結果

問題 No.303 割れません
ユーザー antaanta
提出日時 2015-11-26 00:34:54
言語 C++11
(gcc 11.4.0)
結果
CE  
(最新)
AC  
(最初)
実行時間 -
コード長 31,490 bytes
コンパイル時間 517 ms
コンパイル使用メモリ 76,572 KB
最終ジャッジ日時 2024-04-27 02:16:04
合計ジャッジ時間 1,321 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
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コンパイルエラー時のメッセージ・ソースコードは、提出者また管理者しか表示できないようにしております。（リジャッジ後のコンパイルエラーは公開されます）
ただし、clay言語の場合は開発者のデバッグのため、公開されます。

コンパイルメッセージ
main.cpp: In static member function ‘static multiprec::BigInt::BaseData multiprec::BigInt::_get_basedata(multiprec::BigInt::W)’:
main.cpp:1071:38: error: ‘log’ was not declared in this scope; did you mean ‘long’?
 1071 |                 res.log_base_ratio = log(2.0) / std::log(double(base));
      |                                      ^~~
      |                                      long
main.cpp:1071:54: error: ‘log’ is not a member of ‘std’; did you mean ‘clog’?
 1071 |                 res.log_base_ratio = log(2.0) / std::log(double(base));
      |                                                      ^~~
      |                                                      clog
main.cpp: In static member function ‘static size_t multiprec::BigInt::_estimate_size_in_base(const W*, int, const multiprec::BigInt::BaseData&)’:
main.cpp:1088:36: error: ‘ceil’ was not declared in this scope
 1088 |         return static_cast<size_t>(ceil(static_cast<double>(bit_size) * data.log_base_ratio));
      |                                    ^~~~

ソースコード

diff # 

#include <iostream>
#include <cstdint>
#include <vector>
#include <memory>
#include <algorithm>
#include <numeric>
#ifndef __GNUC__
#include <intrin.h>
#endif
#if !defined(MY_LOCAL_RUN) && !defined(NDEBUG)
#define NDEBUG
#endif
#include <cassert>
#include <initializer_list>
#include <string>
#include <tuple>
using namespace std;

#if defined(_M_X64) || defined(__amd64__)
#define MULTIPREC_64BIT
#endif

#if defined(MY_LOCAL_RUN)
#define MP_TEST
#endif

namespace uint_util {

#if defined(_MSC_VER) && !defined(__clang__)
#pragma section(".mycode", execute)
__declspec(allocate(".mycode")) const unsigned char udiv128Data[] = {0x48, 0x89, 0xD0, 0x48, 0x89, 0xCA, 0x49, 0xF7, 0xF0, 0xC3};
uint64_t(__fastcall *udiv128)(uint64_t numhi, uint64_t numlo, uint64_t den) = (uint64_t(__fastcall *)(uint64_t, uint64_t, uint64_t))(void*)(udiv128Data);
#endif

template<typename T> struct Utils {};

#ifdef MULTIPREC_64BIT

template<>
struct Utils<uint64_t> {

#if defined(_MSC_VER) && !defined(__clang__)
	static void umul_full(uint64_t a, uint64_t b, uint64_t *hi, uint64_t *lo) {
		*lo = _umul128(a, b, hi);
	}

	static uint64_t udiv_full(uint64_t num_hi, uint64_t num_lo, uint64_t den) {
		return udiv128(num_hi, num_lo, den);
	}
#else
	static void umul_full(uint64_t a, uint64_t b, uint64_t *hi, uint64_t *lo) {
		const auto c = (unsigned __int128)a * b;
		*lo = (uint64_t)c;
		*hi = (uint64_t)(c >> 64);
	}

	static uint64_t udiv_full(uint64_t num_hi, uint64_t num_lo, uint64_t den) {
		uint64_t quot;
		asm("div %3":"=a"(quot):"a"(num_lo),"d"(num_hi),"r"(den));
		return quot;
	}
#endif

	static uint64_t div_preinv_invert(uint64_t b) {
		assert(b >> 63 & 1);
		return udiv_full(~0ULL - b, ~0ULL, b);
	}

	static uint64_t addcarry(uint64_t a, uint64_t b, uint64_t *c) {
		uint64_t t = a + b;
		bool ct = t < a;
		uint64_t u = t + *c;
		bool cu = u < t;
		*c = ct + cu;
		return u;
	}

	static uint64_t subborrow(uint64_t a, uint64_t b, uint64_t *c) {
		uint64_t t = a - b;
		bool ct = t > a;
		uint64_t u = t - *c;
		bool cu = u > t;
		*c = ct + cu;
		return u;
	}

	static void div_preinv(uint64_t num_hi, uint64_t num_lo, uint64_t den, uint64_t inv, uint64_t *quot, uint64_t *rem) {
		uint64_t qh, ql;
		umul_full(num_hi, inv, &qh, &ql);
		ql += num_lo;
		qh += ql < num_lo;
		qh += num_hi + 1;
		uint64_t r = num_lo - qh * den;
		uint64_t mask = -(r > ql);
		qh += mask;
		r += mask & den;
		if(r >= den) {
			qh += 1;
			r -= den;
		}
		*quot = qh;
		*rem = r;
	}

	static int count_leading_zeros(uint64_t x) {
#ifndef __GNUC__
		unsigned long pos;
		_BitScanReverse64(&pos, x);
		return 63 - pos;
#else
		return __builtin_clzll(x);
#endif
	}

	static int count_trailing_zeros(uint64_t x) {
#ifndef __GNUC__
		unsigned long pos;
		_BitScanForward64(&pos, x);
		return pos;
#else
		return __builtin_ctzll(x);
#endif
	}
};

