Carmichael Numbers

Again the task is quite simple. You just need to output as many carmichael numbers as you can.

Major Constraints

You can use only 4096 bytes to write the code.

Input Specification

No Input.

Output Specification

If you want to output N Carmichael Numbers then, the output will be - The first line will contain the number N. Then for each carmichael number you output two lines, first line will contain the number itself and in the second line output the number of prime divisors of the carmichale number followed by the actual prime divisors separated by space. Prime divisors should be output in sorted order. Also the carmichael numbers should be output in sorted order. See Sample I/O for more details.
UPDATE : Only Carmichael Numbers less than 10^(5000) will be considered. Bigger number will be judged to wrong answer. We need this constraint to make our checker work in time. Sorry for inconvenience.

Scoring Scheme

Score = N*5 + (Sum Of Number of Digits of each Carmichael number given as Output).
The scoring will be relative to S.

Sample Input

No Input.

Sample Output

2
561
3 3 11 17
1105
3 5 13 17

In this case the score obtained will be 2*5 + (3 + 4) = 17

Constraints

Time limit: 7s   Memory Limit: 32MB

Clarification

Leading zeroes are not allowed.