#include "bits/stdc++.h" using namespace std; typedef long long ll; typedef pair pii; typedef pair pll; const int INF = 1e9; const ll LINF = 1e18; template ostream& operator << (ostream& out,const pair& o){ out << "(" << o.first << "," << o.second << ")"; return out; } template ostream& operator << (ostream& out,const vector V){ for(int i = 0; i < V.size(); i++){ out << V[i]; if(i!=V.size()-1) out << " ";} return out; } template ostream& operator << (ostream& out,const vector > Mat){ for(int i = 0; i < Mat.size(); i++) { if(i != 0) out << endl; out << Mat[i];} return out; } template ostream& operator << (ostream& out,const map mp){ out << "{ "; for(auto it = mp.begin(); it != mp.end(); it++){ out << it->first << ":" << it->second; if(mp.size()-1 != distance(mp.begin(),it)) out << ", "; } out << " }"; return out; } /* 問題文============================================================ ================================================================= 解説============================================================= ================================================================ */ typedef long double ld; typedef complex Point; const ld eps = 1e-9, pi = acos(-1.0); namespace std { bool operator<(const Point &lhs, const Point &rhs) { if (lhs.real() < rhs.real() - eps) return true; if (lhs.real() > rhs.real() + eps) return false; return lhs.imag() < rhs.imag(); } } Point input_point() { ld x, y; cin >> x >> y; return Point(x, y); } // 点の入力 bool eq(ld a, ld b) { return (abs(a - b) < eps); } // 誤差つき等号判定 ld dot(Point a, Point b) { return real(conj(a) * b); } // 内積 ld cross(Point a, Point b) { return imag(conj(a) * b); } // 外積 // 直線の定義 class Line { public: Point a, b; Line() : a(Point(0, 0)), b(Point(0, 0)) {} Line(Point a, Point b) : a(a), b(b) {} Point operator[](const int _num) { if (_num == 0)return a; else if (_num == 1)return b; else assert(false); } }; // 円の定義 class Circle { public: Point p; ld r; Circle() : p(Point(0, 0)), r(0) {} Circle(Point p, ld r) : p(p), r(r) {} }; // 垂線の足 Point proj(Line l, Point p) { ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b); return l.a + t * (l.a - l.b); } // CCW int ccw(Point a, Point b, Point c) { b -= a; c -= a; if (cross(b, c) > eps) return 1; // a,b,cが反時計周りの順に並ぶ if (cross(b, c) < -eps) return -1; // a,b,cが時計周りの順に並ぶ if (dot(b, c) < 0) return 2; // c,a,bの順に直線に並ぶ if (norm(b) < norm(c)) return -2; // a,b,cの順に直線に並ぶ return 0; // a,c,bの順に直線に並ぶ } /* 交差判定 */ // 直線と直線の交差判定 bool isis_ll(Line l, Line m) { return !eq(cross(l.b - l.a, m.b - m.a), 0); } // 直線と線分の交差判定 bool isis_ls(Line l, Line s) { return isis_ll(l, s) && (cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps); } // 線分と線分の交差判定 bool isis_ss(Line s, Line t) { return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 && ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0; } // 点の直線上判定 bool isis_lp(Line l, Point p) { return (abs(cross(l.b - p, l.a - p)) < eps); } // 点の線分上判定 bool isis_sp(Line s, Point p) { return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps); } /* 距離 */ // 直線と直線の交点 Point is_ll(Line s, Line t) { Point sv = s.b - s.a, tv = t.b - t.a; assert(cross(sv, tv) != 0); return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv); } // 直線と点の距離 ld dist_lp(Line l, Point p) { return abs(p - proj(l, p)); } // 直線と直線の距離 ld dist_ll(Line l, Line m) { return isis_ll(l, m) ? 