#endif

template<> struct Utils<uint32_t> {
	
};


//for tests
template<>
struct Utils<uint8_t> {
	static void umul_full(uint8_t a, uint8_t b, uint8_t *hi, uint8_t *lo) {
		auto c = (unsigned)a * b;
		*hi = (uint8_t)(c >> 8), *lo = (uint8_t)c;
	}

	static uint8_t udiv_full(uint8_t num_hi, uint8_t num_lo, uint8_t den) {
		assert(((unsigned)num_hi << 8 | num_lo) / den < 0x100);
		return (uint8_t)(((unsigned)num_hi << 8 | num_lo) / den);
	}

	static uint8_t div_preinv_invert(uint8_t b) {
		assert(b >> 7 & 1);
		return udiv_full(0xff - b, 0xff, b);
	}

	static uint8_t addcarry(uint8_t a, uint8_t b, uint8_t *c) {
		unsigned t = (unsigned)a + b + *c;
		*c = (uint8_t)(t >> 8);
		return (uint8_t)t;
	}

	static uint8_t subborrow(uint8_t a, uint8_t b, uint8_t *c) {
		unsigned t = (unsigned)a - b - *c;
		*c = -(uint8_t)(t >> 8);
		return (uint8_t)t;
	}

	static void div_preinv(uint8_t num_hi, uint8_t num_lo, uint8_t den, uint8_t inv, uint8_t *quot, uint8_t *rem) {
		unsigned num = ((unsigned)num_hi << 8 | num_lo);
		assert(num / den < 0x100);
		*quot = (uint8_t)(num / den);
		*rem = (uint8_t)(num % den);
	}

	static int count_leading_zeros(uint8_t x) {
		assert(x != 0);
		int r = 1;
		while((unsigned)x >> r) ++ r;
		return 8 - r;
	}

	static int count_trailing_zeros(uint64_t x) {
		assert(x != 0);
		int r = 0;
		while(x >> r & 1) ++ r;
		return r;
	}
};

}


namespace multiprec {

class BigInt {
public:
#ifdef MP_TEST
	typedef uint8_t W;
#else
	typedef uint64_t W;
#endif
	typedef uint_util::Utils<W> Util;

	enum { W_BITS = sizeof(W) * 8 };
	enum : W { W_MAX = W(-1) };

private:
	std::vector<W> _words;
	bool _sign;

public:
	BigInt(): _words(), _sign(false) {}
	BigInt(W x) { set(x); }
	BigInt(int x) { set(x); }

	void clear() { _sign = false; _words.clear(); }

	bool zero() const { return _words.empty(); }
	bool negative() const { return _sign; }

private:
	W *data() { return _words.data(); }
	const W *data() const { return _words.data(); }

	int size() const { return static_cast<int>(_words.size()); }
	void resize(int n) { _words.resize(n); }

	bool normalized() const { return _words.empty() ? !_sign : _words.back() != 0; }
	void normalize_size() { while(!_words.empty() && _words.back() == 0) _words.pop_back(); }

public:
	void set(W w) {
		if(w == 0) {
			clear();
		} else {
			_sign = false;
			_words.assign({w});
		}
	}

	void set(int s) {
		if(s > 0) {
			_sign = false;
			_words.assign({static_cast<W>(s)});
		} else if(s < 0) {
			_sign = true;
			_words.assign({static_cast<W>(-s)});
		} else {
			clear();
		}
	}

	void set(const BigInt &that) {
		*this = that;
	}

	template<typename It>
	void set_words(It begin_it, It end_it) {
		_words.assign(begin_it, end_it);
		normalize_size();
		_sign = false;
	}

	bool operator==(const BigInt &that) const { return compare_to(that) == 0; }
	bool operator!=(const BigInt &that) const { return compare_to(that) != 0; }
	bool operator< (const BigInt &that) const { return compare_to(that) <  0; }
	bool operator> (const BigInt &that) const { return compare_to(that) >  0; }
	bool operator<=(const BigInt &that) const { return compare_to(that) <= 0; }
	bool operator>=(const BigInt &that) const { return compare_to(that) >= 0; }

	int compare_to(const BigInt &that) const {
		bool asign = _sign, bsign = that._sign;
		if(asign == bsign) {
			if(!asign)
				return compare_unsigned(*this, that);
			else
				return compare_unsigned(that, *this);
		} else {
			if(!asign)
				return +1;
			else
				return -1;
		}
	}

	static int compare_unsigned(const BigInt &a, const BigInt &b) {
		assert(a.normalized() && b.normalized());
		int an = a.size(), bn = b.size();
		if(an > bn) {
			return +1;
		} else if(an < bn) {
			return -1;
		} else {
			return _compare(a.data(), b.data(), an);
		}
	}

	BigInt &operator+=(const BigInt &that) {
		add_signed(*this, *this, _sign, that, that._sign);
		return *this;
	}
	BigInt operator+(const BigInt &that) const {
		BigInt res;
		add_signed(res, *this, _sign, that, that._sign);
		return res;
	}

	BigInt &operator-=(const BigInt &that) {
		add_signed(*this, *this, _sign, that, !that._sign);
		return *this;
	}
	BigInt operator-(const BigInt &that) const {
		BigInt res;
		add_signed(res, *this, _sign, that, !that._sign);
		return res;
	}

