{"problem":{"name":"Pyramid","description":{"content":"In the Ancient Kingdom of Snuke, there was a pyramid to strengthen the authority of Takahashi, the president of AtCoder Inc.   The pyramid had _center coordinates_ $(C_X, C_Y)$ and _height_ $H$. The a","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc112_c"},"statements":[{"statement_type":"Markdown","content":"In the Ancient Kingdom of Snuke, there was a pyramid to strengthen the authority of Takahashi, the president of AtCoder Inc.  \nThe pyramid had _center coordinates_ $(C_X, C_Y)$ and _height_ $H$. The altitude of coordinates $(X, Y)$ is $max(H - |X - C_X| - |Y - C_Y|, 0)$.\nAoki, an explorer, conducted a survey to identify the center coordinates and height of this pyramid. As a result, he obtained the following information:\n\n*   $C_X, C_Y$ was integers between $0$ and $100$ (inclusive), and $H$ was an integer not less than $1$.\n*   Additionally, he obtained $N$ pieces of information. The $i$\\-th of them is: \"the altitude of point $(x_i, y_i)$ is $h_i$.\"\n\nThis was enough to identify the center coordinates and the height of the pyramid. Find these values with the clues above.\n\n## Constraints\n\n*   $N$ is an integer between $1$ and $100$ (inclusive).\n*   $x_i$ and $y_i$ are integers between $0$ and $100$ (inclusive).\n*   $h_i$ is an integer between $0$ and $10^9$ (inclusive).\n*   The $N$ coordinates $(x_1, y_1), (x_2, y_2), (x_3, y_3), ..., (x_N, y_N)$ are all different.\n*   The center coordinates and the height of the pyramid can be uniquely identified.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$x_1$ $y_1$ $h_1$\n$x_2$ $y_2$ $h_2$\n$x_3$ $y_3$ $h_3$\n$:$\n$x_N$ $y_N$ $h_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc112_c","tags":[],"sample_group":[["4\n2 3 5\n2 1 5\n1 2 5\n3 2 5","2 2 6\n\nIn this case, the center coordinates and the height can be identified as $(2, 2)$ and $6$."],["2\n0 0 100\n1 1 98","0 0 100\n\nIn this case, the center coordinates and the height can be identified as $(0, 0)$ and $100$.  \nNote that $C_X$ and $C_Y$ are known to be integers between $0$ and $100$."],["3\n99 1 191\n100 1 192\n99 0 192","100 0 193\n\nIn this case, the center coordinates and the height can be identified as $(100, 0)$ and $193$."]],"created_at":"2026-03-03 11:01:14"}}