Pumping Water

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###Read problems statements in [Hindi](http://www.codechef.com/download/translated/COOK99/hindi/PUMPWAT.pdf), [Spanish](http://www.codechef.com/download/translated/COOK99/spanish/PUMPWAT.pdf), [Mandarin chinese](http://www.codechef.com/download/translated/COOK99/mandarin/PUMPWAT.pdf), [Russian](http://www.codechef.com/download/translated/COOK99/russian/PUMPWAT.pdf), [Vietnamese](http://www.codechef.com/download/translated/COOK99/vietnamese/PUMPWAT.pdf) and [Bengali](http://www.codechef.com/download/translated/COOK99/bengali/PUMPWAT.pdf) as well. In ChefLand, there is a mountain range consisting of $N$ hills (numbered $1$ through $N$) in a straight line. Let's denote the height of the $i$th hill from the left by $h_i$. Ada is working on the water supply system of ChefLand. On some of the hills, she wants to place water reservoirs; then, for each reservoir, she will decide in which direction the water should flow from it — either to the left or to the right (water may not flow in both directions from the same reservoir). From a reservoir on a hill with height $h$, water flows in the chosen direction until it reaches the first hill that is strictly higher than $h$; all hills before this hill (including the hill containing the reservoir) are therefore supplied with water. For example, suppose we have hills with heights $[7, 2, 3, 5, 8]$. If we place a reservoir on the hill with height $5$, and pump water from it to the left, then the hills with heights $2$, $3$ and $5$ are supplied with water. Help Ada find the minimum numer of reservoirs needed to provide water to all the hills if she chooses the directions optimally. ### Input  The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.  The first line of each test case contains a single integer $N$.  The second line contains $N$ spaceseparated integers $h_1, h_2, \dots, h_N$. ### Output For each test case, print a single line containing one integer — the minimum required number of reservoirs. ### Constraints  $2 \le N \le 10^5$  $1 \le h_i \le 10^9$ for each valid $i$  $h_i \neq h_j $ for any valid $i \neq j$  the sum of $N$ over all test cases does not exceed $5 \cdot 10^5$ ### Example Input ``` 1 6 4 16 32 6 8 2 ``` ### Example Output ``` 2 ``` ### Explanation **Example case 1:** We can place reservoirs on the second and third hill, pumping water to the left and right respectively.Author:  alei 
Editorial  https://discuss.codechef.com/problems/PUMPWAT 
Tags  alei, cook99, easy, observations, preprocessing, taran_1407 
Date Added:  17102018 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, COB, FS 
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