	BigInt operator-() const {
		BigInt res = *this;
		if(!zero())
			res._sign = !res._sign;
		return res;
	}

private:
	static void add_signed(BigInt &res, const BigInt &a, bool a_sign, const BigInt &b, bool b_sign) {
		if(a_sign == b_sign) {
			add_unsigned(res, a, b);
			res._sign = a_sign && !res.zero();
		} else if(b_sign) {
			res._sign = subtract_unsigned(res, a, b);
		} else {
			res._sign = subtract_unsigned(res, b, a);
		}
		assert(res.normalized());
	}

	static void add_unsigned(BigInt &res, const BigInt &a, const BigInt &b) {
		int an = a.size(), bn = b.size();

		if(an < bn)
			return add_unsigned(res, b, a);

		res.resize(an + 1);
		res._words[an] = _add(res.data(), a.data(), an, b.data(), bn);
		res.normalize_size();
	}

	static bool subtract_unsigned(BigInt &res, const BigInt &a, const BigInt &b) {
		int an = a.size(), bn = b.size();

		if(compare_unsigned(a, b) >= 0) {
			subtract_unsigned_guarded(res, a, b);
			return false;
		} else {
			subtract_unsigned_guarded(res, b, a);
			return true;
		}
	}

	//a >= b
	static void subtract_unsigned_guarded(BigInt &res, const BigInt &a, const BigInt &b) {
		int an = a.size(), bn = b.size();
		assert(an >= bn);

		res.resize(an);
		W borrow = _subtract(res.data(), a.data(), an, b.data(), bn);
		assert(borrow == 0);
		res.normalize_size();
	}

public:
	BigInt &operator*=(const BigInt &that) {
		multiply(*this, *this, that);
		return *this;
	}
	BigInt operator*(const BigInt &that) const {
		BigInt r;
		multiply(r, *this, that);
		return r;
	}

	static void multiply(BigInt &res, const BigInt &a, const BigInt &b) {
		int an = a.size(), bn = b.size();

		if(an < bn)
			return multiply(res, b, a);

		if(&res == &a || &res == &b) {
			BigInt ws;
			multiply(ws, a, b);
			res = ws;
			return;
		}

		if(bn == 0) {
			res.clear();
		} else {
			res.resize(an + bn);
			_multiply(res.data(), a.data(), an, b.data(), bn);
			res.normalize_size();
			res._sign = a._sign != b._sign;
		}
	}

public:
	BigInt &operator/=(const BigInt &that) {
		BigInt dummy;
		divide_trunc(*this, dummy, *this, that);
		return *this;
	}
	BigInt operator/(const BigInt &that) const {
		BigInt res, dummy;
		divide_trunc(res, dummy, *this, that);
		return res;
	}

	BigInt &operator%=(const BigInt &that) {
		BigInt dummy;
		divide_trunc(dummy, *this, *this, that);
		return *this;
	}
	BigInt operator%(const BigInt &that) const {
		BigInt res, dummy;
		divide_trunc(dummy, res, *this, that);
		return res;
	}

	static void divide_trunc(BigInt &quot, BigInt &rem, const BigInt &a, const BigInt &b) {
		bool asign = a._sign, bsign = b._sign;

		divide_floor_unsigned(quot, rem, a, b);

		quot._sign = asign != bsign && !quot.zero();
		rem._sign = asign && !rem.zero();
	}

private:
	static void divide_floor_unsigned(BigInt &quot, BigInt &rem, const BigInt &a, const BigInt &b) {
		if(&quot == &rem || &quot == &b) {
			BigInt ws;
			divide_floor_unsigned(ws, rem, a, b);
			quot = ws;
			return;
		}

		if(&rem == &b) {
			BigInt ws;
			divide_floor_unsigned(quot, ws, a, b);
			rem = ws;
			return;
		}

		assert(a.normalized() && b.normalized());
		int an = a.size(), bn = b.size();

		if(an < bn) {
			rem = a;
			quot = BigInt();
			return;
		}

		if(bn == 0) {
			std::cerr << "divide by 0" << std::endl;
			abort();
		}

		rem = a;
		quot.resize(an - bn + 1);
		_divide(quot.data(), rem.data(), an, b.data(), bn);

		quot.normalize_size();
		rem.resize(bn);
		rem.normalize_size();
	}

private:
	struct BaseData {
		W base;
		W bigbase_shifted;
		W invbigbase;
		int shift;
		int bigbase_size;
		double log_base_ratio;
		std::vector<BigInt> powers;	//bigbase_shifted^(2^k)
	};

public:
	std::string to_string() const {
		assert(normalized());
		static BaseData baseinfo_10 = _get_basedata(10);

		int n = size();
		if(n == 0)
			return "0";

		std::string str(_sign + _estimate_size_in_base(data(), n, baseinfo_10), '?');
		if(_sign)
			str[0] = '-';

		unique_ptr<W[]> ws(new W[n]);
		_copy(ws.get(), data(), n);

		const auto begin_it = str.begin() + (_sign ? 1 : 0);
		const auto end_it = _from_binary(begin_it, ws.get(), n, baseinfo_10);

		for(auto it = begin_it; it != end_it; ++ it)
			*it += '0';

		str.resize(end_it - str.begin());

		return str;
	}

	friend std::ostream &operator<<(std::ostream &o, const BigInt &a) {
		return o << a.to_string();
	}

private:
	static void _copy(W *res, const W *a, int n);
	static void _fill_zero(W *res, int n);

	static int _compare(const W *a, const W *b, int n);

	static W _add_1(W *a, int an, W b);
	static W _subtract_1(W *a, int an, W b);

