// https://www.youtube.com/watch?v=wthasN45KuY
// You said I’d fly away
// But my walls have kept me down
// Now I’m lost and I’m afraid
// And I’m close to hit the ground
// 
// You said I’d fly away
// You said I’d fly anywhere
// But I keep on Falling

#ifndef ONLINE_JUDGE
#include "templates/debug.hpp"
#else
#define debug(...)
#endif

#include <bits/stdc++.h>
using namespace std;
using i64 = int64_t;
using u64 = uint64_t;

class ZeroDivisionError : public std::exception {
public:
	const char* what() const throw() {return "BigInteger::divmod";}
};
class FFTLimitExceededError : public std::exception {
public:
	const char* what() const throw() {return "BigInteger::fft_mul";}
};

class BigInteger {
protected:
	using digit_t = long long;
	
	static constexpr int WIDTH = 8;
	static constexpr digit_t BASE = 1e8;
	static constexpr long long FFT_LIMIT = 512;
	static constexpr long long NEWTON_LIMIT = 512;
	static constexpr long long NEWTON_MIN_LEVEL = 16;
	
	digit_t* digits;
	int capacity, size;
	bool flag;
	
	inline void push(const digit_t&);
	inline void pop();
	
	inline int compare(const BigInteger&) const;	
	
	static inline BigInteger fft_mul(const BigInteger&, const BigInteger&);
	
	inline BigInteger move_l(int) const;
	inline BigInteger move_r(int) const;
	BigInteger newton_inv(int) const;
	inline std::pair<BigInteger, BigInteger> newton_div(const BigInteger&) const;
	
	template <class F>
	inline static BigInteger binary_op_helper(const BigInteger&, const BigInteger&, const F&);
	
public:
	inline void reserve(const int&);
protected:
	inline void resize(const int&);
	
public:
	BigInteger() : digits(nullptr), flag(true) {*this = 0;}
	
	BigInteger(const BigInteger& x) : digits(nullptr) {*this = x;}
	BigInteger(const long long& x) : digits(nullptr) {*this = x;}
	BigInteger(const std::string& s) : digits(nullptr) {*this = s;}
	BigInteger(const std::vector<bool>& b) : digits(nullptr) {*this = b;}
	template <class BoolIt>
	BigInteger(const BoolIt& begin, const BoolIt& end) : digits(nullptr) 
	{*this = std::vector<bool>(begin, end);}
	
	BigInteger& operator= (const BigInteger&);
	BigInteger& operator= (const long long&);
	BigInteger& operator= (const std::string&);
	BigInteger& operator= (const std::vector<bool>&);
	
	void clear();
	~BigInteger() {clear();}
	
	friend std::ostream& operator<< (std::ostream& out, const BigInteger& x) {
		if (!x.flag) out << '-';
		out << (long long) x.digits[x.size];
		for (int i = x.size - 1; i >= 1; i--) 
			out << std::setw(WIDTH) << std::setfill('0') << (long long) x.digits[i];
		return out;
	}
	friend std::istream& operator>> (std::istream& in, BigInteger& x) {
		std::string s; in >> s; x = s; 
		return in;
	}
	
	std::string to_string() const;
	long long to_long_long() const;
	std::vector<bool> to_binary() const;
	
	BigInteger operator- () const;
	BigInteger abs() const;
	
	bool operator== (const BigInteger&) const; 
#if __cplusplus >= 202002L
	auto operator<=> (const BigInteger&) const;
#else
	bool operator< (const BigInteger&) const;
	bool operator> (const BigInteger&) const; 
	bool operator!= (const BigInteger&) const;
	bool operator<= (const BigInteger&) const;
	bool operator>= (const BigInteger&) const;
#endif //__cplusplus >= 202002L
	
	BigInteger div2() const;
	std::pair<BigInteger, BigInteger> divmod(const BigInteger&, bool = false) const;
	
	BigInteger operator+ (const BigInteger&) const;
	BigInteger operator- (const BigInteger&) const;
	BigInteger operator* (const int&) const;
	BigInteger operator* (const BigInteger&) const;
	BigInteger operator/ (const long long&) const;
	BigInteger operator/ (const BigInteger&) const;
	BigInteger operator% (const long long&) const;
	BigInteger operator% (const BigInteger&) const;
	
	BigInteger pow(const long long&) const;
	BigInteger pow(const long long&, const BigInteger&) const;
	
	BigInteger root(const long long& = 2) const;
	
	BigInteger gcd(const BigInteger&) const;
	BigInteger lcm(const BigInteger&) const;
	
