結果
問題 | No.1999 Lattice Teleportation |
ユーザー |
![]() |
提出日時 | 2025-01-11 06:17:21 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 209 ms / 2,000 ms |
コード長 | 27,568 bytes |
コンパイル時間 | 9,354 ms |
コンパイル使用メモリ | 241,244 KB |
実行使用メモリ | 45,836 KB |
最終ジャッジ日時 | 2025-01-11 06:17:37 |
合計ジャッジ時間 | 8,793 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 29 |
ソースコード
#include <bits/stdc++.h>using namespace std;typedef __int128_t ll;template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return true; } return false; }template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return true; } return false; }#define vi vector<int>#define vl vector<ll>#define vii vector<pair<int,int>>#define vll vector<pair<ll,ll>>#define vvi vector<vector<int>>#define vvl vector<vector<ll>>#define vvii vector<vector<pair<int,int>>>#define vvll vector<vector<pair<ll,ll>>>#define vst vector<string>#define pii pair<int,int>#define pll pair<ll,ll>#define pb push_back#define all(x) (x).begin(),(x).end()#define mkunique(x) sort(all(x));(x).erase(unique(all(x)),(x).end())#define fi first#define se second#define mp make_pair#define si(x) int(x.size())const int mod=998244353,MAX=600005,INF=15<<26;//modint+畳み込み+逆元テーブル// from: https://gist.github.com/yosupo06/ddd51afb727600fd95d9d8ad6c3c80c9// (based on AtCoder STL)#include <algorithm>#include <array>#ifdef _MSC_VER#include <intrin.h>#endifnamespace atcoder {namespace internal {int ceil_pow2(int n) {int x = 0;while ((1U << x) < (unsigned int)(n)) x++;return x;}int bsf(unsigned int n) {#ifdef _MSC_VERunsigned long index;_BitScanForward(&index, n);return index;#elsereturn __builtin_ctz(n);#endif}} // namespace internal} // namespace atcoder#include <utility>namespace atcoder {namespace internal {constexpr long long safe_mod(long long x, long long m) {x %= m;if (x < 0) x += m;return x;}struct barrett {unsigned int _m;unsigned long long im;barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}unsigned int umod() const { return _m; }unsigned int mul(unsigned int a, unsigned int b) const {unsigned long long z = a;z *= b;#ifdef _MSC_VERunsigned long long x;_umul128(z, im, &x);#elseunsigned long long x =(unsigned long long)(((unsigned __int128)(z)*im) >> 64);#endifunsigned int v = (unsigned int)(z - x * _m);if (_m <= v) v += _m;return v;}};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;}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;for (long long a : {2, 7, 61}) {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);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};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 <= bauto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}if (m0 < 0) m0 += b / s;return {s, m0};}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#include <cassert>#include <numeric>#include <type_traits>namespace atcoder {namespace internal {#ifndef _MSC_VERtemplate <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;#elsetemplate <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;#endiftemplate <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#include <cassert>#include <numeric>#include <type_traits>#ifdef _MSC_VER#include <intrin.h>#endifnamespace 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 internaltemplate <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#include <cassert>#include <type_traits>#include <vector>namespace atcoder {namespace internal {template <class mint, internal::is_static_modint_t<mint>* = nullptr>void butterfly(std::vector<mint>& a) {static constexpr int g = internal::primitive_root<mint::mod()>;int n = int(a.size());int h = internal::ceil_pow2(n);static bool first = true;static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]if (first) {first = false;mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1int cnt2 = bsf(mint::mod() - 1);mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();for (int i = cnt2; i >= 2; i--) {es[i - 2] = e;ies[i - 2] = ie;e *= e;ie *= ie;}mint now = 1;for (int i = 0; i < cnt2 - 2; i++) {sum_e[i] = es[i] * now;now *= ies[i];}}for (int ph = 1; ph <= h; ph++) {int w = 1 << (ph - 1), p = 1 << (h - ph);mint now = 1;for (int s = 0; s < w; s++) {int offset = s << (h - ph + 1);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p] * now;a[i + offset] = l + r;a[i + offset + p] = l - r;}now *= sum_e[bsf(~(unsigned int)(s))];}}}template <class mint, internal::is_static_modint_t<mint>* = nullptr>void butterfly_inv(std::vector<mint>& a) {static constexpr int g = internal::primitive_root<mint::mod()>;int n = int(a.size());int h = internal::ceil_pow2(n);static bool first = true;static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]if (first) {first = false;mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1int cnt2 = bsf(mint::mod() - 1);mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();for (int i = cnt2; i >= 2; i--) {es[i - 2] = e;ies[i - 2] = ie;e *= e;ie *= ie;}mint now = 1;for (int i = 0; i < cnt2 - 2; i++) {sum_ie[i] = ies[i] * now;now *= es[i];}}for (int ph = h; ph >= 1; ph--) {int w = 1 << (ph - 1), p = 1 << (h - ph);mint inow = 1;for (int s = 0; s < w; s++) {int offset = s << (h - ph + 1);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p];a[i + offset] = l + r;a[i + offset + p] =(unsigned long long)(mint::mod() + l.val() - r.val()) *inow.val();}inow *= sum_ie[bsf(~(unsigned int)(s))];}}}} // namespace internaltemplate <class mint, internal::is_static_modint_t<mint>* = nullptr>std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};if (std::min(n, m) <= 60) {if (n < m) {std::swap(n, m);std::swap(a, b);}std::vector<mint> ans(n + m - 1);for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) {ans[i + j] += a[i] * b[j];}}return ans;}int z = 1 << internal::ceil_pow2(n + m - 1);a.resize(z);internal::butterfly(a);b.resize(z);internal::butterfly(b);for (int i = 0; i < z; i++) {a[i] *= b[i];}internal::butterfly_inv(a);a.resize(n + m - 1);mint iz = mint(z).inv();for (int i = 0; i < n + m - 1; i++) a[i] *= iz;return a;}template <unsigned int mod = 998244353,class T,std::enable_if_t<internal::is_integral<T>::value>* = nullptr>std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};using mint = static_modint<mod>;std::vector<mint> a2(n), b2(m);for (int i = 0; i < n; i++) {a2[i] = mint(a[i]);}for (int i = 0; i < m; i++) {b2[i] = mint(b[i]);}auto c2 = convolution(move(a2), move(b2));std::vector<T> c(n + m - 1);for (int i = 0; i < n + m - 1; i++) {c[i] = c2[i].val();}return c;}std::vector<long long> convolution_ll(const std::vector<long long>& a,const std::vector<long long>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};static