	static W _add(W *res, const W *a, int an, const W *b, int bn);
	static W _subtract(W *res, const W *a, int an, const W *b, int bn);

	static W _bitshift_left(W *res, const W *a, int n, int shift);
	static W _bitshift_right(W *res, const W *a, int n, int shift);

	static W _multiply_1(W *res, const W *a, int n, W b);
	static W _multiply_add_1(W *a, const W *b, int n, W c);
	static W _multiply_subtract_1(W *a, const W *b, int n, W c);

	enum {
#ifdef MP_TEST
		KARATSUBA_THRESHOLD = 3
#else
		KARATSUBA_THRESHOLD = 8
#endif
	};

	static void _multiply(W *res, const W *a, int an, const W *b, int bn);
	static void _square(W *res, const W *a, int an);

	static void _multiply_basecase(W *res, const W *a, int an, const W *b, int bn);

	static void _multiply_karatsuba(W *res, const W *a, int an, const W *b, int bn, W *ws);
	static bool _compare_subtract(W *res, int resn, const W *a, int an, const W *b, int bn);

	static W _divide_1(W *res_q, const W *a, int n, W b);
	static W _divide_1_preinv_noshift(W *res_q, W a_n, const W *a, int n, W b, W invb);
	static W _divide_1_preinv_shift(W *res_q, const W *a, int n, W b, W invb, int shift);

	static void _divide(W *res_q, W *a, int an, const W *b, int bn);
	static void _divide_preinv(W *res_q, int qn, W *a, int an, const W *b, int bn, W invbhi);

	static void _divide_basecase_preinv(W *res_q, int qn, W *a, int an, const W *b, int bn, W invbhi);

	static void _divide_blockwise(W *res_q, int qn, W *a, int an, const W *b, int bn, W invbhi, W *ws);

	static void _divide_preinv_invert(W *res, int resn, const W *a, int an);

	static BaseData _get_basedata(W base);
	static void _precompute_base_powers(int n, BaseData &data);

	using CharT = char;
	using StrIt = std::string::iterator;
	static StrIt _from_binary(StrIt res, W *a, int n, BaseData &data);

	static StrIt _from_binary_basecase(StrIt res, W *a, int n, const BaseData &data);
	static StrIt _from_binary_rec(StrIt res, W *a, int n, const BaseData &data);

	static size_t _estimate_size_in_base(const W *a, int n, const BaseData &data);
};

void BigInt::_copy(W *res, const W *a, int n) {
	for(int i = 0; i < n; ++ i)
		res[i] = a[i];
}

void BigInt::_fill_zero(W *res, int n) {
	for(int i = 0; i < n; ++ i)
		res[i] = 0;
}

int BigInt::_compare(const W *a, const W *b, int n) {
	for(int i = n - 1; i >= 0; -- i) {
		if(a[i] != b[i])
			return a[i] > b[i] ? 1 : -1;
	}
	return 0;
}

BigInt::W BigInt::_add_1(W *a, int an, W b) {
	assert(an > 0);
	W c = a[0] + b;
	a[0] = c;
	if(c >= b)
		return 0;
	for(int i = 1; i < an; ++ i) {
		if((++ a[i]) != 0)
			return 0;
	}
	return 1;
}

BigInt::W BigInt::_subtract_1(W *a, int an, W b) {
	assert(an > 0);
	W c = a[0] - b;
	a[0] = c;
	if(c < (W)-b)
		return 0;
	for(int i = 1; i < an; ++ i) {
		if((-- a[i]) != W_MAX)
			return 0;
	}
	return 1;
}

BigInt::W BigInt::_add(W *res, const W *a, int an, const W *b, int bn) {
	assert(an >= bn);
	W carry = 0;
	for(int i = 0; i < bn; ++ i)
		res[i] = Util::addcarry(a[i], b[i], &carry);
	if(res == a) {
		if(carry == 0 || an == bn)
			return carry;
		else
			return _add_1(res + bn, an - bn, 1);
	} else {
		for(int i = bn; i < an; ++ i)
			res[i] = Util::addcarry(a[i], 0, &carry);
		return carry;
	}
}

BigInt::W BigInt::_subtract(W *res, const W *a, int an, const W *b, int bn) {
	assert(an >= bn);
	W borrow = 0;
	for(int i = 0; i < bn; ++ i)
		res[i] = Util::subborrow(a[i], b[i], &borrow);
	if(res == a) {
		if(borrow == 0 || an == bn)
			return borrow;
		else
			return _subtract_1(res + bn, an - bn, 1);
	} else {
		for(int i = bn; i < an; ++ i)
			res[i] = Util::subborrow(a[i], 0, &borrow);
	}
	return borrow;
}

BigInt::W BigInt::_bitshift_left(W *res, const W *a, int n, int shift) {
	assert(n > 0 && 0 < shift && shift < W_BITS);
	W carry = 0;
	for(int i = 0; i < n; ++ i) {
		W a_i = a[i];
		res[i] = a_i << shift | carry;
		carry = a_i >> (W_BITS - shift);
	}
	return carry;
}

BigInt::W BigInt::_bitshift_right(W *res, const W *a, int n, int shift) {
	assert(n > 0 && 0 < shift && shift < W_BITS);
	W carry = 0;
	for(int i = n - 1; i >= 0; -- i) {
		W a_i = a[i];
		res[i] = a_i >> shift | carry;
		carry = a_i << (W_BITS - shift);
	}
	return carry;
}