	BigInteger& operator+= (const BigInteger&);
	BigInteger& operator-= (const BigInteger&);
	BigInteger& operator*= (int);
	BigInteger& operator*= (const BigInteger&);
	BigInteger& operator/= (const long long&);
	BigInteger& operator/= (const BigInteger&);
	BigInteger& operator%= (const long long&);
	BigInteger& operator%= (const BigInteger&);
	
	BigInteger operator<< (const long long&);
	BigInteger operator>> (const long long&);
	BigInteger& operator<<= (const long long&);
	BigInteger& operator>>= (const long long&);
	
	BigInteger operator& (const BigInteger&);
	BigInteger operator| (const BigInteger&);
	BigInteger operator^ (const BigInteger&);
	BigInteger& operator&= (const BigInteger&);
	BigInteger& operator|= (const BigInteger&);
	BigInteger& operator^= (const BigInteger&);
	
	BigInteger& operator++ ();
	BigInteger operator++ (int);
	BigInteger& operator-- ();
	BigInteger operator-- (int);
};

inline void BigInteger::push(const digit_t& val) {
	if (size == capacity) {
		int new_capacity = 0;
		if (capacity < 1000) new_capacity = capacity << 1;
		else new_capacity = (capacity >> 1) * 3;
		if (new_capacity < 0) new_capacity = INT_MAX;
		digit_t* new_digits = new digit_t[new_capacity + 1];
		std::memcpy(new_digits, digits, sizeof(long long) * (capacity + 1));
		delete[] digits;
		digits = new_digits, capacity = new_capacity;
	}
	digits[++size] = val;
}
inline void BigInteger::pop() {digits[size--] = 0;}

inline int BigInteger::compare(const BigInteger& x) const {
	if (flag && !x.flag) return 1;
	if (!flag && x.flag) return -1;
	
	int sgn = (flag && x.flag ? 1 : -1);
	if (size > x.size) return sgn;
	if (size < x.size) return -sgn;
	
	for (int i = size; i >= 1; i--) {
		if (digits[i] > x.digits[i]) return sgn;
		if (digits[i] < x.digits[i]) return -sgn;
	}
	return 0;
}

inline void BigInteger::reserve(const int& sz) {
	if (sz < 0) return;
	if (digits != nullptr) delete[] digits;
	capacity = sz, size = 0;
	digits = new digit_t[sz + 1];
	std::memset(digits, 0, sizeof(digit_t) * (sz + 1));
}
inline void BigInteger::resize(const int& sz) {reserve(sz), size = sz;}

BigInteger& BigInteger::operator= (const BigInteger& x) {
	reserve(x.size + 1);
	flag = x.flag, size = x.size;
	std::memcpy(digits, x.digits, sizeof(digit_t) * (x.size + 1));
	return *this;
}
BigInteger& BigInteger::operator= (const long long& x) {
	flag = (x >= 0), reserve(4);
	if (x == 0) return size = 1, digits[1] = 0, *this;
	if (x == LLONG_MIN) return *this = "-9223372036854775808";
	long long n = std::abs(x);
	do {push(n % BASE), n /= BASE;} while (n);
	return *this;
}
BigInteger& BigInteger::operator= (const std::string& s) {
	flag = true, reserve(s.size() / WIDTH + 1);
	if (s.empty() || s == "-") return *this = 0;
	int i = 0; if (s[0] == '-') flag = false, i++;
	for (int j = s.size() - 1; j >= i; j -= WIDTH) {
		int start = std::max(i, j - WIDTH + 1), len = j - start + 1;
		push(std::stoll(s.substr(start, len)));
	}
	return *this;
}

BigInteger& BigInteger::operator= (const std::vector<bool>& b) {
	*this = 0;
	if (b.empty() || (b.size() == 1 && b[0] == 0)) return *this;
	BigInteger pow2 = 1;
	for (int i = b.size() - 1; i >= 0; i--, pow2 += pow2) if (b[i]) *this += pow2;
	return *this;
}

void BigInteger::clear() {if (digits != nullptr) delete[] digits, digits = nullptr;}

std::string BigInteger::to_string() const {std::stringstream ss; ss << *this; return ss.str();}
long long BigInteger::to_long_long() const {return std::stoll(to_string());}
std::vector<bool> BigInteger::to_binary() const {
	if (*this == 0) return {0};
	std::vector<bool> res;
	for (BigInteger x = *this; x != 0; x = x.div2()) res.emplace_back(x.digits[1] & 1);
	std::reverse(res.begin(), res.end());
	return res;
};

