Rating changes for last rounds are temporarily rolled back. They will be returned soon.
×

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
E. Fox And Dinner

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputFox 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.

Input

The first line contains single integer *n* (3 ≤ *n* ≤ 200): the number of foxes in this party.

The second line contains *n* integers *a*_{i} (2 ≤ *a*_{i} ≤ 10^{4}).

Output

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.

Examples

Input

4

3 4 8 9

Output

1

4 1 2 4 3

Input

5

2 2 2 2 2

Output

Impossible

Input

12

2 3 4 5 6 7 8 9 10 11 12 13

Output

1

12 1 2 3 6 5 12 9 8 7 10 11 4

Input

24

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Output

3

6 1 2 3 6 5 4

10 7 8 9 12 15 14 13 16 11 10

8 17 18 23 22 19 20 21 24

Note

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.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/25/2022 15:16:23 (i2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|