{"problem":{"name":"Dowsing Rod","description":{"content":"A psychic, Takahashi, has discovered a treasure map. According to the map, there are $50$ buried treasures under the ground of an uninhabited island. The island has a circular shape with a radius of $","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"future_contest_2023_final_a"},"statements":[{"statement_type":"Markdown","content":"A psychic, Takahashi, has discovered a treasure map. According to the map, there are $50$ buried treasures under the ground of an uninhabited island. The island has a circular shape with a radius of $R=10^9$. Unfortunately, the map does not indicate the locations of the buried treasures. Since it is impossible to dig up all the ground, he decided to use his psychic powers to search for the treasures in the following way.\n\n1. Choose a desired location and stand a wooden rod.\n2. If there is a treasure within a radius of $D=10^6$ from the chosen location, the rod will remain standing, and he can find the treasure by digging all the area within the radius $D$.\n3. If there are no treasures within a radius of $D$ from the chosen location, the rod will fall in a certain direction according to the rule described below, providing a clue to the location of the treasures.\n\nBy repeating this process up to $1000$ times, find as many treasures as possible, as quickly as possible.\n\n#### The law of the falling direction of the rod\n\nLet $q=(qx, qy)$ be the coordinates at which the rod stands, then the falling direction $\\theta (0\\leq \\theta<2\\pi)$ is calculated as follows, using a constant $\\sigma$ given as an input.\n\n1. Among the treasures that have not yet been dug up, one is chosen with probability proportional to the inverse of the squared Euclidean distance to $q$.\n2. Let $p=(px,py)$ be the coordinates of the chosen treasure, and calculate the direction $\\hat{\\theta}=\\mathrm{atan2}(py-qy,px-qx)$ of $p-q$.\n3. Sample a value from Gaussian distribution with mean $\\hat{\\theta}$ and standard deviation $\\sigma$ and let $\\theta$ be its remainder divided by $2\\pi$.\n\n## Input And Output\n\nFirst, the standard deviation $\\sigma$ is given in a single line from Standard Input. $\\sigma$ is a multiple of $0.001$ and satisfies $0.001\\leq \\sigma\\leq 0.100$.\nAfter reading the input, repeat the following process up to $1000$ times. In the $k$\\-th process, first choose the location $(qx_k, qy_k)$ to stand the rod, and output a single line to Standard Output in the following format.\n\n$qx_k$ $qy_k$\n\n$qx_k$ and $qy_k$ must be integers satisfying $qx_k^2+qy_k^2\\leq R^2$. If you specify a point outside the range, you will get WA. The output must be followed by a new line, and you have to flush Standard Output. Otherwise, the submission might be judged as TLE.\nThen, the information about what happened to the rod is given in a single line from Standard Input as follows.\nIf the rod falls in the direction of $\\theta_k$:\n\n$0$ $\\theta_k$\n\n$\\theta_k$ is between $0$ and $2\\pi$ and is given rounded to $10$ decimal places.\nIf the rod remains standing and you find a treasure at the coordinates $(x_k,y_k)$:\n\n$r_k$ $x_k$ $y_k$\n\n$r_k$ is `2` if the found treasure is the last one, and `1` otherwise. The distance between different treasures is guaranteed to be greater than $2D$, so you will not find more than one treasure simultaneously. When you have found all the treasures, you must immediately terminate the program. Otherwise, any subsequent queries will not return a response so the submission might be judged as TLE or RE.\n\n#### Example\n\n$k$\n\nOutput\n\nInput\n\n0\n\n0.051\n\n1\n\n\\-449800796 341903569\n\n0 4.2119508044\n\n2\n\n\\-302629026 250885846\n\n0 4.7012310463\n\n3\n\n\\-132900000 -988000000\n\n1 -132899921 -988157302\n\n$\\vdots$\n\n## Input Generation\n\nLet $\\mathrm{rand}(L,U)$ be a function that generates a uniform random integer between $L$ and $U$, inclusive. $\\sigma$ is generated by $0.001\\times \\mathrm{rand}(1,100)$. The coordinates $p_0\\cdots,p_{49}$ of $50$ buried treasures are generated as follows.\n\n1. Generate the coordinates $p_i=(px_i,py_i)$ of the $i$\\-th buried treasure uniformly at random among integers satisfying $px_i^2+py_i^2\\leq R^2$.\n2. While there is an already generated $p_j$ ($j