BigInteger BigInteger::operator- () const {
	if (*this == 0) return 0;
	BigInteger res = *this; res.flag = !flag; return res;
}
BigInteger BigInteger::abs() const {BigInteger res = *this; res.flag = true; return res;}

bool BigInteger::operator== (const BigInteger& x) const {return compare(x) == 0;}
#if __cplusplus >= 202002L
auto BigInteger::operator<=> (const BigInteger& x) const {return compare(x);}
#else
bool BigInteger::operator< (const BigInteger& x) const {return compare(x) < 0;}
bool BigInteger::operator> (const BigInteger& x) const {return compare(x) > 0;}
bool BigInteger::operator!= (const BigInteger& x) const {return compare(x) != 0;}
bool BigInteger::operator<= (const BigInteger& x) const {return compare(x) <= 0;}
bool BigInteger::operator>= (const BigInteger& x) const {return compare(x) >= 0;}
#endif //__cplusplus >= 202002L

BigInteger BigInteger::operator+ (const BigInteger& x) const {
	if (!x.flag) return *this - x.abs();
	if (!flag) return x - abs();
	
	BigInteger res; 
	res.flag = !(flag ^ x.flag);
	int n = std::max(size, x.size) + 1;
	res.reserve(n);
	digit_t carry = 0;
	for (int i = 1; i <= n; i++) {
		digit_t d1 = i <= size ? digits[i] : 0, d2 = i <= x.size ? x.digits[i] : 0;
		res.push(d1 + d2 + carry);
		carry = res.digits[i] / BASE;
		res.digits[i] %= BASE;
	}
	while (res.size > 1 && res.digits[res.size] == 0) res.pop();
	return res;
}
BigInteger BigInteger::operator- (const BigInteger& x) const {
	if (!x.flag) return *this + x.abs();
	if (!flag) return -(abs() + x);
	BigInteger res;
	if (*this < x) res.flag = false;
	digit_t carry = 0;
	int n = std::max(size, x.size);
	res.reserve(n);
	for (int i = 1; i <= n; i++) {
		digit_t d1 = i <= size ? digits[i] : 0, d2 = i <= x.size ? x.digits[i] : 0;
		if (res.flag) res.push(d1 - d2 - carry);
		else res.push(d2 - d1 - carry);
		if (res.digits[i] < 0) res.digits[i] += BASE, carry = 1;
		else carry = 0;
	}
	while (res.size > 1 && res.digits[res.size] == 0) res.pop();
	return res;
}

namespace __FFT {
	constexpr long long FFT_BASE = 1e4;
	constexpr double PI2 = 6.283185307179586231995927;
	constexpr double PI6 = 18.84955592153875869598778;
	
	constexpr int RECALC_WIDTH = 10;
	constexpr int RECALC_BASE = (1 << RECALC_WIDTH) - 1;
	
	struct complex {
		double real, imag;
		
		complex(double x = 0.0, double y = 0.0) : real(x), imag(y) {}
		
		complex operator+ (const complex& other) const {return complex(real + other.real, imag + other.imag);}
		complex operator- (const complex& other) const {return complex(real - other.real, imag - other.imag);}
		complex operator* (const complex& other) const {return complex(real * other.real - imag * other.imag, real * other.imag + other.real * imag);}
		
		complex& operator+= (const complex& other) {return real += other.real, imag += other.imag, *this;}
		complex& operator-= (const complex& other) {return real -= other.real, imag -= other.imag, *this;}
		complex& operator*= (const complex& other) {return *this = *this * other;}
	};
	
	complex* arr = nullptr;
	
	inline void init(int n) {
		if (arr != nullptr) delete[] arr, arr = nullptr;
		arr = new complex[n + 1];
	}
	
	template <const int n> 
	inline void fft(complex* a) {
		const int n2 = n >> 1, n4 = n >> 2;
		complex w(1.0, 0.0), w3(1.0, 0.0);
		const complex wn(std::cos(PI2 / n), std::sin(PI2 / n)), wn3(std::cos(PI6 / n), std::sin(PI6 / n));
		for (int i = 0; i < n4; i++, w *= wn, w3 *= wn3) {
			if (!(i & RECALC_BASE)) w = complex(std::cos(PI2 * i / n), std::sin(PI2 * i / n)), w3 = w * w * w;
			complex x = a[i] - a[i + n2], y = a[i + n4] - a[i + n2 + n4];
			y = complex(y.imag, -y.real);
			a[i] += a[i + n2], a[i + n4] += a[i + n2 + n4];
			a[i + n2] = (x - y) * w, a[i + n2 + n4] = (x + y) * w3;
		}
		fft<n2>(a), fft<n4>(a + n2), fft<n4>(a + n2 + n4);
	}
	template <> inline void fft<1>(complex* a) {}
	template <> inline void fft<0>(complex* a) {}
	template <> inline void fft<2>(complex* a) {
		complex x = a[0], y = a[1];
		a[0] += y, a[1] = x - y;
	}
	template <> inline void fft<4>(complex* a) {
		complex a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3];
		complex x = a0 - a2, y = a1 - a3;
		y = complex(y.imag, -y.real);
		a[0] += a2, a[1] += a3, a[2] = x - y, a[3] = x + y;
		fft<2>(a);
	}
	
