Edward is learning about prime numbers in math class today. Having just learnt what arrays are the day before, he decided to invent what he now calls a prime array. Specifically, he calls an array prime if the greatest common divisor of all its elements is ~1~. For example, ~[4, 5, 2]~ and ~~ are prime but ~[3, 9, 6]~ and ~~ are not. Having caught him dozing off in class, Mr. Brown challenges Edward to find an array that has exactly ~K~ prime non-empty subarrays. Since Mr. Brown is not looking forward to spending more than a few hours reading over the array, he specifies that the array must contain no more than ~100~ elements, and that all the elements of the array must be integers in the range ~[1, 10^9]~. Now on the spot, Edward is asking you to help him solve this problem. Please help him find an array satisfying Mr. Brown's requirements.
For this problem, you MUST pass the sample case in order to receive points.
~0 \le K \le 5 \times 10^3~
It can be proven that an array satisfying the requirements always exists under the given constraints.
The first and only line of input contains an integer ~K~, as described in the problem statement.
First, output one line containing ~N~ ~(1 \le N \le 100)~, the length of the array ~A~ you have found.
Then output ~N~ space separated integers ~A_i~ ~(1 \le A_i \le 10^9)~, representing the elements of the array ~A~.
5 5 8 2 6 3
The prime subarrays are: ~[5, 8], [5, 8, 2], [2, 6, 3], [5, 8, 2, 6], [8, 2, 6, 3], [5, 8, 2, 6, 3]~.