0 and c < 0)) {
				d *= -1;
				c *= -1;
			}
		}
		a = c;
		b = d;
	}
	bool operator <(Fraction rhs) const {
		if (a < 0 and rhs.a > 0) return 1;
		if (a > 0 and rhs.a < 0) return 0;
		return a * rhs.b < rhs.a* b;
	}
	bool operator ==(Fraction rhs) const {
		return a == rhs.a and b == rhs.b;
	}
};
class Dice {
public:
	vector<ll> vertexs;
	Dice(vector<ll> init) :vertexs(init) {
	}
	void RtoL() {
		for (int q = 1; q < 4; ++q) {
			swap(vertexs[q], vertexs[q + 1]);
		}
	}
	void LtoR() {
		for (int q = 3; q >= 1; --q) {
			swap(vertexs[q], vertexs[q + 1]);
		}
	}
	void UtoD() {
		swap(vertexs[5], vertexs[4]);
		swap(vertexs[2], vertexs[5]);
		swap(vertexs[0], vertexs[2]);
	}
	void DtoU() {
		swap(vertexs[0], vertexs[2]);
		swap(vertexs[2], vertexs[5]);
		swap(vertexs[5], vertexs[4]);
	}
	bool ReachAble(Dice now) {
		set<Dice> hoge;
		queue<Dice> next;
		next.push(now);
		hoge.insert(now);
		while (next.empty() == false) {
			Dice seeing = next.front();
			next.pop();
			if (seeing == *this) return true;
			seeing.RtoL();
			if (hoge.count(seeing) == 0) {
				hoge.insert(seeing);
				next.push(seeing);
			}
			seeing.LtoR();
			seeing.LtoR();
			if (hoge.count(seeing) == 0) {
				hoge.insert(seeing);
				next.push(seeing);
			}
			seeing.RtoL();
			seeing.UtoD();
			if (hoge.count(seeing) == 0) {
				hoge.insert(seeing);
				next.push(seeing);
			}
			seeing.DtoU();
			seeing.DtoU();
			if (hoge.count(seeing) == 0) {
				hoge.insert(seeing);
				next.push(seeing);
			}
		}
		return false;
	}
	bool operator ==(const Dice& a) {
		for (int q = 0; q < 6; ++q) {
			if (a.vertexs[q] != (*this).vertexs[q]) {
				return false;
			}
		}
		return true;
	}
	bool operator <(const Dice& a) const {
		return (*this).vertexs < a.vertexs;
	}
};
pair<Dice, Dice> TwoDimDice(int center, int up) {
	int target = 1;
	while (true) {
		if (center != target && 7 - center != target && up != target && 7 - up != target) {
			break;
		}
		target++;
	}
	return mp(Dice(vector<ll>{up, target, center, 7 - target, 7 - center, 7 - up}), Dice(vector<ll>{up, 7 - target, center, target, 7 - center, 7 - up}));
}
tuple<Dice, Dice, Dice, Dice> OneDimDice(int center) {
	int bo = min(center, 7 - center);
	pair<int, int> goa;
	if (bo == 1) {
		goa = mp(2, 3);
	}
	else if (bo == 2) {
		goa = mp(1, 3);
	}
	else if (bo == 3) {
		goa = mp(1, 2);
	}
	tuple<Dice, Dice, Dice, Dice> now = make_tuple(Dice(vector<ll>{goa.first, goa.second, center, 7 - goa.second, 7 - center, 7 - goa.first}),
		Dice(vector<ll>{goa.first, 7 - goa.second, center, goa.second, 7 - center, 7 - goa.first}),
		Dice(vector<ll>{7 - goa.first, goa.second, center, 7 - goa.second, 7 - center, goa.first}),
		Dice(vector<ll>{7 - goa.first, 7 - goa.second, center, goa.second, 7 - center, goa.first}));
	return now;
}
class HLDecomposition {
public:
	vector<vector<int>> vertexs;
	vector<int> depth;
	vector<int> backs;
	vector<int> connections;
	vector<int> zip, unzip;
	HLDecomposition(int n) {
		vertexs = vector<vector<int>>(n, vector<int>());
		depth = vector<int>(n);
		zip = vector<int>(n);
		unzip = zip;
	}
	void add_edge(int a, int b) {
		vertexs[a].push_back(b);
		vertexs[b].push_back(a);
	}
	int depth_dfs(int now, int back) {
		depth[now] = 0;
		for (auto x : vertexs[now]) {
			if (x == back) continue;
			depth[now] = max(depth[now], 1 + depth_dfs(x, now));
		}
		return depth[now];
	}
	void dfs(int now, int backing) {
		zip[now] = backs.size();
		unzip[backs.size()] = now;
