{"problem":{"name":"A. Square Root Partitioning","description":{"content":"Consider the following expression: $$\\sqrt{a_1} \\pm \\sqrt{a_2} \\pm \\dots \\pm \\sqrt{a_n} = 0\\text{.}$$ Calculate the number of ways to replace each $plus.minus$ with $+$ or $-$ so that it holds true. ","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF10235A"},"statements":[{"statement_type":"Markdown","content":"Consider the following expression: $$\\sqrt{a_1} \\pm \\sqrt{a_2} \\pm \\dots \\pm \\sqrt{a_n} = 0\\text{.}$$ Calculate the number of ways to replace each $plus.minus$ with $+$ or $-$ so that it holds true.\n\nThe first line of input contains a single integer $n$ ($2 <= n <= 36$).\n\nSecond line of input contains $n$ integers $a_1, a_2, \\\\dots, a_n$ ($1 <= a_i <= 10^(10^5)$). \n\nOutput a single integer: the answer to the problem.\n\n## Input\n\nThe first line of input contains a single integer $n$ ($2 <= n <= 36$).Second line of input contains $n$ integers $a_1, a_2, \\\\dots, a_n$ ($1 <= a_i <= 10^(10^5)$). \n\n## Output\n\nOutput a single integer: the answer to the problem.\n\n[samples]","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"**Definitions**  \nLet $ n \\in \\mathbb{Z} $ with $ 2 \\leq n \\leq 36 $.  \nLet $ A = (a_1, a_2, \\dots, a_n) $ be a sequence of positive integers, where $ 1 \\leq a_i \\leq 10^{10^5} $ for all $ i $.\n\n**Constraints**  \nNone beyond those specified in definitions.\n\n**Objective**  \nCount the number of sign vectors $ s = (s_1, s_2, \\dots, s_n) \\in \\{+1, -1\\}^n $ such that:  \n$$\n\\sum_{i=1}^n s_i \\sqrt{a_i} = 0\n$$","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF10235A","tags":[],"sample_group":[],"created_at":"2026-03-03 11:00:39"}}