#include #define ll long long #define INF 1000000005 #define MOD 1000000007 #define EPS 1e-10 #define rep(i,n) for(int i=0;i<(int)n;++i) #define each(a, b) for(auto (a): (b)) #define all(v) (v).begin(),(v).end() #define fi first #define se second #define pb push_back #define show(x) cout <<#x<<" = "<<(x)< C; typedef pairP; const double PI = 4*atan(1.0); namespace std { bool operator < (const C a, const C b) { return a.real() != b.real() ? a.real() < b.real() : a.imag() < b.imag(); } } struct L : public vector { L(const C a, const C b) { push_back(a); push_back(b); } }; bool eq(double a,double b) { return (-EPS 0) return +1; // counter clockwise if (cross(b, c) < 0) return -1; // clockwise if (dot(b, c) < 0) return +2; // c--a--b on line if (norm(b) < norm(c)) return -2; // a--b--c on line return 0; } //直線どうしの交差判定(同一直線はTrue) bool intersectLL(const L &l, const L &m) { return abs(cross(l[1]-l[0], m[1]-m[0])) > EPS || abs(cross(l[1]-l[0], m[0]-l[0])) < EPS; } //直線と線分の交差判定(一点共有も交差と判定) bool intersectLS(const L &l, const L &s) { return cross(l[1]-l[0], s[0]-l[0]) * cross(l[1]-l[0], s[1]-l[0]) < EPS; } //直線と点の交差(共有)判定 bool intersectLP(const L &l, const C p) { return abs(cross(l[1]-p, l[0]-p)) < EPS; } //線分どうしの交差判定(一点共有も交差と判定) bool intersectSS(const L &s, const L &t) { return ccw(s[0],s[1],t[0])*ccw(s[0],s[1],t[1]) <= 0 && ccw(t[0],t[1],s[0])*ccw(t[0],t[1],s[1]) <= 0; } //線分と点の交差(共有)判定 bool intersectSP(const L &s, const C p) { return abs(s[0]-p)+abs(s[1]-p)-abs(s[1]-s[0]) < EPS; } //点pを直線l上に射影 C projection(const L &l, const C p) { double t = dot(p-l[0], l[0]-l[1]) / norm(l[0]-l[1]); return l[0] + t*(l[0]-l[1]); } //点pを直線lを軸として対称移動 C reflection(const L &l, const C p) { return p + (projection(l, p) - p)*2.0; } //点と直線の距離 double distanceLP(const L &l, const C p) { return abs(p - projection(l, p)); } //直線と直線の距離 double distanceLL(const L &l, const L &m) { return intersectLL(l, m) ? 0 : distanceLP(l, m[0]); } //直線と線分の距離 double distanceLS(const L &l, const L &s) { if (intersectLS(l, s)) return 0; return min(distanceLP(l, s[0]), distanceLP(l, s[1])); } //線分と点の距離 double distanceSP(const L &s, const C p) { const C r = projection(s, p); if (intersectSP(s, r)) return abs(r - p); return min(abs(s[0] - p), abs(s[1] - p)); } //線分と線分の距離 double distanceSS(const L &s, const L &t) { if (intersectSS(s, t)) return 0; return min(min(distanceSP(s, t[0]), distanceSP(s, t[1])),min(distanceSP(t, s[0]), distanceSP(t, s[1]))); } //直線および線分の交点 C crosspointLL(const L &l, const L &m) { double A = cross(l[1] - l[0], m[1] - m[0]); double B = cross(l[1] - l[0], l[1] - m[0]); //同一直線のとき if(abs(A) < EPS && abs(B) < EPS){ return m[0]; } return m[0] + B / A * (m[1] - m[0]); } //円と直線の交点 double gettime(C c1,C c2) { return (dot(c1,c2) < 0 ? -1.0 : 1.0 ) * abs(c2) / abs(c1); } //円と直線の交点 vector crosspointCL(C c1,double r1,L l) { C a=l[0], b=l[1]; vector res; C base=b-a, target=projection(L(a,b),c1); double length=abs(base), h=abs(c1-target); base/=length; if(r1+EPS crosspointCS(C c1,double r1,L s) { vector