{"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 Haoren is very good at solving mathematic problems. Today he is working a problem like this: \u003cbr\u003e Find three positive integers X, Y and Z (X \u0026lt; Y, Z \u0026gt; 1) that holds\u003cbr\u003e X^Z + Y^Z + XYZ \u003d K\u003cbr\u003e where K is another given integer.\u003cbr\u003e Here the operator “^” means power, e.g., 2^3 \u003d 2 * 2 * 2.\u003cbr\u003e Finding a solution is quite easy to Haoren. Now he wants to challenge more: What’s the total number of different solutions?\u003cbr\u003e Surprisingly, he is unable to solve this one. It seems that it’s really a very hard mathematic problem.\u003cbr\u003e Now, it’s your turn.\u003cbr\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":" There are multiple test cases. \u003cbr\u003e For each case, there is only one integer K (0 \u0026lt; K \u0026lt; 2^31) in a line.\u003cbr\u003e K \u003d 0 implies the end of input.\u003cbr\u003e \u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":" Output the total number of solutions in a line for each test case.\u003cbr\u003e"}},{"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\u003e9\r\n53\r\n6\r\n0\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\r\n1\r\n0\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\u003e9 \u003d 1^2 + 2^2 + 1 * 2 * 2\u003cbr\u003e53 \u003d 2^3 + 3^3 + 2 * 3 * 3\u003cbr\u003e"}}]}