BigInt::W BigInt::_multiply_1(W *res, const W *a, int an, W b) {
	W carry = 0;
	for(int i = 0; i < an; ++ i) {
		W lo, hi;
		Util::umul_full(a[i], b, &hi, &lo);
		W c = lo + carry;
		res[i] = c;
		carry = hi + (c < lo);
	}
	return carry;
}

BigInt::W BigInt::_multiply_add_1(W *a, const W *b, int n, W c) {
	W carry = 0;
	for(int i = 0; i < n; ++ i) {
		W lo, hi;
		Util::umul_full(b[i], c, &hi, &lo);
		a[i] = Util::addcarry(a[i], lo, &carry);
		carry += hi;
	}
	return carry;
}

BigInt::W BigInt::_multiply_subtract_1(W *a, const W *b, int n, W c) {
	W borrow = 0;
	for(int i = 0; i < n; ++ i) {
		W lo, hi;
		Util::umul_full(b[i], c, &hi, &lo);
		a[i] = Util::subborrow(a[i], lo, &borrow);
		borrow += hi;
	}
	return borrow;
}

void BigInt::_multiply(W *res, const W *a, int an, const W *b, int bn) {
	assert(res != a && res != b);
	assert(an >= bn && bn > 0);

	if(a == b) {
		assert(an == bn);
		_square(res, a, an);
		return;
	}

	if(bn == 1) {
		res[an] = _multiply_1(res, a, an, b[0]);
	} else if(bn < KARATSUBA_THRESHOLD) {
		_multiply_basecase(res, a, an, b, bn);
	} else {
		unique_ptr<W[]> ws(new W[an * 5]);
		_multiply_karatsuba(res, a, an, b, bn, ws.get());
	}
}

void BigInt::_square(W *res, const W *a, int an) {
	if(an == 1) {
		Util::umul_full(a[0], a[0], &res[1], &res[0]);
	} else if(an < KARATSUBA_THRESHOLD) {
		//todo
		_multiply_basecase(res, a, an, a, an);
	} else {
		//todo
		unique_ptr<W[]> ws(new W[an * 5]);
		_multiply_karatsuba(res, a, an, a, an, ws.get());
	}
}

void BigInt::_multiply_basecase(W *res, const W *a, int an, const W *b, int bn) {
	res[an] = _multiply_1(res, a, an, b[0]);
	for(int i = 1; i < bn; ++ i)
		res[i + an] = _multiply_add_1(res + i, a, an, b[i]);
}

void BigInt::_multiply_karatsuba(W *res, const W *a, int an, const W *b, int bn, W *ws) {
	if(bn < KARATSUBA_THRESHOLD || (an + 1) / 2 >= bn) {
		//todo: unbalanced case
		_multiply_basecase(res, a, an, b, bn);
		return;
	}

	int lo = (an + 1) / 2, ha = an - lo, hb = bn - lo;
	assert(an >= bn && 0 < hb);

	W *am1 = ws, *bm1 = ws + lo, *rm1 = bm1 + lo, *nws = rm1 + lo * 2;
	W *r0 = res, *rinf = res + lo * 2;

	bool rm1_sign = true;
	rm1_sign ^= _compare_subtract(am1, lo, a, lo, a + lo, ha);
	rm1_sign ^= _compare_subtract(bm1, lo, b, lo, b + lo, hb);

	_multiply_karatsuba(r0, a, lo, b, lo, nws);
	_multiply_karatsuba(rinf, a + lo, ha, b + lo, hb, nws);
	_multiply_karatsuba(rm1, am1, lo, bm1, lo, nws);

	W rm1_carry = 0;
	if(!rm1_sign)
		rm1_carry += _add(rm1, rm1, lo * 2, r0, lo * 2);
	else
		rm1_sign = _compare_subtract(rm1, lo * 2, r0, lo * 2, rm1, lo * 2);
	if(!rm1_sign)
		rm1_carry += _add(rm1, rm1, lo * 2, rinf, ha + hb);
	else
		rm1_sign = _compare_subtract(rm1, lo * 2, rinf, ha + hb, rm1, lo * 2);

	if(rm1_sign) {
		_subtract(res + lo, res + lo, an + bn - lo, rm1, lo * 2);
	} else {
		_add(res + lo, res + lo, an + bn - lo, rm1, lo * 2);
		if(rm1_carry > 0)
			_add_1(res + lo * 3, ha + hb - lo, rm1_carry);
	}
}

bool BigInt::_compare_subtract(W *res, int resn, const W *a, int an, const W *b, int bn) {
	int aan = an;
	while(aan > 0 && a[aan - 1] == 0) -- aan;
	int abn = bn;
	while(abn > 0 && b[abn - 1] == 0) -- abn;

	if(aan < abn || (aan == abn && _compare(a, b, aan) < 0)) {
		_subtract(res, b, abn, a, aan);
		_fill_zero(res + abn, resn - abn);
		return true;
	} else {
		_subtract(res, a, aan, b, abn);
		_fill_zero(res + aan, resn - aan);
		return false;
	}
}

BigInt::W BigInt::_divide_1(W *res_q, const W *a, int n, W b) {
	assert(n > 0);
	int shift = Util::count_leading_zeros(b);
	W invb = Util::div_preinv_invert(b << shift);
	W rem = _divide_1_preinv_shift(res_q, a, n, b << shift, invb, shift);
	return rem >> shift;
}