0 : dist_lp(l, m.a); } // 直線と線分の距離 ld dist_ls(Line l, Line s) { return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b)); } // 線分と点の距離 ld dist_sp(Line s, Point p) { Point r = proj(s, p); return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p)); } // 線分と線分の距離 ld dist_ss(Line s, Line t) { if (isis_ss(s, t)) return 0; return min({ dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b) }); } /* 円 */ // 円と円の交点 vector is_cc(Circle c1, Circle c2) { vector res; ld d = abs(c1.p - c2.p); ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d); ld dfr = c1.r * c1.r - rc * rc; if (abs(dfr) < eps) dfr = 0.0; else if (dfr < 0.0) return res; // no intersection ld rs = sqrt(dfr); Point diff = (c2.p - c1.p) / d; res.push_back(c1.p + diff * Point(rc, rs)); if (dfr != 0.0) res.push_back(c1.p + diff * Point(rc, -rs)); return res; } // 円と直線の交点 vector is_lc(Circle c, Line l) { vector res; ld d = dist_lp(l, c.p); if (d < c.r + eps) { ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d); //safety; Point nor = (l.a - l.b) / abs(l.a - l.b); res.push_back(proj(l, c.p) + len * nor); res.push_back(proj(l, c.p) - len * nor); } return res; } // 円と線分の距離 vector is_sc(Circle c, Line l) { vector v = is_lc(c, l), res; for (Point p : v) if (isis_sp(l, p)) res.push_back(p); return res; } // 円と点の接線 vector tangent_cp(Circle c, Point p) { vector ret; Point v = c.p - p; ld d = abs(v); ld l = sqrt(norm(v) - c.r * c.r); if (isnan(l)) { return ret; } Point v1 = v * Point(l / d, c.r / d); Point v2 = v * Point(l / d, -c.r / d); ret.push_back(Line(p, p + v1)); if (l < eps) return ret; ret.push_back(Line(p, p + v2)); return ret; } // 円と円の接線 vector tangent_cc(Circle c1, Circle c2) { vector ret; if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps) { Point center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r); ret = tangent_cp(c1, center); } if (abs(c1.r - c2.r) > eps) { Point out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r); vector nret = tangent_cp(c1, out); ret.insert(ret.end(), nret.begin(), nret.end()); } else { Point v = c2.p - c1.p; v /= abs(v); Point q1 = c1.p + v * Point(0, 1) * c1.r; Point q2 = c1.p + v * Point(0, -1) * c1.r; ret.push_back(Line(q1, q1 + v)); ret.push_back(Line(q2, q2 + v)); } return ret; } /* 多角形 */ typedef vector Polygon; // 面積 ld area(const Polygon &p) { ld res = 0; int n = (int)p.size(); for (int j = 0;j < n;j++) res += cross(p[j], p[(j + 1) % n]); return res / 2; } // 多角形の回転方向 bool is_counter_clockwise(const Polygon &poly) { ld angle = 0; int n = (int)poly.size(); for (int i = 0;i < n;i++) { Point a = poly[i], b = poly[(i + 1) % n], c = poly[(i + 2) % n]; angle += arg((c - b) / (b - a)); } return angle > eps; } // 凸性判定 bool isConvex(const Polygon &poly){ int n = (int)poly.size(); if(n < 3) return false; int s = -3; for(int i = 0; i < n;i++){ int r = ccw(poly[(i+n-1)%n],poly[i%n],poly[(i+1)%n]); if(r == 1 && s == -3) s = r; if(s*r == -1) return false; } return true; } // 点の内外判定 // 0 => out : 1 => on : 2 => in int is_in_polygon(const Polygon &poly, Point p) { ld angle = 0; int n = (int)poly.size(); for (int i = 0;i < n;i++) { Point a = poly[i], b = poly[(i + 1) % n]; if (isis_sp(Line(a, b), p)) return 1; angle += arg((b - p) / (a - p)); } return eq(angle, 0) ? 0 : 2; } // 凸包 : 凸多角形のある一辺上にある点を含まない Polygon convex_hull(vector ps) { int n = (int)ps.size(); if(n < 3) return ps; int k = 0; sort(ps.begin(), ps.end()); Polygon 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; } // 凸包 : 凸多角形のある一辺上にある点も含む Polygon convex_hull2(vector ps) { int n = (int)ps.size(); if (n < 3) return ps; sort(ps.begin(), ps.end()); Polygon u = { ps[0], ps[1] }, l = { ps[n - 1],ps[n - 2] }; for (int i = 2; i < n; i++) { for (int j = (int)u.size(); j >= 2 && ccw(u[j - 2], u[j - 1], ps[i]) >= 0;j--)u.pop_back(); u.push_back(ps[i]); } for (int i = n - 3;i >= 0;i--) { for (int j = (int)l.size(); j >= 2 && ccw(l[j - 2], l[j - 1], ps[i]) >= 0;j--)l.pop_back(); l.push_back(ps[i]); } reverse(l.begin(), l.end()); for (int i = (int)u.size() - 2; i >= 1; i--)l.push_back(u[i]); return