{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eYou are given a \u003cspan class\u003d\"tex-font-style-bf\"\u003eprime\u003c/span\u003e number $$$p$$$, $$$n$$$ integers $$$a_1, a_2, \\ldots, a_n$$$, and an integer $$$k$$$. \u003c/p\u003e\u003cp\u003eFind the number of pairs of indexes $$$(i, j)$$$ ($$$1 \\le i \u0026lt; j \\le n$$$) for which $$$(a_i + a_j)(a_i^2 + a_j^2) \\equiv k \\bmod p$$$.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains integers $$$n, p, k$$$ ($$$2 \\le n \\le 3 \\cdot 10^5$$$, $$$2 \\le p \\le 10^9$$$, $$$0 \\le k \\le p-1$$$). $$$p$$$ is guaranteed to be prime.\u003c/p\u003e\u003cp\u003eThe second line contains $$$n$$$ integers $$$a_1, a_2, \\ldots, a_n$$$ ($$$0 \\le a_i \\le p-1$$$). It is guaranteed that all elements are different.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eOutput a single integer\u0026nbsp;— answer to the problem.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3 3 0\n0 1 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e6 7 2\n1 2 3 4 5 6\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eIn the first example:\u003c/p\u003e\u003cp\u003e$$$(0+1)(0^2 + 1^2) \u003d 1 \\equiv 1 \\bmod 3$$$.\u003c/p\u003e\u003cp\u003e$$$(0+2)(0^2 + 2^2) \u003d 8 \\equiv 2 \\bmod 3$$$.\u003c/p\u003e\u003cp\u003e$$$(1+2)(1^2 + 2^2) \u003d 15 \\equiv 0 \\bmod 3$$$.\u003c/p\u003e\u003cp\u003eSo only $$$1$$$ pair satisfies the condition.\u003c/p\u003e\u003cp\u003eIn the second example, there are $$$3$$$ such pairs: $$$(1, 5)$$$, $$$(2, 3)$$$, $$$(4, 6)$$$.\u003c/p\u003e"}}]}