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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≠b_t, where at means the t-th element of a and bt 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≤K≤10⁹)

For each testcase print two lines.

The first line contains one integers n (n≤min(K,10⁵⁾).

The second line contains n space-separated integer Ai (1≤Ai≤n) - the sequence you find.

10

4
1 2 3 4

2015 Multi-University Training Contest 4