l; } // 凸多角形の直径 pair convex_diameter(const Polygon& poly){ int n = (int)poly.size(); if(n == 2) return make_pair(pll(0,1),abs(poly[0]-poly[1])); int ii = 0, jj = 0; for(int i = 1;i < n;i++){ if(poly[i].imag() > poly[ii].imag())ii = i; if(poly[i].imag() < poly[jj].imag())jj = i; } pll resp = make_pair(-1,-1); ld resd = 0; int i, maxi,j,maxj; i = maxi = ii; j = maxj = jj; while(i != maxj || j != maxi){ ld cur = abs(poly[i] - poly[j]); if(resd + eps < cur){ resd = cur; resp = pll(i,j); } int di = (i+1)%n, dj = (j+1)%n; if(cross(poly[di]-poly[i],poly[dj]-poly[j]) < 0) i = di; else j = dj; } return make_pair(resp,resd); } // 凸カット Polygon convex_cut(const Polygon &ps, Line l) { int n = (int)ps.size(); Polygon Q; for (int i = 0;i < n;i++) { Point A = ps[i], B = ps[(i + 1) % n]; Line m = Line(A, B); if (ccw(l.a, l.b, A) != -1) Q.push_back(A); if (ccw(l.a, l.b, A) * ccw(l.a, l.b, B) < 0 && isis_ll(l, m)) Q.push_back(is_ll(l, m)); } return Q; } // 円と多角形の共通部分 double area_of_polygon_and_circle(const Polygon& poly, const Circle c) { int n = (int)poly.size(); ld r = 0; for (int i = n - 1, j = 0; j < n; i=j++) { Point v = abs(poly[j] - poly[i]) / (poly[j] - poly[i]); if (poly[j] == poly[i])continue; assert(poly[j] != poly[i]); Point a = (poly[i] - c.p)*v, b = (poly[j] - c.p)*v; ld d = norm(c.r) - norm(a.imag()); if (abs(a.imag()) < eps) continue; if (d < 0)d = 0; d = sqrt(d); double l, m; r += norm(c.r)*((l = atan2(b.imag(), min(b.real(), -d)) - atan2(a.imag(), min(a.real(), -d))) + (m = atan2(b.imag(), max(b.real(), d)) - atan2(a.imag(), max(a.real(), d)))) + a.imag()*(min(d, max(a.real(), -d)) - max(-d, min(b.real(), d))); assert(-pi < l && -pi < m && l < pi && m < pi); } return r / 2; } // 凸多角形と凸多角形のAND O(nm)ぐらい そのうち線形時間のやつも書く Polygon convex_polygon_and_convex_polygon(const Polygon& in1,const Polygon& in2){ Polygon ret; if(in1.size()==0 || in2.size()==0) return ret; Polygon ps1 = in1,ps2 = in2; // ポリゴンを凸+並びを揃える(反時計回り) // この2点が保証されているのであればコメントアウト可 ps1 = convex_hull(in1);ps2 = convex_hull(in2); int n = (int)ps1.size(),m = (int)ps2.size(); // p2に含まれるp1の点、p1に含まれるp2の点をそれぞれ探索する vector inpoint_of_ps1(n),inpoint_of_ps2(m); for(int i = 0; i < n;i++) if(is_in_polygon(ps2, ps1[i])){ ret.push_back(ps1[i]); inpoint_of_ps1[i] = 1; } for(int i = 0; i < m;i++) if(is_in_polygon(ps1, ps2[i])){ ret.push_back(ps2[i]); inpoint_of_ps2[i] = 1; } if(n>=2 && m >= 2){ // p1とp2が交わる点を探索する for(int i = 0; i < n;i++){ Line l1(ps1[i],ps1[(i+1)%n]); for(int j = 0; j < m;j++){ Line l2(ps2[j],ps2[(j+1)%m]); if(dist_ss(l1,l2) < eps) ret.push_back(is_ll(l1,l2)); } } } // ポリゴンを凸+並びを揃える(反時計回り) ret = convex_hull(ret); return ret; } /* gcd : 最大公約数 lcm : 最小公倍数 */ inline ll gcd(ll a, ll b) { return b ? gcd(b, a%b) : a; } inline ll lcm(ll a, ll b) { return a / gcd(a, b)*b; } ll solve(){ ll res = 0; Polygon ps1,ps2; ld x1,y1,x2,y2,d; cin >> x1 >> y1 >> x2 >> y2 >> d; ps1.push_back(Point(x1,y1)); ps1.push_back(Point(x1,y2)); ps1.push_back(Point(x2,y1)); ps1.push_back(Point(x2,y2)); if(d==0){ ps2.push_back(Point(0,0)); }else{ ps2.push_back(Point(d,0)); ps2.push_back(Point(0,d)); ps2.push_back(Point(-d,0)); ps2.push_back(Point(0,-d)); } auto intersect_ps = convex_polygon_and_convex_polygon(ps1, ps2); ld intersect_area = area(intersect_ps); if(intersect_ps.empty()) return res; ll on_the_point = 0; int sz = (int)intersect_ps.size(); for(int i = 0; i < sz;i++){ Point diffvec = intersect_ps[i] - intersect_ps[(i+1)%sz]; ll x = abs(diffvec.real()),y = abs(diffvec.imag()); on_the_point += gcd(x,y); } res += on_the_point; res += round(intersect_area-on_the_point/2.0 + 1); return res; } int main(void) { cin.tie(0); ios_base::sync_with_stdio(false); cout << solve() << endl; return 0; }