BigInt::W BigInt::_divide_1_preinv_noshift(W *res_q, W a_n, const W *a, int n, W b, W invb) {
	assert(a_n < b);
	W rem = a_n;
	for(int i = n - 1; i >= 0; -- i)
		Util::div_preinv(rem, a[i], b, invb, &res_q[i], &rem);
	return rem;
}

BigInt::W BigInt::_divide_1_preinv_shift(W *res_q, const W *a, int n, W b, W invb, int shift) {
	if(shift == 0)
		return _divide_1_preinv_noshift(res_q, 0, a, n, b, invb);
	assert(n > 0);
	W a_i = a[n - 1], rem = a_i >> (W_BITS - shift);
	for(int i = n - 1; i > 0; -- i) {
		W a_im1 = a[i - 1];
		W a_shifted = a_i << shift | a_im1 >> (W_BITS - shift);
		Util::div_preinv(rem, a_shifted, b, invb, &res_q[i], &rem);
		a_i = a_im1;
	}
	Util::div_preinv(rem, a_i << shift, b, invb, &res_q[0], &rem);
	return rem;
}

void BigInt::_divide(W *res_q, W *a, int an, const W *b, int bn) {
	assert(res_q != a && res_q != b && a != b && an >= bn && bn > 0);
	if(bn == 1) {
		a[0] = _divide_1(res_q, a, an, b[0]);
		_fill_zero(a + 1, an - 1);
	} else {
		int qn = an - bn + 1;
		int shift = Util::count_leading_zeros(b[bn - 1]);
		if(shift == 0) {
			W invbhi = Util::div_preinv_invert(b[bn - 1] << shift);
			_divide_preinv(res_q, qn, a, an, b, bn, invbhi);
		} else {
			unique_ptr<W[]> ws(new W[an + 1 + bn]);
			W *shifted_a = ws.get(), *shifted_b = shifted_a + (an + 1);
			_bitshift_left(shifted_b, b, bn, shift);
			shifted_a[an] = _bitshift_left(shifted_a, a, an, shift);
			W invbhi = Util::div_preinv_invert(shifted_b[bn - 1]);
			_divide_preinv(res_q, qn, shifted_a, an + 1, shifted_b, bn, invbhi);
//			assert(shifted_a[an] == 0);
			_bitshift_right(a, shifted_a, an, shift);
		}
	}
}

void BigInt::_divide_preinv(W *res_q, int qn, W *a, int an, const W *b, int bn, W invbhi) {
	unique_ptr<W[]> ws(new W[bn * 5]);
	_divide_blockwise(res_q, qn, a, an, b, bn, invbhi, ws.get());
}


void BigInt::_divide_basecase_preinv(W *res_q, int qn, W *a, int an, const W *b, int bn, W invbhi) {
	assert(res_q != a && b != res_q && b != a && an >= bn && bn > 0 && (b[bn - 1] >> (W_BITS - 1) & 1));
	assert(qn <= an - bn + 1);
	W bhi = b[bn - 1];
	for(int i = an - bn; i >= 0; -- i) {
		W numhi = i == an - bn ? 0 : a[i + bn], q;
		if(numhi >= bhi) {
			q = W_MAX;
		} else {
			W dummy;
			Util::div_preinv(numhi, a[i + bn - 1], bhi, invbhi, &q, &dummy);
		}
		//[a / b] <= q <= [a / b] + 2
		if(q != 0) {
			W borrow = _multiply_subtract_1(a + i, b, bn, q);
			if(numhi < borrow) {
				numhi -= borrow;
				-- q;
				W carry = _add(a + i, a + i, bn, b, bn);
				if((numhi += carry) >= carry) {
					-- q;
					numhi += _add(a + i, a + i, bn, b, bn);
				}
			} else {
				numhi -= borrow;
			}
		}
		assert(numhi == 0);
		if(i < an - bn)
			a[i + bn] = 0;
		if(i < qn)
			res_q[i] = q;
	}
}

void BigInt::_divide_blockwise(W *res_q, int qn, W *a, int an, const W *b, int bn, W invbhi, W *ws) {
	assert(an >= bn && bn > 0);
	assert(b[bn - 1] >> (W_BITS - 1) & 1);
	assert(qn <= an - bn + 1);

	if(bn < KARATSUBA_THRESHOLD) {
		_divide_basecase_preinv(res_q, qn, a, an, b, bn, invbhi);
		return;
	}

	int block = (bn + 1) / 2;
	W *q = ws, *prod = q + (block + 1), *num = prod;
	W *nws = ws + block * 2 + 1 + bn;

	int initi = 0;
	while(initi + block < an - bn + 1) initi += block;
	for(int i = initi; i >= 0; i -= block) {
		int hn;
		if(i == initi) {
			hn = an - (i + bn);
		}else {
			hn = block;
		}
		_copy(num, a + (i + bn - block), block + hn);
		_divide_blockwise(q, hn + 1, num, block + hn, b + (bn - block), block, invbhi, nws);
		if(q[hn] > 0) {
			if(hn == block) {
				for(int j = 0; j < hn; ++ j)
					q[j] = W_MAX;
				q[hn] = 0;
			} else {
				++ hn;
			}
		}
		if(hn > 0) {
			_multiply_karatsuba(prod, b, bn, q, hn, nws);
			int prodn = bn + hn;
			if(i + prodn > an) {
				while(prod[prodn - 1] > 0) {
					_subtract_1(q, hn, 1);
					_subtract(prod, prod, prodn, b, bn);
				}
				-- prodn;
			}
			if(_subtract(a + i, a + i, prodn, prod, prodn) > 0) {
				_subtract_1(q, hn, 1);
				if(_add(a + i, a + i, prodn, b, bn) == 0) {
					_subtract_1(q, hn, 1);
					_add(a + i, a + i, prodn, b, bn);
				}
			}
		}
		if(qn > i)
			_copy(res_q + i, q, std::min(block, qn - i));
	}
}

