#ifdef LOCAL111 #else #pragma GCC optimize ("O3") #define NDEBUG #endif // #define _USE_MATH_DEFINES #include const int INF = 1e9; using namespace std; template ostream& operator<< (ostream& os, const pair& p) { os << '(' << p.first << ' ' << p.second << ')'; return os; } #define endl '\n' #define ALL(a) (a).begin(),(a).end() #define SZ(a) int((a).size()) #define FOR(i,a,b) for(int i=(a);i<(b);++i) #define RFOR(i,a,b) for (int i=(b)-1;i>=(a);i--) #define REP(i,n) FOR(i,0,n) #define RREP(i,n) for (int i=(n)-1;i>=0;i--) #ifdef LOCAL111 #define DEBUG(x) cout<<#x<<": "<<(x)< void dpite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;} #else #define DEBUG(x) true template void dpite(T a, T b){ return; } #endif #define F first #define S second #define SNP string::npos #define WRC(hoge) cout << "Case #" << (hoge)+1 << ": " template void pite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;} template bool chmax(T& a, T b){if(a < b){a = b; return true;} return false;} template bool chmin(T& a, T b){if(a > b){a = b; return true;} return false;} template vector make_v(size_t a){return vector(a);} template auto make_v(size_t a,Ts... ts){ return vector(ts...))>(a,make_v(ts...)); } template typename enable_if::value!=0>::type fill_v(U &u,const V... v){u=U(v...);} template typename enable_if::value==0>::type fill_v(U &u,const V... v){ for(auto &e:u) fill_v(e,v...); } const array dx = {0, 1, 0, -1}; const array dy = {1, 0, -1, 0}; typedef long long int LL; typedef unsigned long long ULL; typedef pair P; void ios_init(){ //cout.setf(ios::fixed); //cout.precision(12); #ifdef LOCAL111 return; #endif ios::sync_with_stdio(false); cin.tie(0); } #define EPS 1e-9 //library template class Matrix { public: vector > v; int n,m; Matrix(int n){ this->n = this->m = n; v.resize(n,vector(n,0)); } Matrix(int n, int m){ this -> n = n; this -> m = m; v.resize(n,vector(m,0)); } size_t size() const { return v.size(); } int row() const { return n; } int col() const { return m; } Matrix operator+ (Matrix x) const { Matrix res(n,m); for(int i = 0; i < n; i++){ for(int j = 0; j < m; j++){ res.v[i][j] = x.v[i][j]+v[i][j]; } } return res; } Matrix operator-(Matrix x) const { Matrix res(n,m); for(int i = 0; i < n; i++){ for(int j = 0; j < m; j++){ res.v[i][j] = v[i][j]-x.v[i][j]; } } } Matrix operator*(Matrix x) const { Matrix res(n,x.m); for(int i = 0; i < n; i++){ for(int j = 0; j < x.m; j++){ for(int k = 0; k < m; k++){ res.v[i][j] += v[i][k]*x.v[k][j]; } } } return res; } Matrix operator-() const { Matrix res = *this; for(int i = 0; i < (int)v.size(); ++i) { for(int j = 0; j < (int)v[i].size(); ++j) { res [i][j] *= -1; } } return res; } vector operator*(vector x) const { assert(x.size() == v.size()); vector res(v.size()); for(int i = 0; i < n; i++){ T tmp = 0; for(int j = 0; j < m; j++){ tmp += v[i][j]*x[j]; } res[i] = tmp; } return res; } Matrix pow(long long x) const { assert(n == m); Matrix m = (*this); Matrix res(n); for(int i = 0; i < n; i++) res[i][i] = 1; while(x != 0) { if(x&1) { res = res*m; } m = m*m; x >>= 1; } return res; } vector& operator[](int x){ return v[x]; } const vector& operator[](int x) const { return v[x]; } Matrix inverse() const{ assert(n == m); Matrix res(n); for(int i = 0; i < n; ++i) { res[i][i] = 1; } // vector> swap_log; Matrix mat = *this; for(int k = 0; k < n; ++k) { T max_val = abs(mat[k][k]); int max_point = k; for(int i = k+1; i < n; ++i) { if(max_val < abs(mat[i][k])){ max_val = abs(mat[i][k]); max_point = i; } } swap(mat[k],mat[max_point]); swap(res[k],res[max_point]); // swap_log.emplace_back(k,max_point); for(int i = k+1; i < n; ++i) { T m = mat[i][k]/mat[k][k]; for(int j = 0; j < n; ++j) { mat[i][j] -= m*mat[k][j]; res[i][j] -= m*res[k][j]; } } } for(int k = n-1; k >= 0; --k) { for(int i = 0; i < k; ++i) { T m = mat[i][k]/mat[k][k]; for(int j = 0; j < n; ++j) { // mat[i][j] -= mat[k][j]*m; res[i][j] -= res[k][j]*m; } } } for(int i = 0; i < n; ++i) { for(int j = 0; j < n; ++j) { res[i][j] /= mat[i][i]; } } // for(auto&& e : swap_log) { // swap(res[e.first],res[e.second]); // } return