E. Fox And Dinnertime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputFox Ciel is participating in a party in Prime Kingdom. There are n foxes there (include Fox Ciel). The i-th fox is ai years old.They will have dinner around some round tables. You want to distribute foxes such that:  Each fox is sitting at some table.  Each table has at least 3 foxes sitting around it.  The sum of ages of any two adjacent foxes around each table should be a prime number. If k foxes f1, f2, ..., fk are sitting around table in clockwise order, then for 1 ≤ i ≤ k - 1: fi and fi + 1 are adjacent, and f1 and fk are also adjacent.If it is possible to distribute the foxes in the desired manner, find out a way to do that.InputThe first line contains single integer n (3 ≤ n ≤ 200): the number of foxes in this party. The second line contains n integers ai (2 ≤ ai ≤ 104).OutputIf it is impossible to do this, output "Impossible".Otherwise, in the first line output an integer m (): the number of tables.Then output m lines, each line should start with an integer k -=– the number of foxes around that table, and then k numbers — indices of fox sitting around that table in clockwise order.If there are several possible arrangements, output any of them.ExamplesInput43 4 8 9Output14 1 2 4 3Input52 2 2 2 2OutputImpossibleInput122 3 4 5 6 7 8 9 10 11 12 13Output112 1 2 3 6 5 12 9 8 7 10 11 4Input242 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25Output36 1 2 3 6 5 410 7 8 9 12 15 14 13 16 11 108 17 18 23 22 19 20 21 24NoteIn 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.
Input43 4 8 9
Output14 1 2 4 3
['flows', '*2300']