//todo
void BigInt::_divide_preinv_invert(W *res, int resn, const W *a, int an) {
	/*
	assert(an > 0 && (a[an - 1] >> (W_BITS - 1) & 1));

	unique_ptr<W[]> buf(new W[resn * 4]);
	W *tmp1 = buf.get(), *tmp2 = tmp1 + resn * 2;

	W inv_a0 = Util::div_preinv_invert(a[0]);

	int curn = 1;
	while(curn < resn) {
		//res / W^{(an - 1) + curn}
		int nextn = std::min(resn, curn * 2);
		_square(tmp1, res, curn);
		int htmp1 = curn * 2, ha = std::min(nextn, an);
		_multiply(tmp2, tmp1 + (curn * 2 - htmp1), htmp1, a + (an - ha), ha);
		int diff = nextn - curn;
		_bitshift_left(res + diff, res, curn, 1);
		_subtract(res, res, nextn, tmp2, nextn);
	}
	*/
}

BigInt::StrIt BigInt::_from_binary(StrIt res, W *a, int n, BaseData &data) {
	_precompute_base_powers(n, data);
	StrIt it = _from_binary_rec(res, a, n, data);
	std::reverse(res, it);
	return it;
}

BigInt::StrIt BigInt::_from_binary_rec(StrIt res, W *a, int n, const BaseData &data) {
	if(n == 0)
		return res;
	if(n < KARATSUBA_THRESHOLD)
		return _from_binary_basecase(res, a, n, data);

	int j = 0;
	while(j + 1 < (int)data.powers.size() && data.powers[j + 1].size() < n)
		++ j;
	BigInt x, quot, rem;
	x.set_words(a, a + n);
	const BigInt &pow = data.powers[j];
	size_t pow_size = (size_t)data.bigbase_size << j;

	BigInt::divide_floor_unsigned(quot, rem, x, pow);
	StrIt mid = res + pow_size;
	StrIt it = _from_binary_rec(res, rem.data(), rem.size(), data);
	for(; it != mid; ++ it)
		*it = static_cast<CharT>(0);
	return _from_binary_rec(it, quot.data(), quot.size(), data);
}

BigInt::StrIt BigInt::_from_binary_basecase(StrIt res, W *a, int n, const BaseData &data) {
	const W base = data.base;
	const W bigbase_shifted = data.bigbase_shifted;
	const W invbigbase = data.invbigbase;
	const int shift = data.shift;
	const int bigbase_size = data.bigbase_size;

	assert(n > 0);
	auto p = res;
	int remn = n;
	while(remn > 1 || a[0] >= bigbase_shifted >> shift) {
		W rem, frac, dummy, digit;
		rem = _divide_1_preinv_shift(a, a, n, bigbase_shifted, invbigbase, shift);
		Util::div_preinv(rem, 0, bigbase_shifted, invbigbase, &frac, &dummy);
		++ frac;
		for(int i = bigbase_size - 1; i >= 0; -- i) {
			Util::umul_full(frac, base, &digit, &frac);
			p[i] = static_cast<CharT>(digit);
		}
		p += bigbase_size;
		remn -= a[remn - 1] == 0;
	}
	W frac, dummy, digit;
	Util::div_preinv(a[0] << shift, 0, bigbase_shifted, invbigbase, &frac, &dummy);
	++ frac;
	int last_digits = bigbase_size;
	for(;; -- last_digits) {
		Util::umul_full(frac, base, &digit, &frac);
		if(digit != 0) break;
	}
	p[last_digits - 1] = static_cast<CharT>(digit);
	for(int i = last_digits - 2; i >= 0; -- i) {
		Util::umul_full(frac, base, &digit, &frac);
		p[i] = static_cast<CharT>(digit);
	}
	p += last_digits;
	return p;
}

BigInt::BaseData BigInt::_get_basedata(W base) {
	assert(base > 1);

	W bigbase_shifted = base;
	int bigbase_size = 1;
	const W limit = W_MAX / base;
	while(bigbase_shifted <= limit) bigbase_shifted *= base, ++ bigbase_size;

	int shift = Util::count_leading_zeros(bigbase_shifted);
	bigbase_shifted <<= shift;
	const W invbigbase = Util::div_preinv_invert(bigbase_shifted);

	BaseData res;
	res.base = base;
	res.bigbase_shifted = bigbase_shifted;
	res.invbigbase = invbigbase;
	res.shift = shift;
	res.bigbase_size = bigbase_size;
	if((base & (base - 1)) == 0)
		res.log_base_ratio = Util::count_trailing_zeros(base);
	else
		res.log_base_ratio = log(2.0) / std::log(double(base));
	return res;
}

void BigInt::_precompute_base_powers(int n, BaseData &data) {
	std::vector<BigInt> &powers = data.powers;
	if(powers.empty())
		powers.push_back(BigInt(data.bigbase_shifted >> data.shift));
	while(powers.back().size() * 2 < n) {
		const auto &a = powers.back();
		powers.push_back(a * a);
	}
}

size_t BigInt::_estimate_size_in_base(const W *a, int n, const BaseData &data) {
	if(n == 0) return 1;
	size_t bit_size = static_cast<size_t>(n) * W_BITS - Util::count_leading_zeros(a[n - 1]);
	return static_cast<size_t>(ceil(static_cast<double>(bit_size) * data.log_base_ratio));
}


