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: 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 f 1 , f 2 , ..., f k are sitting around table in clockwise order, then for 1 ≤ i ≤ k - 1: f i and f i + 1 are adjacent, and f 1 and f k are also adjacent. If it is possible to distribute the foxes in the desired manner, find out a way to do that.
输入描述:
The 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).
输出描述:
If 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.
示例1
输入
4<br />3 4 8 9<br />5<br />2 2 2 2 2<br />12<br />2 3 4 5 6 7 8 9 10 11 12 13<br />24<br />2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25<br />
输出
1<br />4 1 2 4 3<br />Impossible<br />1<br />12 1 2 3 6 5 12 9 8 7 10 11 4<br />3<br />6 1 2 3 6 5 4<br />10 7 8 9 12 15 14 13 16 11 10<br />8 17 18 23 22 19 20 21 24<br />
备注:
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.
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