tmp=crosspointCL(c1,r1,s); vector res; rep(i,tmp.size()){ if(eq(abs(s[1]-s[0]),abs(s[0]-tmp[i])+abs(s[1]-tmp[i]))){ res.push_back(tmp[i]); } } return res; } //円どうしの交点 L crosspointCC(const C c1, const double r1, const C c2, const double r2) { C a = conj(c2-c1), b = (r2*r2-r1*r1-(c2-c1)*conj(c2-c1)), c = r1*r1*(c2-c1); C d = b*b-4.0*a*c; C z1 = (-b+sqrt(d))/(2.0*a)+c1, z2 = (-b-sqrt(d))/(2.0*a)+c1; return L(z1, z2); } //円と多角形の共通部分の面積 double getarea(C c1,double r1,C a,C b) { C va=c1-a,vb=c1-b; double A=abs(va),B=abs(vb); double f=cross(va,vb),d=distanceSP(L(a,b),c1),res=0; if(eq(f,0.0)) return 0; if(A < r1+EPS && B < r1+EPS) return f*0.5; if(d>r1-EPS) return r1*r1*M_PI*getarg(va,vb)/(2.0*M_PI); vector u=crosspointCS(c1,r1,L(a,b)); u.insert(u.begin(),a),u.push_back(b); for(int i=0;i+1<(int)u.size();i++){ res+=getarea(c1,r1,u[i],u[i+1]); } return res; } double getcrossarea(vector t,C c1,double r1) { int n=t.size(); if(n<3) return 0; double res=0; rep(i,n){ C a=t[i], b=t[(i+1)%n]; res += getarea(c1,r1,a,b); } return res; } //凸包を求める vector convex_full(vector ps) { int n = ps.size(), k = 0; sort(ps.begin(), ps.end()); vector ch(2*n); for (int i = 0; i < n; ch[k++] = ps[i++]){ while (k >= 2 && ccw(ch[k-2], ch[k-1], ps[i]) <= 0) k--; } for (int i = n-2, t = k+1; i >= 0; ch[k++] = ps[i--]){ while (k >= t && ccw(ch[k-2], ch[k-1], ps[i]) <= 0) k--; } ch.resize(k-1); return ch; } //凸性判定 bool isconvex(const vector &ps) { rep(i,ps.size()){ if (ccw(ps[(i+ps.size()-1) % ps.size()],ps[i],ps[(i+1) % ps.size()])) return false; } return true; } //多角形の面積 double area(const vector &ps) { double A = 0; rep(i,ps.size()){ A += cross(ps[i],ps[(i+1) % ps.size()]); } return A / 2.0; } //凸多角形を直線で切断した時の左側の図形 vector convex_cut(const vector &ps, const L &l) { vector Q; rep(i,ps.size()){ C A = ps[i], B = ps[(i+1)%ps.size()]; if (ccw(l[0], l[1], A) != -1) Q.push_back(A); if (ccw(l[0], l[1], A)*ccw(l[0], l[1], B) < 0) Q.push_back(crosspointLL(L(A, B),l)); } return Q; } //点が多角形に包含されているか(0は含まれない,1は辺上,2は含まれる) int contains(const vector& ps, const C p) { bool flag = false; rep(i,ps.size()) { C a = ps[i] - p, b = ps[(i+1)%ps.size()] - p; if (imag(a) > imag(b)) swap(a, b); if (imag(a) <= 0 && 0 < imag(b)){ if (cross(a, b) < 0) flag = !flag; } if (cross(a, b) == 0 && dot(a, b) <= 0) return 1; } return flag ? 2 : 0; } //凸多角形の交差 vector convex_intersection(vector& ps,vector& qs) { vector rs; int a = ps.size(),b = qs.size(); rep(i,a){ if(contains(qs,ps[i])){ rs.push_back(ps[i]); } } rep(i,b){ if(contains(ps,qs[i])){ rs.push_back(qs[i]); } } rep(i,a){ rep(j,b){ L l1(ps[i],ps[(i+1)%a]),l2(qs[j],qs[(j+1)%b]); if(intersectSS(l1,l2)){ rs.push_back(crosspointLL(l1,l2)); } } } sort(rs.begin(),rs.end()); rs.erase(unique(all(rs)),rs.end()); if(rs.size() <= 1){ return rs; } return convex_full(rs); } //凸多角形の直径を求める(キャリパー法) //maxi,maxjが最遠点対となる double convex_diameter(const vector &ps) { const int n = ps.size(); int is = 0, js = 0; for (int i = 1; i < n; ++i) { if (imag(ps[i]) > imag(ps[is])) is = i; if (imag(ps[i]) < imag(ps[js])) js = i; } double maxd = abs(ps[is]-ps[js]); int i, maxi, j, maxj; i = maxi = is; j = maxj = js; do{ if (cross(ps[(i+1)%ps.size()]-ps[i],ps[(j+1)%ps.size()]-ps[j]) >= 0) j = (j+1) % n; else i = (i+1) % n; if (abs(ps[i]-ps[j]) > maxd) { maxd = abs(ps[i]-ps[j]); maxi = i; maxj = j; } } while (i != is || j != js); return maxd; } bool compyx(C c1,C c2) { return c1.imag() != c2.imag() ? c1.imag() < c2.imag() : c1.real() < c2.real(); } //最近点対を求める double closest_pair(C *a, int n) { if(n<=1) return INF; int m=n/2; double x=a[m].real(); double d=min(closest_pair(a,m),closest_pair(a+m,n-m)); inplace_merge(a,a+m,a+n,compyx); vector b; rep(i,n){ if(abs(x-a[i].real())>=d) continue; rep(j,b.size()){ C dp=a[i]-b[b.size()-1-j]; if(dp.imag()>=d) break; d=min(d,abs(dp)); } b.push_back(a[i]); } return d; } double compute_shortest(C *a,int n) { sort(a,a+n); return closest_pair(a,n); } //2円の位置関係を示す(返り値は2円の間の共通接線の数) int getstateCC(C c1,double r1,C c2,double r2) { double d=abs(c1-c2); if(d>r1+r2+EPS)return 4; if(d>r1+r2-EPS)return 3; if(d>abs(r1-r2)+EPS)return 2; if(d>abs(r1-r2)-EPS)return 1; return 0; } //点から円へ接線を引いた時の接点 C gettangentCP_(C c1,double r1,C p,int flg){ C base=c1-p; double w=Sqrt(norm(base)-r1*r1); C s=p+base*C(w,r1 * flg)/norm(base)*w; return s; } //点から円への接線 vector gettangentCP(C c1,double r1,C p){ vector res; C s=gettangentCP_(c1,r1,p,1); C t=gettangentCP_(c1,r1,p,-1); //点が円の周上にある場合 if(eq(s,t)){ res.push_back(L(s,s+(c1-p)*C(0,1))); }else{ res.push_back(L(p,s)); res.push_back(L(p,t)); } return res; } //2円の共通内接線を求める L getintangent(C c1,double r1,C c2,double r2,double flg) { C base=c2-c1; double w=r1+r2; double h=Sqrt(norm(base)-w*w); C k=base*C(w,h*flg)/norm(base); return L(c1+k*r1,c2-k*r2); } //2円の共通外接線を求める L getouttangent(C c1,double r1,C c2,double r2,double flg) { C base=c2-c1; double h=r2-r1; double w=Sqrt(norm(base)-h*h); C k=base*C(w,h*flg)/norm(base)*C(0,flg); return L(c1+k*r1,c2+k*r2); } //2円の共通接線を求める(各直線の2点はそれぞれの円の接点) vector gettangentCC(C c1,double r1,C c2,double r2) { vector res; double d=abs(c1-c2); if(d>r1+r2+EPS) res.push_back(getintangent(c1,r1,c2,r2,1)); if(d>r1+r2-EPS) res.push_back(getintangent(c1,r1,c2,r2,-1)); if(d>abs(r1-r2)+EPS) res.push_back(getouttangent(c1,r1,c2,r2,1)); if(d>abs(r1-r2)-EPS) res.push_back(getouttangent(c1,r1,c2,r2,-1)); return res; } ll gcd(ll a,ll b) { if(a == 0 || b == 0){ return max(a,b); } if(a%b == 0){ return b; }else{ return gcd(b,a%b); } } ll cnt(C p1,C p2) { ll res = gcd((ll)(abs(p2.real()-p1.real())+0.1),(ll)(abs(p2.imag()-p1.imag())+0.1)); return res; } int main() { cin.tie(0); ios::sync_with_stdio(false); ll x1,y1,x2,y2,d; cin >> x1 >> y1 >> x2 >> y2 >> d; vector v1,v2; v1.pb(C(x1,y1)),v1.pb(C(x2,y1)),v1.pb(C(x2,y2)),v1.pb(C(x1,y2)); v2.pb(C(0,-d)),v2.pb(C(d,0)),v2.pb(C(0,d)),v2.pb(C(-d,0)); vector res = convex_intersection(v1,v2); ll sm = 0; rep(i,res.size()){ sm += cnt(res[i],res[(i+1)%(int)(res.size())]); } ll S = area(res); ll inc = S - sm/2 + 1; cout << inc+sm << endl; return 0; }