constexpr unsigned long long MOD1 = 754974721; // 2^24static constexpr unsigned long long MOD2 = 167772161; // 2^25static constexpr unsigned long long MOD3 = 469762049; // 2^26static constexpr unsigned long long M2M3 = MOD2 * MOD3;static constexpr unsigned long long M1M3 = MOD1 * MOD3;static constexpr unsigned long long M1M2 = MOD1 * MOD2;static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;static constexpr unsigned long long i1 =internal::inv_gcd(MOD2 * MOD3, MOD1).second;static constexpr unsigned long long i2 =internal::inv_gcd(MOD1 * MOD3, MOD2).second;static constexpr unsigned long long i3 =internal::inv_gcd(MOD1 * MOD2, MOD3).second;auto c1 = convolution<MOD1>(a, b);auto c2 = convolution<MOD2>(a, b);auto c3 = convolution<MOD3>(a, b);std::vector<long long> c(n + m - 1);for (int i = 0; i < n + m - 1; i++) {unsigned long long x = 0;x += (c1[i] * i1) % MOD1 * M2M3;x += (c2[i] * i2) % MOD2 * M1M3;x += (c3[i] * i3) % MOD3 * M1M2;long long diff =c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));if (diff < 0) diff += MOD1;static constexpr unsigned long long offset[5] = {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};x -= offset[diff % 5];c[i] = x;}return c;}} // namespace atcoderusing mint=atcoder::modint1000000007;vector<mint> inv,fac,finv;void make(){inv.resize(MAX);fac.resize(MAX);finv.resize(MAX);fac[0]=fac[1]=1;finv[0]=finv[1]=1;inv[1]=1;for(int i=2;i<MAX;i++){inv[i]=-inv[mod%i]*(mod/i);fac[i]=fac[i-1]*i;finv[i]=finv[i-1]*inv[i];}}mint comb(ll a,ll b){if(a<b) return 0;return fac[a]*finv[b]*finv[a-b];}mint perm(ll a,ll b){if(a<b) return 0;return fac[a]*finv[a-b];}//int128//https://kopricky.github.io/code/Misc/int128.html// __int128の入出力using LL = __int128;istream& operator>>(istream& is, LL& v){string s;is >> s;v = 0;for (int i = 0; i < (int)s.size(); i++) {if (isdigit(s[i])) { v = v * 10 + s[i] - '0'; }}if (s[0] == '-') { v *= -1; }return is;}ostream& operator<<(ostream& os, const LL& v){if (v == 0) { return (os << "0"); }LL num = v;if (v < 0) {os << '-';num = -num;}string s;for (; num > 0; num /= 10) { s.push_back((char)(num % 10) + '0'); }reverse(s.begin(), s.end());return (os << s);}//幾何ライブラリ(整数)class Point{public:ll x,y;Point(ll x=0,ll y=0):x(x),y(y){}Point operator + (Point p){return Point(x+p.x,y+p.y);}Point operator - (Point p){return Point(x-p.x,y-p.y);}Point operator * (ll a){return Point(a*x,a*y);}double norm(){return x*x+y*y;}bool operator < (const Point &p)const{return x<p.x||(x==p.x&&y<p.y);}bool operator == (const Point &p)const{return x==p.x&&y==p.y;}};typedef Point Vector;ll norm(Vector a){return a.x*a.x+a.y*a.y;}ll dot(Vector a,Vector b){return a.x*b.x+a.y*b.y;}ll cross(Vector a,Vector b){return a.x*b.y-a.y*b.x;}struct Segment{Point p1,p2;};bool isOrthogonal(Vector a,Vector b){return dot(a,b)==0;}bool isOrthogonal(Point a1,Point a2,Point b1,Point b2){return isOrthogonal(a1-a2,b1-b2);}bool isOrthogonal(Segment s1,Segment s2){return dot(s1.p2-s1.p1,s2.p2-s2.p1)==0;}bool isParallel(Vector a,Vector b){return cross(a,b)==0;}bool isParallel(Point a1,Point a2,Point b1,Point b2){return isParallel(a1-a2,b1-b2);}bool isParallel(Segment s1,Segment s2){return cross(s1.p2-s1.p1,s2.p2-s2.p1)==0;}//p0,p1,p2の順に見たときどうなるか?static const int counter_clockwise=1;static const int clockwise=-1;static const int