}

using multiprec::BigInt;
pair<BigInt, BigInt> fib_pair(int n) {
	if(n <= 2)
		return make_pair(BigInt((n + 1) / 2), BigInt((n + 2) / 2));
	BigInt a, b;
	tie(a, b) = fib_pair(n / 2 - 1);
	a *= a;
	b *= b;
	BigInt c = b + a;
	BigInt d = b * 4 - a + (n >> 1 & 1 ? -2 : 2);
	if(n & 1)
		return make_pair(d, d * 2 - c);
	else
		return make_pair(d - c, d);
}


struct Xor128 {
	unsigned x, y, z, w;
	Xor128(): x(123456789), y(362436069), z(521288629), w(88675123) { }

	//[0, 2^32)
	unsigned operator()() {
		unsigned t = x ^ (x << 11);
		x = y; y = z; z = w;
		return w = w ^ (w >> 19) ^ (t ^ (t >> 8));
	}
	//[0, 2^64)
	unsigned long long nextLL() {
		unsigned x = (*this)();
		unsigned y = (*this)();
		return (unsigned long long)x << 32 | y;
	}
	//[0, n)
	unsigned operator()(unsigned n) {
		unsigned mask = calculateMask(n - 1), x;
		do {
			x = (*this)() & mask;
		}while(x >= n);
		return x;
	}
	//[0, n)
	signed int operator()(signed int n) { return (*this)((unsigned int)n); }
	//[L, U]
	signed int operator()(signed int L, signed int U) {
		return L + (*this)(U - L + 1);
	}
	//[0, n)
	unsigned long long operator()(unsigned long long n) {
		unsigned long long mask = calculateMask(n - 1), x;
		do {
			x = (*this).nextLL() & mask;
		}while(x >= n);
		return x;
	}
	//[0, n)
	signed long long operator()(signed long long n) { return (*this)((unsigned long long)n); }
	//[L, U]
	signed long long operator()(signed long long L, signed long long U) {
		return L + (*this)(U - L + 1);
	}
private:

	static unsigned calculateMask(unsigned v) {
		v |= v >> 1; v |= v >> 2; v |= v >> 4; v |= v >> 8; v |= v >> 16;
		return v;
	}
	static unsigned long long calculateMask(unsigned long long v) {
		v |= v >> 1; v |= v >> 2; v |= v >> 4; v |= v >> 8; v |= v >> 16;
		v |= v >> 32;
		return v;
	}
};

BigInt genBigInt(int maxN, Xor128 &xor128, bool sign = false) {
	int n = xor128(1, maxN);
	vector<BigInt::W> v(n);
	int P = xor128(100), X = xor128(2);
	for(int i = 0; i < n; ++ i) {
		if(xor128(100) < P)
			v[i] = (BigInt::W)xor128(-X, X);
		else
			v[i] = (BigInt::W)xor128.nextLL();
	}
	BigInt a;
	a.set_words(v.begin(), v.end());
	if(sign && xor128(2) == 0) a = -a;
	return a;
}

void test_add(int N, Xor128 &xor128) {
	BigInt a, b;
	a = genBigInt(N, xor128, true);
	b = genBigInt(N, xor128, true);
	BigInt sum = a + b;
	int P = 127;
	if((((a % P) + (b % P)) % P + P) % P != (sum % P + P) % P) {
		cerr << a << " + " << b << " != " << sum << endl;
	}
}

void test_multiply(int N, Xor128 &xor128) {
	BigInt a, b;
	a = genBigInt(N, xor128);
	b = genBigInt(N, xor128);
	BigInt prod = a * b;
	int P = 127;
	if((a % P) * (b % P) % P != prod % P) {
		cerr << a << " * " << b << " != " << prod << endl;
	}
}

void test_divide(int N, Xor128 &xor128) {
	BigInt a, b;
	a = genBigInt(N, xor128);
	b = genBigInt(N, xor128);
	if(b.zero()) return;
	BigInt q, r;
	BigInt::divide_trunc(q, r, a, b);
	if(a - b * q != r || !(BigInt() <= r && r < b)) {
		cerr << a << " `quotRem` " << b << endl;
		cerr << q << ", " << r << endl;
		cerr << "aaa" << endl;
	}
}

void test_all() {
#ifdef NDEBUG
	cerr << "warning: NDEBUG is enabled" << endl;
#endif
	Xor128 xor128;
	const int TT = 1000000;
	for(int k = 3; k < 10; ++ k) {
		const int N = k == 0 ? 2 : k == 1 ? 4 : k == 2 ? 6 : 1 << k, T = TT / max(1, N >> 3);
		cerr << "test N = " << N << ", T = " << T << endl;
		for(int ii = 0; ii < T; ++ ii) {
//			test_add(N, xor128);
			test_multiply(N, xor128);
			test_divide(N, xor128);
		}
	}
	cerr << "end" << endl;
}

int main() {
#ifdef MY_LOCAL_RUN
	test_all();
#endif
	int n;
	while(cin >> n) {
		if(n == 2) {
			puts("3\nINF");
		} else {
			BigInt ans;
			if(n % 2 == 1) {
				ans = fib_pair(n).first;
			} else {
				BigInt a, b;
				tie(a, b) = fib_pair(n / 2 - 1);
				ans = a * b * 2;
			}
			printf("%d\n", n);
			std::string s = ans.to_string();
			puts(s.c_str());
		}
	}
}
0