F. Circular Xor Reversaltime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou have an array a_0, a_1, \ldots, a_{n-1} of length n. Initially, a_i = 2^i for all 0 \le i \lt n. Note that array a is zero-indexed. You want to reverse this array (that is, make a_i equal to 2^{n-1-i} for all 0 \le i \lt n). To do this, you can perform the following operation no more than 250\,000 times:  Select an integer i (0 \le i \lt n) and replace a_i by a_i \oplus a_{(i+1)\bmod n}. Here, \oplus denotes the bitwise XOR operation.Your task is to find any sequence of operations that will result in the array a being reversed. It can be shown that under the given constraints, a solution always exists.InputThe first line contains a single integer n (2 \le n \le 400) — the length of the array a.OutputOn the first line print one integer k (0 \le k \le 250\,000) — the number of operations performed.On the second line print k integers i_1,i_2,\ldots,i_k (0 \le i_j \lt n). Here, i_j should be the integer selected on the j-th operation.Note that you don't need to minimize the number of operations.ExamplesInput
2
Output
3
1 0 1
Input
3
Output
9
1 0 1 0 2 1 0 1 0 NoteIn the notes, the elements on which the operations are performed are colored red.In the first test case, array a will change in the following way: [1,\color{red}{2}] \rightarrow [\color{red}{1},3] \rightarrow [2,\color{red}{3}] \rightarrow [2,1].In the second test case, array a will change in the following way:[1,\color{red}{2},4] \rightarrow [\color{red}{1},6,4] \rightarrow [7,\color{red}{6},4] \rightarrow [\color{red}{7},2,4] \rightarrow [5,2,\color{red}{4}] \rightarrow [5,\color{red}{2},1] \rightarrow [\color{red}{5},3,1] \rightarrow [6,\color{red}{3},1] \rightarrow [\color{red}{6},2,1] \rightarrow [4,2,1].
2

3 1 0 1 
['bitmasks', 'constructive algorithms', '*3000']