Heap Partition ZOJ - 3963

A sequence S = {s1, s2, ..., sn} is called heapable if there exists a binary tree T with nnodes such that every node is labelled with exactly one element from the sequence S, and for every non-root node si and its parent sj, sj ≤ si and j < i hold. Each element in sequence S can be used to label a node in tree T only once.

Chiaki has a sequence a1, a2, ..., an, she would like to decompose it into a minimum number of heapable subsequences.

Note that a subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.

Input

There are multiple test cases. The first line of input contains an integer T, indicating the number of test cases. For each test case:

The first line contain an integer n (1 ≤ n ≤ 105) — the length of the sequence.

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ n).

It is guaranteed that the sum of al