Game with Psycho

Statement:

This is an interesting game. There are n psychos standing in a line. Each psycho is assigned a unique integer from 1 to n. At each step every psycho who has an id greater than the psycho to his right (if exists) kills his right neighbor in the line. Note that a psycho might kill and get killed at the same step.

You’re given the initial arrangement of the psychos in the line. Calculate how many steps are needed to the moment of time such, that nobody kills his neighbor after that moment. Look notes to understand the statement more precise.

Input:

The first line of the input contains an integer T (1 ≤ T ≤ 30), meaning the number of the test cases. For each test case: The first line of input contains integer n denoting the number of psychos, (1 ≤ n ≤ 105). In the second line there will be a list of n distinct integers separated by a single space, each one in then range from 1 to n, inclusive, indicating the ids of the psychos in the line from left to right.

Output:

Print the number of steps, so that the line remains the same afterward.

Example input:
1
10
10 9 7 8 6 5 3 4 2 1
Example output:
2
Explanation:

Note: In the sample line of the psychos transforms as follows:
[10 9 7 8 6 5 3 4 2 1]  →  [10 8 4]  →  [10]. So, there are two steps.

Time and memory limit:

  • 2s
  • 128MB

Problem source: Caribbean Online Judge