	template <const int n> 
	inline void ifft(complex* a) {
		const int n2 = n >> 1, n4 = n >> 2;
		ifft<n2>(a), ifft<n4>(a + n2), ifft<n4>(a + n2 + n4);
		complex w(1.0, 0.0), w3(1.0, 0.0);
		const complex wn(std::cos(PI2 / n), -std::sin(PI2 / n)), wn3(std::cos(PI6 / n), -std::sin(PI6 / n));
		for (int i = 0; i < n4; i++, w *= wn, w3 *= wn3) {
			if (!(i & RECALC_BASE)) w = complex(std::cos(PI2 * i / n), -std::sin(PI2 * i / n)), w3 = w * w * w;
			complex p = w * a[i + n2], q = w3 * a[i + n2 + n4];
			complex x = a[i], y = p + q, x1 = a[i + n4], y1 = p - q;
			y1 = complex(y1.imag, -y1.real);
			a[i] += y, a[i + n4] += y1, a[i + n2] = x - y, a[i + n2 + n4] = x1 - y1;
		}
	}
	template <> inline void ifft<1>(complex* a) {}
	template <> inline void ifft<0>(complex* a) {}
	template <> inline void ifft<2>(complex* a) {
		complex x = a[0], y = a[1];
		a[0] += y, a[1] = x - y;
	}
	template <> inline void ifft<4>(complex* a) {
		ifft<2>(a);
		complex p = a[2], q = a[3];
		complex x = a[0], y = p + q, x1 = a[1], y1 = p - q;
		y1 = complex(y1.imag, -y1.real);
		a[0] += y, a[1] += y1, a[2] = x - y, a[3] = x1 - y1;
	}
	
	inline void dft(complex* a, int n) {
		if (n <= 1) return;
		switch (n) {
			case 1 << 2: fft<1 << 2>(a); break;
			case 1 << 3: fft<1 << 3>(a); break;
			case 1 << 4: fft<1 << 4>(a); break;
			case 1 << 5: fft<1 << 5>(a); break;
			case 1 << 6: fft<1 << 6>(a); break;
			case 1 << 7: fft<1 << 7>(a); break;
			case 1 << 8: fft<1 << 8>(a); break;
			case 1 << 9: fft<1 << 9>(a); break;
			case 1 << 10: fft<1 << 10>(a); break;
			case 1 << 11: fft<1 << 11>(a); break;
			case 1 << 12: fft<1 << 12>(a); break;
			case 1 << 13: fft<1 << 13>(a); break;
			case 1 << 14: fft<1 << 14>(a); break;
			case 1 << 15: fft<1 << 15>(a); break;
			case 1 << 16: fft<1 << 16>(a); break;
			case 1 << 17: fft<1 << 17>(a); break;
			case 1 << 18: fft<1 << 18>(a); break;
			case 1 << 19: fft<1 << 19>(a); break;
			case 1 << 20: fft<1 << 20>(a); break;
			case 1 << 21: fft<1 << 21>(a); break;
			case 1 << 22: fft<1 << 22>(a); break;
			case 1 << 23: fft<1 << 23>(a); break;
			case 1 << 24: fft<1 << 24>(a); break;
			case 1 << 25: fft<1 << 25>(a); break;
			case 1 << 26: fft<1 << 26>(a); break;
			case 1 << 27: fft<1 << 27>(a); break;
			case 1 << 28: fft<1 << 28>(a); break;
			case 1 << 29: fft<1 << 29>(a); break;
			case 1 << 30: fft<1 << 30>(a); break;
			case 1 << 31: fft<1 << 31>(a); break;
			throw FFTLimitExceededError();
		}
	}
	inline void idft(complex* a, int n) {
		if (n <= 1) return;
		switch (n) {
			case 1 << 2: ifft<1 << 2>(a); break;
			case 1 << 3: ifft<1 << 3>(a); break;
			case 1 << 4: ifft<1 << 4>(a); break;
			case 1 << 5: ifft<1 << 5>(a); break;
			case 1 << 6: ifft<1 << 6>(a); break;
			case 1 << 7: ifft<1 << 7>(a); break;
			case 1 << 8: ifft<1 << 8>(a); break;
			case 1 << 9: ifft<1 << 9>(a); break;
			case 1 << 10: ifft<1 << 10>(a); break;
			case 1 << 11: ifft<1 << 11>(a); break;
			case 1 << 12: ifft<1 << 12>(a); break;
			case 1 << 13: ifft<1 << 13>(a); break;
			case 1 << 14: ifft<1 << 14>(a); break;
			case 1 << 15: ifft<1 << 15>(a); break;
			case 1 << 16: ifft<1 << 16>(a); break;
			case 1 << 17: ifft<1 << 17>(a); break;
			case 1 << 18: ifft<1 << 18>(a); break;
			case 1 << 19: ifft<1 << 19>(a); break;
			case 1 << 20: ifft<1 << 20>(a); break;
			case 1 << 21: ifft<1 << 21>(a); break;
			case 1 << 22: ifft<1 << 22>(a); break;
			case 1 << 23: ifft<1 << 23>(a); break;
			case 1 << 24: ifft<1 << 24>(a); break;
			case 1 << 25: ifft<1 << 25>(a); break;
			case 1 << 26: ifft<1 << 26>(a); break;
			case 1 << 27: ifft<1 << 27>(a); break;
			case 1 << 28: ifft<1 << 28>(a); break;
			case 1 << 29: ifft<1 << 29>(a); break;
			case 1 << 30: ifft<1 << 30>(a); break;
			case 1 << 31: ifft<1 << 31>(a); break;
			throw FFTLimitExceededError();
		}
	}
}

