A. Square Root Partitioning

Codeforces

IDCF10235A

Time3000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

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. The first line of input contains a single integer $n$ ($2 <= n <= 36$). Second line of input contains $n$ integers $a_1, a_2, \\dots, a_n$ ($1 <= a_i <= 10^(10^5)$). Output a single integer: the answer to the problem. ## Input The first line of input contains a single integer $n$ ($2 <= n <= 36$).Second line of input contains $n$ integers $a_1, a_2, \\dots, a_n$ ($1 <= a_i <= 10^(10^5)$). ## Output Output a single integer: the answer to the problem. [samples]

**Definitions** Let $ n \in \mathbb{Z} $ with $ 2 \leq n \leq 36 $. Let $ 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 $. **Constraints** None beyond those specified in definitions. **Objective** Count the number of sign vectors $ s = (s_1, s_2, \dots, s_n) \in \{+1, -1\}^n $ such that: $$ \sum_{i=1}^n s_i \sqrt{a_i} = 0 $$

API Response (JSON)

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