{"trustable":true,"prependHtml":"\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003e\u0026nbsp;\u0026nbsp;Pizzahat has released a new pizza with triangular shaped pieces. This pizza is composed of some equal-sized equilateral triangle. Moreover, all the triangles are connected. Also, if two triangles are directly connected, they must share a common edge.\u003cbr\u003e\u0026nbsp;\u0026nbsp;How many different shapes of this kind of N-pieces pizza are there? Two patterns are considered as same if they can completely overlap after rotation and shifting (note that flipping is not included).\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u0026nbsp;\u0026nbsp;There are multiple test cases. The first line of input contains a single integer denoting the number of test cases.\u003cbr\u003e\u0026nbsp;\u0026nbsp;For each test case, there is only one line with only one integer N denoting the number of pieces that can be used. (1 \u0026lt;\u003d N \u0026lt;\u003d 16)"}},{"title":"Output","value":{"format":"HTML","content":"\u0026nbsp;\u0026nbsp;For each test case, output a single integer denoting the number of possible different shapes of the pizza."}},{"title":"Sample","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\u003e3\r\n2\r\n4\r\n10\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase #1: 1\r\nCase #2: 4\r\nCase #3: 866\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Hint","value":{"format":"HTML","content":"\u003cbr\u003eCase2:\u003cbr\u003e\u003cimg style\u003d\"max-width:100%;\" src\u003d\"CDN_BASE_URL/77ca41ef50122d26aeb16e943cd37c1b?v\u003d1726090828\"\u003e\u003cbr\u003e"}}]}