BigInteger BigInteger::fft_mul(const BigInteger& a, const BigInteger& b) {
	static_assert(__FFT::FFT_BASE * __FFT::FFT_BASE == BASE);
	int least = (a.size + b.size) << 1, lim = 1 << std::__lg(least);
	if (lim < least) lim <<= 1;
	__FFT::init(lim);
	using __FFT::arr;
	for (int i = 0; i < a.size; i++) {
		arr[i << 1].real = a.digits[i + 1] % 10000;
		arr[i << 1 | 1].real = a.digits[i + 1] / 10000 % 10000;
	}
	for (int i = 0; i < b.size; i++) {
		arr[i << 1].imag = b.digits[i + 1] % 10000;
		arr[i << 1 | 1].imag = b.digits[i + 1] / 10000 % 10000;
	}
	__FFT::dft(arr, lim);
	for (int i = 0; i < lim; i++) arr[i] *= arr[i];
	__FFT::idft(arr, lim);
	BigInteger res;
	res.resize(a.size + b.size + 1);
	digit_t carry = 0;
	double inv = 0.5 / lim;
	for (int i = 0; i <= a.size + b.size; i++) {
		carry += (digit_t)(arr[i << 1].imag * inv + 0.5);
		carry += (digit_t)(arr[i << 1 | 1].imag * inv + 0.5) * 10000LL;
		res.digits[i + 1] += carry % BASE, carry /= BASE;
	}
	while (res.size > 1 && res.digits[res.size] == 0) res.pop();
	return res;
}

BigInteger BigInteger::operator* (const BigInteger& x) const {
	BigInteger zero = 0;
	if (*this == zero || x == zero) return zero;
	int n = size, m = x.size;
	long long lim = 1LL * n * m;
	
	if (lim >= FFT_LIMIT) {
		BigInteger res = fft_mul(*this, x);
		res.flag = !(flag ^ x.flag);
		return res;
	}
	
	BigInteger res;
	res.flag = !(flag ^ x.flag);
	res.resize(n + m + 2);
	for (int i = 1; i <= n; i++) {
		for (int j = 1; j <= m; j++) {
			res.digits[i + j - 1] += digits[i] * x.digits[j];
			res.digits[i + j] += res.digits[i + j - 1] / BASE;
			res.digits[i + j - 1] %= BASE;
		}
	}
	for (int i = 1; i <= n + m + 1; i++) {
		res.digits[i + 1] += res.digits[i] / BASE;
		res.digits[i] %= BASE;
	}
	while (res.size > 1 && res.digits[res.size] == 0) res.pop();
	return res;
}

