Recently, YCC is studying sequence problems. And he is struggling with it!!!= =
For such an ACMer like you, it is commonly believed that you must know the Longest Increasing Subsequence problem. Now Let’s define some useful functions and symbols:
Let U(A) be the length of the longest increasing subsequence of the original sequence A;
Let D(A) be the length of the longest decreasing subsequence of the original sequence A;
Let H(A) be the maximum value of U(A) and D(A), that is H(A) = max{U(A), D(A)}.
H(A)!!! Ah... Zauber anzahl, ist es nicht?
Now YCC wants to study the attributes of all the permutations of integer numbers from 1 to N. He wants to get such permutation P having minimum H(P). If more than one permutation satisfies the condition, you should give the lexicographically smallest one.