{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cbr\u003eYou\u0027re playing a new game at the shooting range. First, a target is placed on a square board. The target itself is a convex polygon strictly inside the board.\u003cbr\u003eThen, you\u0027re allowed to shoot twice. In case at least one of your shots gets inside the target, you win. Moreover, if the segment connecting the points of your shots intersects the target, you still win. If none of the above holds, you lose.\u003cbr\u003eAssuming your aiming is very bad (i.e., the points of your shots are independently uniformly distributed all over the board), compute the probability of you winning.\u003cbr\u003e\u003cdiv align\u003d\"left\" style\u003d\"margin-top: 1.0em;\"\u003e\u003cb\u003eInput\u003c/b\u003e\u003c/div\u003eThe first line of input contains an integer \u003ci\u003eN\u003c/i\u003e, 3 ≤ \u003ci\u003eN\u003c/i\u003e ≤ 8,\u0026nbsp;— the number of vertices of the target. The next \u003ci\u003eN\u003c/i\u003e lines contain two integers each, \u003ci\u003ex\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e and \u003ci\u003ey\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, 1 ≤ \u003ci\u003ex\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 99, decribing the coordinates of the vertices of the target (a convex polygon) in the counter-clockwise direction. No three vertices of the target lie on the same line. The coordinate system is chosen so that the corners of the board have coordinates (0, 0), (0, 100), (100, 0) and (100, 100).\u003cbr\u003e\u003cdiv align\u003d\"left\" style\u003d\"margin-top: 1.0em;\"\u003e\u003cb\u003eOutput\u003c/b\u003e\u003c/div\u003eOutput the required probability. Your solution will be accepted if it is within 10\u003csup\u003e-7\u003c/sup\u003e of the correct one.\u003cbr\u003e"}},{"title":"Sample 1","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e4\n25 25\n75 25\n75 75\n25 75\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0.7328341830\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}