#include using namespace std; using ld = long double; using vec = complex; vec find_center(ld p, array ps){ ld ip = 1/p; auto dist = [&](int i, vec v){ v -= ps[i]; ld sum = powl(abs(v.real()),p) + powl(abs(v.imag()),p); return powl(sum,ip); }; vec memo_vec; auto which = [&](vec v){ ld dmin = 1e30; int id = -1; for (int i = 0; i < 3; i++){ ld d = dist(i,v); if (dmin > d){ dmin = d; id = i; } } memo_vec = v; assert(id != -1); return id; }; auto which_bound = [&](vec dir){ dir /= vec(abs(dir)); if (which(ps[0]+vec(1e12)*dir) == 0){ return 0; } ld le = 0, ri = 1e12; int test = 100; int pre_w = -1; while (test--){ ld md = (le + ri) / 2; int cur_w = which(ps[0]+vec(md)*dir); if (cur_w == 0){ le = md; } else { pre_w = cur_w; ri = md; } } assert(pre_w != -1); return pre_w; }; vec rev1 = ps[0] + ps[0]-ps[1]; vec rev2 = ps[0] + ps[0]-ps[2]; vec dir0 = (rev1 + rev2) * vec(0.5); vec dir12 = [&]{ vec dir1 = ps[1] - ps[0]; if (which_bound(dir1) != 0){ return dir1; } vec dir2 = ps[2] - ps[0]; if (which_bound(dir2) != 0){ return dir2; } abort(); }(); // cout << dir0 << ' ' << dir12 << endl; int w12 = which(dir12); // cout << w12 << endl; vec dir21(100,100); auto from_to = [&](vec dir1, int w1, vec dir2, int w2){ ld arg1 = arg(dir1); ld arg2 = arg(dir2); if (arg2 < arg1){ arg2 += numbers::pi *2; } int test = 100; while (test--){ ld arg12 = (arg1 + arg2) / 2; vec dirt = vec(cosl(arg12),sinl(arg12)); int w = which_bound(dirt); if (w == w1){ arg1 = arg12; } else if (w == w2){ arg2 = arg12; } else { dir21 = dirt; return ; } } }; from_to(dir0,0,dir12,w12); from_to(dir12,w12,dir0,0); assert(abs(dir21) < 100); // cout << dir21 << endl; // cout << which_bound(dir21) << endl; vec memo_ans(1e7,1e7); auto find12 = [&](vec dir1, int w1, vec dir2, int w2){ ld arg1 = arg(dir1); ld arg2 = arg(dir2); if (arg2 < arg1){ arg2 += std::numbers::pi *2; } // cout << arg1 << ' ' << arg2 << endl; int test = 100; while (test--){ ld arg12 = (arg1 + arg2) / 2; vec dirt = vec(cosl(arg12),sinl(arg12)); int w = which_bound(dirt); if (w == 0){ return ; } if (w == w1){ arg1 = arg12; } else { arg2 = arg12; } } which_bound(vec(cosl(arg1),sinl(arg1))); memo_ans = memo_vec; }; find12(dir12,w12,dir21,3-w12); find12(dir21,3-w12,dir12,w12); assert(abs(memo_ans) < 1e7); return memo_ans; } int main(){ cout << fixed << setprecision(20); ld p; cin >> p; ld ip = 1/p; array ps; for (int i = 0; i < 3; i++){ ld x, y; cin >> x >> y; ps[i] = vec(x,y); } auto dist = [&](int i, vec v){ v -= ps[i]; ld sum = powl(abs(v.real()),p) + powl(abs(v.imag()),p); return powl(sum,ip); }; auto score = [&](vec v){ ld mi = 1e30, ma = -1e30; for (int i = 0; i < 3; i++){ ld d = dist(i,v); mi = min(mi,d); ma = max(ma,d); } return ma - mi; }; ld minscore = 1e30; vec ans(0,0); for (int i = 0; i < 3; i++){ vec cur = find_center(p,ps); ld curscore = score(cur); if (minscore > curscore){ minscore = curscore; ans = cur; } swap(ps[0],ps[1]); swap(ps[1],ps[2]); } cout << ans.real() << ' ' << ans.imag() << endl; // cout << minscore << endl; }