B'Integer factorisation is hard. The RSA Factoring Challenge offered $100 ,000 for factoring RSA- 1024 , a 1024 -bit long product of two prime numbers. To this date, nobody was able to claim the prize. We want you to factorise a 1024 -bit number. Since your programming language of choice might not offer facilities for handling large integers, we will provide you with a very simple calculator. To use this calculator, you can print queries on the standard output and retrieve the results from the standard input. The operations are as follows: Find the factorisation of n that is a product of between 2 and 10 distinct prime numbers, all of form 4x + 3 for some integer x . Because of technical issues, we restrict number of requests to 100 . The only line contains a single integer n ( 21 <= q n <= q 2^{1024} ). It is guaranteed that n is a product of between 2 and 10 distinct prime numbers, all of form 4x + 3 for some integer x . You can print as many queries as you wish, adhering to the time limit (see the Interaction section for more details). When you think you know the answer, output a single line of form ! k p_1 p_2 ... p_k, where k is the number of prime factors of n , and p_i are the distinct prime factors. You may print the factors in any order. Hacks input For hacks, use the following format:. The first should contain k ( 2 <= q k <= q 10 ) -- the number of prime factors of n . The second should contain k space separated integers p_1, p_2, ... , p_k ( 21 <= q n <= q 2^{1024} ) -- the prime factors of n . All prime factors have to be of form 4x + 3 for some integer x . They all have to be distinct. After printing a query do not forget to output end of line and flush the output. Otherwise you will get Idleness limit exceeded. To do this, use: The number of queries is not limited. However, you'...