---{"category_name":"easy","problem_code":"ADTCHP","problem_name":"A DT Chip","problemComponents":{"constraints":"","constraintsState":false,"subtasks":"","subtasksState":false,"inputFormat":"","inputFormatState":false,"outputFormat":"","outputFormatState":false,"sampleTestCases":{}},"video_editorial_url":"","languages_supported":{"0":"CPP14","1":"C","2":"JAVA","3":"PYTH 3.6","4":"CPP17","5":"PYTH","6":"PYP3","7":"CS2","8":"ADA","9":"PYPY","10":"TEXT","11":"PAS fpc","12":"NODEJS","13":"RUBY","14":"PHP","15":"GO","16":"HASK","17":"TCL","18":"PERL","19":"SCALA","20":"LUA","21":"kotlin","22":"BASH","23":"JS","24":"LISP sbcl","25":"rust","26":"PAS gpc","27":"BF","28":"CLOJ","29":"R","30":"D","31":"CAML","32":"FORT","33":"ASM","34":"swift","35":"FS","36":"WSPC","37":"LISP clisp","38":"SQL","39":"SCM guile","40":"PERL6","41":"ERL","42":"CLPS","43":"ICK","44":"NICE","45":"PRLG","46":"ICON","47":"COB","48":"SCM chicken","49":"PIKE","50":"SCM qobi","51":"ST","52":"SQLQ","53":"NEM"},"max_timelimit":1,"source_sizelimit":50000,"problem_author":"hackcyborg","problem_tester":"","date_added":"16-12-2020","tags":{"0":"bytr2020","1":"easy","2":"hackcyborg"},"problem_difficulty_level":"Easy-Medium","best_tag":"","editorial_url":"https://discuss.codechef.com/problems/ADTCHP","time":{"view_start_date":1104528600,"submit_start_date":1104528600,"visible_start_date":1104528600,"end_date":1735669800},"is_direct_submittable":false,"problemDiscussURL":"https://discuss.codechef.com/search?q=ADTCHP","is_proctored":false,"visitedContests":{},"layout":"problem"}---Cyberverse is in the form of a rectangular grid of $N$ rows and $M$ columns. There is one cyborg living in each cell of the grid. The rows of the grid are numbered from $1$ to $N$, top to bottom. The columns of the grid numbered from $1$ to $M$, left to right.Each cell contains a DT chip designed by doctor Aditi and each DT chip is connected with 4 side adjacent DT chips ( if it exists) in the grid.Initially all DT chips are working. Hence every cyborg in cyberverse can communicate with each other. DT chip at $(x, y)$ is directly connected to its 4 neighboring DT chips and Cyborg at $(x1, y1)$ can communicate with cyborg at $(x2, y2)$ if and only if there exists a path of connected working DT chips between them. Cyborg Vaishakh wants to destroy the cyberverse so he starts with taking down communication. Doctor Aditi will have to keep a check on the connectivity of the cyborgs in order to build a better DT chip from time to time.In total $Q$ events take place and there are only two types of events.In the first type, Vaishakh can cut connections of every cyborg present in some sub-rectangle, with every other cyborg outside the sub-rectangle. The top-leftmost cell of sub-rectangle will be $(x1, y1)$ and down-rightmost cell will be $(x2, y2)$.**All the sub-rectangles in first type of event are non overlapping. But they can be nested. Consider sub-rectangles as hollow rectangular frames**In second type, given two cells $(x1,y1)$ and $(x2,y2)$, Doctor Aditi checks if cyborgs living in those cells can communicate with each other or not.Since Doctor Aditi is busy upgrading DT chips. Help her to save the cyberverse.### Input:- The first line of input contains three space-separated integers $N$, $M$, and $Q$ respectively.- Each of the next $Q$ lines will contain 5 space-separated integers in one of the two forms:$1\:x1\:y1\:x2\:y2$$2\:x1\:y1\:x2\:y2$- If the first integer is $1$, it represents event of first type with $(x1, y1)$ as top-leftmost cell of subrectangle and $(x2,y2)$ as down-rightmost cell of the subrectangle.- If the first integer is $2$, it represents event of second type with $(x1, y1)$ as first cell and $(x2, y2)$ as second cell.### Output:For each event of second type, print $YES$ if two cyborgs can communicate with each other and $NO$ if they cannot.**Please note that output is case sensitive**.### Constraints:- $1 \leq Q \leq 300000$- $1 \leq N*M \leq 200000$- $1 \leq x1,x2 \leq N$- $1 \leq y1,y2 \leq M$- All the sub-rectangles in first type of event are non overlapping. But they can be nested.### Sample Input 1:```4 5 31 1 2 4 42 2 3 3 32 1 1 4 5```### Sample output 1:```YESNO```### Sample Input 2:```5 6 31 2 2 5 52 1 1 5 62 1 1 3 4```### Sample output 2:```YESNO```### Explanation:- Here ``B`` represents disconnected DT chips and ``D`` represents working DT chips- In Sample $1$: $N=4,M=5$```DDDDDDDDDDDDDDDDDDDD```If Cyborg Vaishakh Disconnected rectangle $((1,2),(4,4))$```DBBBDDBDBDDBDBDDBBBD```Then the grid will become like thisso cyborg at $(2,3)$ can communicate with cyborg at $(3,3)$ but Cyborg at $(1,1)$ can not communicate with cyborg at $(4,5)$- In Sample $2$: $N=5,M=6$```DDDDDDDDDDDDDDDDDDDDDDDDDDDDDD```If Cyborg Vaishakh Disconnected rectangle $((2,2),(5,5))$```DDDDDDDBBBBDDBDDBDDBDDBDDBBBBD```Then the grid will become like thisso cyborg at $(1,1)$ can communicate with cyborg at $(5,6)$ but not with cyborg at $(3,4)$<aside style='background: #f8f8f8;padding: 10px 15px;'><div>All submissions for this problem are available.</div></aside>