How horrible! The empire of galactic chickens tries to conquer a beautiful city "Z", they have built a huge incubator that produces millions of chicken soldiers a day, and fenced it around. The huge incubator looks like a polygon on the plane *Oxy* with *n* vertices. Naturally, DravDe can't keep still, he wants to destroy the chicken empire. For sure, he will start with the incubator.

DravDe is strictly outside the incubator's territory in point *A*(*x*<sub class="lower-index">*a*</sub>, *y*<sub class="lower-index">*a*</sub>), and wants to get inside and kill all the chickens working there. But it takes a lot of doing! The problem is that recently DravDe went roller skating and has broken both his legs. He will get to the incubator's territory in his jet airplane LEVAP-41.

LEVAP-41 flies at speed *V*(*x*<sub class="lower-index">*v*</sub>, *y*<sub class="lower-index">*v*</sub>, *z*<sub class="lower-index">*v*</sub>). DravDe can get on the plane in point *A*, fly for some time, and then air drop himself. DravDe is very heavy, that's why he falls vertically at speed *F*<sub class="lower-index">*down*</sub>, but in each point of his free fall DravDe can open his parachute, and from that moment he starts to fall at the wind speed *U*(*x*<sub class="lower-index">*u*</sub>, *y*<sub class="lower-index">*u*</sub>, *z*<sub class="lower-index">*u*</sub>) until he lands. Unfortunately, DravDe isn't good at mathematics. Would you help poor world's saviour find such an air dropping plan, that allows him to land on the incubator's territory? If the answer is not unique, DravDe wants to find the plan with the minimum time of his flight on the plane. If the answers are still multiple, he wants to find the one with the minimum time of his free fall before opening his parachute
The first line contains the number *n* (3 ≤ *n* ≤ 10<sup class="upper-index">4</sup>) — the amount of vertices of the fence. Then there follow *n* lines containing the coordinates of these vertices (two integer numbers *x*<sub class="lower-index">*i*</sub>, *y*<sub class="lower-index">*i*</sub>) in clockwise or counter-clockwise order. It's guaranteed, that the fence does not contain self-intersections.

The following four lines contain coordinates of point *A*(*x*<sub class="lower-index">*a*</sub>, *y*<sub class="lower-index">*a*</sub>), speeds *V*(*x*<sub class="lower-index">*v*</sub>, *y*<sub class="lower-index">*v*</sub>, *z*<sub class="lower-index">*v*</sub>), *F*<sub class="lower-index">*down*</sub> and speed *U*(*x*<sub class="lower-index">*u*</sub>, *y*<sub class="lower-index">*u*</sub>, *z*<sub class="lower-index">*u*</sub>). All the input numbers are integer. All the coordinates don't exceed 10<sup class="upper-index">4</sup> in absolute value. It's guaranteed, that *z*<sub class="lower-index">*v*</sub> &gt; 0 and *F*<sub class="lower-index">*down*</sub>, *z*<sub class="lower-index">*u*</sub> &lt; 0, and point *A* is strictly outside the incubator's territory.
print("_RANDOM_GUESS_1692563152.4707477")# 1692563152.4707632