As we know, Rikka is poor at math. Yuta is worrying about this situation, so he asks rikka to have some practice on codeforces. Then she opens the problem B:
Given an integer $K$, she needs to come up with an sequence of integers $A$ satisfying that the number of different continuous subsequence of $A$ is equal to $k$.
Two continuous subsequences $a,\ b$ are different if and only if one of the following conditions is satisfied:
1. The length of $a$ is not equal to the length of $b$.
2. There is at least one $t$ that $a_{t} \neq b_{t}$, where $a_{t}$ means the $t$-th element of $a$ and $b_{t}$ means the $t$-th element of $b$.
Unfortunately, it is too difficult for Rikka. Can you help her?
There are at most 20 testcases，each testcase only contains a single integer $K\ (1 \leq K \leq 10^9)$
For each testcase print two lines.
The first line contains one integers $n\ (n \leq \min(K,10^5))$.
The second line contains $n$ space-separated integer $A_i\ (1 \leq A_i \leq n)$ - the sequence you find.