BigInteger& BigInteger::operator*= (int x) {
	if (x == 0 || *this == 0) return *this = 0;
	if (x < 0) flag = !flag, x = -x;
	digit_t carry = 0;
	for (int i = 1; i <= size || carry; i++) {
		if (i > size) push(0);
		digit_t cur = digits[i] * x + carry;
		carry = cur / BigInteger::BASE;
		digits[i] = cur % BigInteger::BASE;
	}
	while (size > 1 && digits[size] == 0) pop();
	return *this;
}
BigInteger BigInteger::operator* (const int& x) const {BigInteger t = *this; return t *= x;}

BigInteger BigInteger::div2() const {
	BigInteger res = *this;
	for (int i = size; i >= 1; i--) {
		if ((res.digits[i] & 1) && (i > 1)) res.digits[i - 1] += BASE;
		res.digits[i] >>= 1;
	}
	while (res.size > 1 && res.digits[res.size] == 0) res.pop();
	return res;
}
BigInteger BigInteger::operator/ (const long long& x) const {
	if (x == 0) throw -1;
	if (*this == 0) return 0;
	if (x == 2) return div2();
	if (x == -2) {BigInteger res = div2(); res.flag = !res.flag; return res;}
	
	BigInteger res;
	res.flag = !(flag ^ (x >= 0));
	
	digit_t cur = 0, div = std::abs(x);
	res.resize(size);
	
	for (int i = size; i >= 1; i--) {
		cur = cur * BASE + digits[i];
		res.digits[i] = res.flag ? (cur / div) : (-cur / -div);
		cur %= div;
	}
	while (res.size > 1 && res.digits[res.size] == 0) res.pop();
	return res;
}

inline BigInteger BigInteger::move_r(int d) const {
	if (*this == 0 || d >= size) return 0;
	if (d == 0) return *this;
	BigInteger res; res.reserve(size - d + 1);
	for (int i = d + 1; i <= size; i++) res.push(digits[i]);
	return res;
}
inline BigInteger BigInteger::move_l(int d) const {
	if (*this == 0) return 0;
	if (d == 0) return *this;
	BigInteger res; res.reserve(size + d + 1);
	for (int i = 1; i <= d; i++) res.push(0);
	for (int i = 1; i <= size; i++) res.push(digits[i]);
	return res;
}

BigInteger BigInteger::newton_inv(int n) const {
	if (*this == 0) throw ZeroDivisionError();
	if (std::min(size, n - size) <= NEWTON_MIN_LEVEL) {
		BigInteger a; a.resize(n + 1);
		std::memset(a.digits, 0, sizeof(digit_t) * a.size);
		a.digits[n + 1] = 1;
		return a.divmod(*this, true).first;
	}
	int k = (n - size + 5) >> 1, k2 = k > size ? 0 : size - k;
	BigInteger x = move_r(k2);
	int n2 = k + x.size;
	BigInteger y = x.newton_inv(n2), a = y + y, b = (*this) * y * y;
	
	return a.move_l(n - n2 - k2) - b.move_r(2 * (n2 + k2) - n) - 1;
}

std::pair<BigInteger, BigInteger> BigInteger::newton_div(const BigInteger& x) const {
	int k = size - x.size + 5, k2 = k > x.size ? 0 : x.size - k;
	BigInteger x2 = x.move_r(k2);
	if (k2 != 0) x2 += 1;
	int n2 = k + x2.size;
	BigInteger u = (*this) * x2.newton_inv(n2);
	BigInteger q = u.move_r(n2 + k2), r = (*this) - q * x;
	while (r >= x) q += 1, r -= x;
	return std::make_pair(q, r);
}

std::pair<BigInteger, BigInteger> BigInteger::divmod(const BigInteger& x, bool dis_newton) const {
	static const int base = BigInteger::BASE;
	BigInteger a = abs(), b = x.abs();
	if (b == 0) throw ZeroDivisionError();
	if (a < b) return std::make_pair(0, flag ? a : -a);
	if (!dis_newton && size > NEWTON_LIMIT) return newton_div(x);
	
	int t = base / (x.digits[x.size] + 1);
	a *= t, b *= t;
	int n = a.size, m = b.size;
	BigInteger q = 0, r = 0;
	q.resize(n);
	for (int i = n; i >= 1; i--) {
		r *= base, r += a.digits[i];
		digit_t d1 = m < r.size ? r.digits[m + 1] : 0, d2 = m - 1 < r.size ? r.digits[m] : 0;
		int d = (d1 * base + d2) / b.digits[m];
		r -= b * d;
		while (!r.flag) r += b, d--;
		q.digits[i] = d;
	}
	q.flag = !(flag ^ x.flag), r.flag = flag;
	while (q.size > 1 && q.digits[q.size] == 0) q.pop();
	return std::make_pair(q, r / t);
}
BigInteger BigInteger::operator/ (const BigInteger& x) const {return divmod(x).first;}

