CF510E Fox And Dinner

Fox Ciel is participating in a party in Prime Kingdom. There are $ n $ foxes there (include Fox Ciel). The i-th fox is $ a_{i} $ years old. They will have dinner around some round tables. You want to distribute foxes such that: 1. Each fox is sitting at some table. 2. Each table has at least 3 foxes sitting around it. 3. The sum of ages of any two adjacent foxes around each table should be a prime number. If $ k $ foxes $ f_{1} $ , $ f_{2} $ , ..., $ f_{k} $ are sitting around table in clockwise order, then for $ 1

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In example 1, they can sit around one table, their ages are: 3-8-9-4, adjacent sums are: 11, 17, 13 and 7, all those integers are primes. In example 2, it is not possible: the sum of 2+2 = 4 is not a prime number.