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.
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.
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.
样例
4
3 4 8 9
1
4 1 2 4 3
5
2 2 2 2 2
Impossible
12
2 3 4 5 6 7 8 9 10 11 12 13
1
12 1 2 3 6 5 12 9 8 7 10 11 4
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
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
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