BigInteger BigInteger::operator% (const long long& x) const {
	if (x == 2) return digits[1] & 1;
	if (x == 5) return digits[1] % 5;
	return *this - (*this / x * x);
} 
BigInteger BigInteger::operator% (const BigInteger& x) const {return divmod(x).second;}
BigInteger BigInteger::pow(const long long& x) const {
	BigInteger res = 1, a = *this;
	for (long long t = x; t != 0; t >>= 1) {
		if (t & 1) res *= a;
		a *= a;
	}
	return res;
}
BigInteger BigInteger::pow(const long long& x, const BigInteger& p) const {
	BigInteger res = 1, a = *this % p;
	for (long long t = x; t != 0; t >>= 1) {
		if (t & 1) res = res * a % p;
		a = a * a % p;
	}
	return res;
}

BigInteger BigInteger::root(const long long& m) const {
	if (*this == 0 || m == 1) return *this;
	static constexpr long long base = BigInteger::BASE;
	BigInteger n = *this, t = base, x = std::min(n, t.move_l((n.size + m) / m));
	int l = 0, r = base - 1;
	while (l < r) {
		int mid = (l + r) >> 1;
		x.digits[x.size] = mid;
		if (x.pow(m) <= n) l = mid + 1;
		else r = mid;
	}
	x.digits[x.size] = l;
	while (x.size > 1 && x.digits[x.size] == 0) x.pop();
	BigInteger x2 = (x * (m - 1) + n / x.pow(m - 1)) / m;
	while (x2 < x) std::swap(x2, x), x2 = (x * (m - 1) + n / x.pow(m - 1)) / m;
	return x;
}

BigInteger BigInteger::gcd(const BigInteger& x) const {
	BigInteger a = *this, b = x;
	if (a < b) std::swap(a, b);
	if (b == 0) return a;
	int t = 0;
	while (a % 2 == 0 && b % 2 == 0) a = a.div2(), b = b.div2(), t++;
	while (b > 0) {
		if (a % 2 == 0) a = a.div2();
		else if (b % 2 == 0) b = b.div2();
		else a -= b;
		if (a < b) std::swap(a, b);
	}
	while (t--) a += a;
	return a;
}
BigInteger BigInteger::lcm(const BigInteger& x) const {return *this / gcd(x) * x;}

BigInteger& BigInteger::operator+= (const BigInteger& x) {return *this = *this + x;}
BigInteger& BigInteger::operator-= (const BigInteger& x) {return *this = *this - x;}
BigInteger& BigInteger::operator*= (const BigInteger& x) {return *this = *this * x;}
BigInteger& BigInteger::operator/= (const long long& x) {return *this = *this / x;}
BigInteger& BigInteger::operator/= (const BigInteger& x) {return *this = *this / x;}
BigInteger& BigInteger::operator%= (const long long& x) {return *this = *this / x;}
BigInteger& BigInteger::operator%= (const BigInteger& x) {return *this = *this % x;}

BigInteger BigInteger::operator<< (const long long& x) {
	if (x <= 0) return *this;
	BigInteger res = *this;
	for (long long i = 1; i <= x; i++) res += res;
	return res;
}
BigInteger BigInteger::operator>> (const long long& x) {
	if (x <= 0) return *this;
	BigInteger res = *this;
	for (long long i = 1; i <= x; i++) res = res.div2();
	return res;
}
BigInteger& BigInteger::operator<<= (const long long& x) {return *this = *this << x;}
BigInteger& BigInteger::operator>>= (const long long& x) {return *this = *this >> x;}

template <class F>
inline BigInteger BigInteger::binary_op_helper(const BigInteger& x, const BigInteger& y, const F& func) {
	auto to_bin = [](BigInteger x) -> std::vector<bool> {
		if (x == 0) return {0};
		std::vector<bool> res;
		for (; x != 0; x = x.div2()) res.emplace_back(x.digits[1] & 1);
		return res;
	};
	std::vector<bool> a = to_bin(x), b = to_bin(y);
	int n = a.size(), m = b.size(), lim = std::max(n, m);
	std::vector<bool> res(lim, 0);
	for (int i = lim - 1; i >= 0; i--) 
		res[i] = func(i < n ? a[i] : 0, i < m ? b[i] : 0);
	std::reverse(res.begin(), res.end());
	return res;
}
BigInteger BigInteger::operator& (const BigInteger& x) {return binary_op_helper(*this, x, [](bool a, bool b) -> bool {return a & b;});}
BigInteger BigInteger::operator| (const BigInteger& x) {return binary_op_helper(*this, x, [](bool a, bool b) -> bool {return a | b;});}
BigInteger BigInteger::operator^ (const BigInteger& x) {return binary_op_helper(*this, x, [](bool a, bool b) -> bool {return a ^ b;});}
BigInteger& BigInteger::operator&= (const BigInteger& x) {return *this = *this & x;}
BigInteger& BigInteger::operator|= (const BigInteger& x) {return *this = *this | x;}
BigInteger& BigInteger::operator^= (const BigInteger& x) {return *this = *this ^ x;}