online_back=2;static const int online_front=-2;static const int on_segment=0;int ccw(Point p0,Point p1,Point p2){Vector a=p1-p0;Vector b=p2-p0;if(cross(a,b)>0) return counter_clockwise;if(cross(a,b)<0) return clockwise;if(dot(a,b)<0) return online_back;if(a.norm()<b.norm()) return online_front;return on_segment;}bool intersect(Point p1,Point p2,Point p3,Point p4){return(ccw(p1,p2,p3)*ccw(p1,p2,p4)<=0&&ccw(p3,p4,p1)*ccw(p3,p4,p2)<=0);}bool intersect(Segment s1,Segment s2){return intersect(s1.p1,s1.p2,s2.p1,s2.p2);}bool overlap(Segment s1,Segment s2){int a=ccw(s1.p1,s1.p2,s2.p1),b=ccw(s1.p1,s1.p2,s2.p2);if(a&1||b&1) return 0;if(a==2){if(b==-2||(b==0&&!(s2.p2==s1.p1))) return 1;else return 0;}if(a==-2){if(b==2||(b==0&&!(s2.p2==s1.p2))) return 1;else return 0;}if(a==0){if(s1.p1==s2.p1){if(b!=2) return 1;else return 0;}else if(s1.p2==s2.p1){if(b!=-2) return 1;else return 0;}else return 1;}return 0;}//s1とs2の共通の線分(長さ0より大きい)があるかどうかtypedef Segment Line;//ネットの適当を書いたのであってるか全く知りません→あってそうclass Circle{public:Point c;ll r;Circle(Point c=Point(),ll r=0.0):c(c),r(r){}};typedef vector<Point> Polygon;/*IN 2ON 1OUT 0*/Polygon andrewScan(Polygon s,bool ok){Polygon u,l;sort(all(s));if(int(s.size())<3) return s;int n=int(s.size());u.push_back(s[0]);u.push_back(s[1]);l.push_back(s[n-1]);l.push_back(s[n-2]);if(ok){for(int i=2;i<n;i++){for(int j=int(u.size());j>=2&&ccw(u[j-2],u[j-1],s[i])==counter_clockwise;j--){u.pop_back();}u.push_back(s[i]);}for(int i=int(s.size())-3;i>=0;i--){for(int j=int(l.size());j>=2&&ccw(l[j-2],l[j-1],s[i])==counter_clockwise;j--){l.pop_back();}l.push_back(s[i]);}}if(!ok){for(int i=2;i<n;i++){for(int j=int(u.size());j>=2&&ccw(u[j-2],u[j-1],s[i])!=clockwise;j--){u.pop_back();}u.push_back(s[i]);}for(int i=int(s.size())-3;i>=0;i--){for(int j=int(l.size());j>=2&&ccw(l[j-2],l[j-1],s[i])!=clockwise;j--){l.pop_back();}l.push_back(s[i]);}}reverse(all(l));for(int i=int(u.size())-2;i>=1;i--) l.push_back(u[i]);return l;}//ok==1なら辺の上も含める// 倍ll gcdd(ll a,ll b){if(b==0) return a;return gcdd(b,a%b);}ll abss(ll x){if(x<0) return -x;else return x;}bool compare(pair<ll,ll> a,pair<ll,ll> b){int at,bt;if(a.se<0||(a.se==0&&a.fi>0)) at=0;else if(a.fi==0&&a.se==0) at=1;else at=2;if(b.se<0||(b.se==0&&b.fi>0)) bt=0;else if(b.fi==0&&b.se==0) bt=1;else bt=2;if(at!=bt) return at<bt;return a.fi*b.se-a.se*b.fi>0;}int main(){std::ifstream in("text.txt");std::cin.rdbuf(in.rdbuf());cin.tie(0);ios::sync_with_stdio(false);ll N;cin>>N;vll S;for(int i=0;i<N;i++){ll a,b;cin>>a>>b;if(a==0&&b==0) continue;S.pb(mp(a,b));}if(si(S)==0){cout<<1<<endl;return 0;}sort(all(S),compare);vector<Point> P;for(auto [a,b]:S){if(si(P)&&ccw(Point{a,b},Point{0,0},P.back())==0){P.back()=P.back()+Point{a,b};}else{P.pb(Point{a,b});}}if(si(P)==1){ll a=P[0].x,b=P[0].y;a=abss(a);b=abss(b);ll g=gcd(a,b);cout<<g+1<<endl;return 0;}N=si(P);for(int i=0;i<N;i++){P.pb(P[i]);}vector<Point> Q;int i=0,j=i;ll xsum=0,ysum=0;Q.pb(Point{xsum,ysum});while(i<N){while(ccw(P[i],Point{0,0},P[j])<=0&&j<i+N){xsum+=P[j].x;ysum+=P[j].y;j++;Q.pb(Point{xsum,ysum});}xsum-=P[i].x;ysum-=P[i].y;i++;Q.pb(Point{xsum,ysum});}Q=andrewScan(Q,0);mint ans=0,ss=0,tt=0;for(int i=0;i<si(Q);i++){ans+=cross(Q[i],Q[(i+1)%si(Q)]);auto [a,b]=Q[(i+1)%si(Q)]-Q[i];a=abss(a);b=abss(b);ll g=gcdd(a,b);ans-=g;ss+=g;}ans+=2;ans=ans/2+ss;cout<<ans.val()<<endl;}