res; } T det() const { Matrix mat = *this; T res = 1; for(int k = 0; k < n; ++k) { T max_val = abs(mat[k][k]); int max_point = k; for(int i = k+1; i < n; ++i) { if(max_val < abs(mat[i][k])){ max_val = abs(mat[i][k]); max_point = i; } } swap(mat[k],mat[max_point]); if(k != max_point) res *= -1; for(int i = k+1; i < n; ++i) { T m = mat[i][k]/mat[k][k]; for(int j = 0; j < n; ++j) { mat[i][j] -= m*mat[k][j]; } } } for(int i = 0; i < n; ++i) { res *= mat[i][i]; } return res; } pair> getMaxEigenvalue(int iterNum = 10) const { assert(n == m); vector xk_(n, 1); xk_ = (*this).pow(iterNum)*xk_; auto xk = (*this)*xk_; T xk_xk = 0, xk_xk_ = 0; for(int i = 0; i < n; i++) { xk_xk += xk[i]*xk[i]; xk_xk_ += xk[i]*xk_[i]; } T xkAbs = sqrt(xk_xk); auto res = xk; for(auto&& e : res) { e /= xkAbs; } return { xk_xk/xk_xk_, res }; } void debug() const { for(auto&& ee : v) { for(auto&& e : ee) { cout << e << ' '; } cout << endl; } cout << endl; } }; template Matrix companion_pow(const Matrix& A, long long m) { assert(A.col() == A.row()); int n = A.col(); Matrix u(1, n), Ak = A; u[0][n-1] = 1; while(m > 0) { if(m&1) { u = u*Ak; } Matrix a(1, n); for(int i = 0; i < n; ++i) { a[0][i] = Ak[n-1][i]; } a = a*Ak; for(int i = n-1; i >= 0; --i) { for(int j = 0; j < n; ++j) { Ak[i][j] = a[0][j]; } auto a00 = a[0][0]; for(int j = 0; j < n-1; ++j) { a[0][j] = a[0][j+1]+A[0][j]*a00; } a[0][n-1] = A[0][n-1]*a00; } m >>= 1; } Matrix res(n); for(int i = n-1; i >= 0; --i) { for(int j = 0; j < n; ++j) { res[i][j] = u[0][j]; } auto u00 = u[0][0]; for(int j = 0; j < n-1; ++j) { u[0][j] = u[0][j+1]+A[0][j]*u00; } u[0][n-1] = A[0][n-1]*u00; } return res; } //library class UFTree { //private: public: vector par; vector rank; vector num; //public: UFTree(int n) { par = vector(n); rank = vector(n); num = vector(n); for(int i = 0; i < n; i++){ par[i] = i; rank[i] = 0; num[i] = 1; } } int find(int x) { if(par[x] == x){ return x; }else{ return par[x] = find(par[x]); } } void unite(int x, int y) { x = find(x); y = find(y); if(x == y) return; if(rank[x] < rank[y]){ par[x] = y; num[y] += num[x]; }else{ par[y] = x; num[x] += num[y]; if(rank[x] == rank[y]) rank[x]++; } } int count(int x) { return num[find(x)]; } bool same(int x, int y) { return find(x) == find(y); } }; //library template long long gcd(T x, T y){ return y==0 ? x : gcd(y, x%y); } int main() { ios_init(); LL a, b, c, d; while(cin >> a >> b >> c >> d) { using P = pair; int n; cin >> n; vector x(n), y(n); REP(i, n) cin >> x[i] >> y[i]; const double eps = 1e-15; if(a * d == b * c) { // if(b == 0) { // assert(d == 0); // int e = gcd(a, c); // } else if(a == 0) { // assert(c == 0); // int f = gcd(d, d); // } else { LL e = gcd(a, c), f = gcd(b, d); DEBUG(e); DEBUG(f); map> ma; REP(i, n) { int t; if(e == 0) { t = y[i] / f; } else if(f == 0) { t = x[i] / e; } else { t = min(x[i] / e, y[i] / f); } P ke = {x[i] - t * e, y[i] - t * f}; DEBUG(ke); ma[ke].push_back(i); } UFTree uf(n); for(auto&& e : ma) { REP(i, SZ(e.S) - 1) { uf.unite(e.S[i], e.S[i+1]); } } set se; REP(i, n) { se.insert(uf.find(i)); } cout << se.size() << endl; // } } else { // Matrix mat(2, 2); // mat[0] = {a, c}; // mat[1] = {b, d}; // mat = mat.inverse(); // Matrix mai(2); LL det = abs(a * d - c * b); // DEBUG(det); // REP(i, 2) REP(j, 2) { // mai[i][j] = round(mat[i][j] * det); // DEBUG(mai[i][j]); // } // DEBUG(det); Matrix mai(2); mai[0] = {d, -c}; mai[1] = {-b, a}; if(det < 0) { REP(i, 2) REP(j, 2) mai[i][j] *= -1; } map> ma; DEBUG(det); REP(i, n) { DEBUG(i); vector v = {x[i], y[i]}; DEBUG(x[i]); DEBUG(y[i]); auto st = mai * v; dpite(ALL(st)); // { // Matrix mat(2, 2); // mat[0] = {a, c}; // mat[1] = {b, d}; // vector st0(2); // REP(i, SZ(st)) st0[i] = st[i]; // auto v = mat * st0; // dpite(ALL(v)); // } LL mx = st[0] % det; if(mx < 0) mx += det; LL my = st[1] % det; if(my < 0) my += det; DEBUG(mx); DEBUG(my); ma[{mx, my}].push_back(i); } UFTree uf(n); for(auto&& e : ma) { DEBUG(e.F); REP(i, SZ(e.S) - 1) { uf.unite(e.S[i], e.S[i+1]); } } set se; REP(i, n) { se.insert(uf.find(i)); } cout << se.size() << endl; } } return 0; }