BigInteger& BigInteger::operator++ () {return *this += 1;}
BigInteger BigInteger::operator++ (int) {BigInteger t = *this; return *this += 1, t;}
BigInteger& BigInteger::operator-- () {return *this -= 1;}
BigInteger BigInteger::operator-- (int) {BigInteger t = *this; return *this -= 1, t;}


using BigInt = BigInteger;
map<int, BigInt> cache;

const BigInt& fib(int n) {
    if (cache.count(n)) return cache[n];
    if (cache.count(n - 1) && cache.count(n - 2)) {
        return cache[n] = cache[n - 1] + cache[n - 2];
    }
    int k = n / 2;
    if (n % 2 == 1) {
        return cache[n] = fib(k) * fib(k) + fib(k + 1) * fib(k + 1);
    } else {
        return cache[n] = fib(k) * (fib(k + 1) + fib(k + 1) - fib(k));
    }
}

vector<const BigInt*> fibRange(const BigInt &l, const BigInt &r, int estLen) {
    vector<const BigInt*> res;
    auto vl = (int)(estLen * 4.73 - 64), vr = (int)(estLen * 4.83 + 64);
    vl = max(vl, 1);
    auto v = views::iota(vl, vr);
    int nl = *ranges::partition_point(v, [&](int n) { return fib(n) < l; });
    while (fib(nl) <= r) {
        res.emplace_back(&fib(nl++));
    }
    return res;
}

template <typename T> vector<pair<T, i64>> runLengthEncoding(const vector<T>& v) {
    if (v.empty()) return {};
    vector<pair<T, i64>> res;
    T prev = v[0];
    int cnt = 1;
    for (int i = 1; i < v.size(); i++) {
        if (v[i] == prev) {
            cnt++;
        } else {
            res.emplace_back(prev, cnt);
            prev = v[i];
            cnt = 1;
        }
    }
    res.emplace_back(prev, cnt);
    return res;
}

vector<pair<BigInt, i64>> runLengthCombine(const vector<pair<BigInt, i64>>& v) {
    if (v.empty()) return {};
    vector<pair<BigInt, i64>> res;
    BigInt prev = v[0].first;
    int cnt = v[0].second;
    for (int i = 1; i < v.size(); i++) {
        if (v[i].first == prev) {
            cnt += v[i].second;
        } else {
            res.emplace_back(prev, cnt);
            prev = v[i].first;
            cnt = v[i].second;
        }
    }
    res.emplace_back(prev, cnt);
    return res;
}

#define int i64
void solve() {
    cache[0] = BigInt("0");
    cache[1] = BigInt("1");
    for (int i = 2; i <= 3000; i++) {
        cache[i] = cache[i - 1] + cache[i - 2];
    }
    int n; cin >> n;
    vector<pair<BigInt, int>> a(n);
    for (int i = 0; i < n; i++) {
        string s; cin >> s;
        a[i] = {s, s.size()};
    }
    vector<pair<BigInt, int>> check;
    sort(a.begin(), a.end());
    auto ra = runLengthEncoding(a);
    int ans = 0;
    for (const auto& [p, c]: ra) {
        const auto& [x, l] = p;
        for (const auto &y : fibRange(x + 1, x + x, l)) {
            if (*y == x + x) {
                ans += c * (c - 1) / 2;
            }
            else check.emplace_back(*y - x, c);
        }
    }
    sort(check.begin(), check.end());
    auto rck = runLengthCombine(check);
    int pnt = 0, m = ra.size();
    for (const auto &[x, c]: rck) {
        while (pnt < m && ra[pnt].first.first < x) pnt++;
        if (pnt == m) break;
        if (ra[pnt].first.first == x) {
            ans += c * ra[pnt].second;
        }
    }
    cout << ans << '\n';
}
#undef int

// Make bold hypotheses and verify carefully
int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int t = 1;
    // cin >> t;
    while (t--) {
        solve();
    }
}