		backs.push_back(backing);
		int now_max = -1;
		int itr = -1;
		for (auto x : vertexs[now]) {
			if (depth[x] > depth[now]) continue;
			if (now_max < depth[x]) {
				now_max = depth[x];
				itr = x;
			}
		}
		if (itr == -1) return;
		connections.push_back(connections.back());
		dfs(itr, backing);
		for (auto x : vertexs[now]) {
			if (depth[x] > depth[now]) continue;
			if (x == itr) continue;
			connections.push_back(zip[now]);
			dfs(x, backs.size());
		}
		return;
	}
	void build() {
		depth_dfs(0, -1);
		connections.push_back(-1);
		dfs(0, -1);
	}
	vector<pair<int, int>> query(int a, int b) {
		a = zip[a];
		b = zip[b];
		vector<pair<int, int>> ans;
		while (backs[a] != backs[b]) {
			if (a < b) swap(a, b);
			ans.push_back(mp(backs[a], a + 1));
			a = connections[a];
		}
		if (a > b) swap(a, b);
		ans.push_back(mp(a, b + 1));
		return ans;
	}
	int lca(int a, int b) {
		a = zip[a];
		b = zip[b];
		while (backs[a] != backs[b]) {
			if (a < b) swap(a, b);
			a = connections[a];
		}
		return unzip[min(a, b)];
	}
};
void init() {
	iostream::sync_with_stdio(false);
	cout << fixed << setprecision(50);
}
using namespace atcoder;
#define int ll

pair<int, int> ut[3100][3100];
bool bad_left[3100][3100];
bool bad_up[3100][3100];
pair<int, int> uf(pair<int, int> now) {
	if (ut[now.first][now.second] == now) return now;
	return ut[now.first][now.second] = uf(ut[now.first][now.second]);
}
void um(pair<int, int> a, pair<int, int> b) {
	a = uf(a);
	b = uf(b);
	ut[a.first][a.second] = b;
	return;
}
void solve() {
	int n, m;
	cin >> n >> m;
	map<int, int> X, Y;
	REP(q, 3) {
		X[-1e10 + q] = 0;
		X[1e10 + q] = 0;
		Y[-1e10 + q] = 0;
		Y[1e10 + q] = 0;
	}
	X[0] = 0;
	Y[0] = 0;
	vector<tuple<int, int, int>> inputs[2];
	REP(i, n) {
		int a, b, c;
		cin >> a >> b >> c;
		inputs[0].push_back(make_tuple(a, b, c));
		X[a] = 0;
		X[b] = 0;
		Y[c] = 0;
	}
	REP(i, m) {
		int a, b, c;
		cin >> a >> b >> c;
		inputs[1].push_back(make_tuple(a, b, c));
		X[a] = 0;
		Y[b] = 0;
		Y[c] = 0;
	}
	{
		int itr = 0;
		for (auto& x : X) {
			x.second = itr;
			itr++;
		}
	}
	{
		int itr = 0;
		for (auto& x : Y) {
			x.second = itr;
			itr++;
		}
	}
	REP(i, n) {
		int x_min = X[get<0>(inputs[0][i])];
		int x_max = X[get<1>(inputs[0][i])];
		int y = Y[get<2>(inputs[0][i])];
		for (int q = x_min; q < x_max; ++q) {
			bad_left[q][y] = 1;
		}
	}
	REP(i, m) {
		int x = X[get<0>(inputs[1][i])];
		int y_min = Y[get<1>(inputs[1][i])];
		int y_max = Y[get<2>(inputs[1][i])];
		for (int q = y_min; q < y_max; ++q) {
			bad_up[x][q] = 1;
		}
	}
	REP(i, X.size()) {
		REP(q, Y.size()) {
			ut[i][q] = mp(i, q);
		}
	}
	REP(i, X.size()) {
		for (int q = 1; q < Y.size(); ++q) {
			if (bad_left[i][q] == 0) {
				um(mp(i, q), mp(i, q - 1));
			}
		}
	}
	REP(q, Y.size()) {
		for (int i = 1; i < X.size(); ++i) {
			if (bad_up[i][q] == 0) {
				um(mp(i, q), mp(i - 1, q));
			}
		}
	}
	if ((uf(mp(0, 0)) == uf(mp(X[0], Y[0])))) {
		cout << "INF" << endl;
		return;
	}
	int ans = 0;
	vector<int> XS, YS;
	for (auto& x : X) {
		XS.push_back(x.first);
	}
	for (auto& x : Y) {
		YS.push_back(x.first);
	}
	sort(ALL(XS));
	sort(ALL(YS));
	for (int i = 1; i < X.size() - 1; ++i) {
		for (int q = 1; q < Y.size() - 1; ++q) {
			if (uf(mp(i, q)) == uf(mp(X[0], Y[0]))) {
				ans += (XS[i + 1] - XS[i]) * (YS[q + 1] - YS[q]);
			}
		}
	}
	cout << ans << endl;
}
#undef int
int main() {
	init();
	int t = 1;
	REP(tea, t) {
		solve();
	}
}





Measured memory_bytes: 164396