LaTeX\LaTeX Club (for trying codes and making genius ideas!)

Exactly what the title says, welcome to the LaTeX\LaTeX club!

Anyone is free to join. We test latex code, and share our genius ideas with each other.


Awesome Latex Guides -\large\underline{\text{Awesome Latex Guides -}}

Formatting Guide - Páll Márton

Beginner Latex Guide - Daniel Liu


Current Members -\large\underline{\text{Current Members -}} (comment below if you want to join) -

Percy Jackson (Creator)

Frisk Dreemur (First Member, previously Hamza Anushath)

Yajat Shamji (Latex Warden)

Páll Márton (no activity) (Most Contributions...currently inactive)

NSCS 747 (previously Nathan Soliman)

Lâm Lê

Katniss Everdeen (The Girl on Fire, Victor of 74th Hunger Games, blah, blah, blah)


Contributions -\large\underline{\text{Contributions -}}


Genius Ideas -\large\underline{\text{Genius Ideas -}}

\large\star - \large \star

=def\overset{def}{=} - \overset{def}{=}

\large\dagger - \large \dagger

\large\ddagger - \large \ddagger (double dagger)

\(\) - \ \ ( \ ) ( \ \ ) (unformatted, remove the spaces)

Yellow sucks!\colorbox{#CEBB00}{\text{Yellow sucks!}} - \colorbox{YourColour}{YourText}

Buttons - [[show-hide-button | Button Text]] [[start-hidden]] Hidden Text(revealed when button is clicked) [[end-hidden]] (only works in notes and wikis)

Faces - Use \bigodot for round big eyes, or \boxtimes for square eyes with cross in middle. Use \smile and \frown for the mouth. (see comments)

Example Box and the Timer code has also been given below as a comment by Márton.

Custom Tables by Páll is in the storage note made by me - here

Rainbow lines have too long a code, so I will add it later in the storage note.


Current Member with Most Contributions -\underline{\text{Current Member with Most Contributions -}}

Paˊll Maˊrton\colorbox{#3D99F6}{\color{#FFFFFF}\text{Páll Márton}}

Note by Percy Jackson
9 months, 2 weeks ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

\fcolorbox{border-color}{inner-color}{some-text}

Comes with border!\fcolorbox{#D61F06}{#CEBB00}{\color{gold}\text{Comes with border!}}

Jason Gomez - 2 months, 1 week ago

Log in to reply

@Percy Jackson @Frisk Dreemurr Is this already known?\fcolorbox{#333333}{gold}{\text{Is this already known?}}

Jason Gomez - 2 months, 1 week ago

Log in to reply

No, none of us knew this. You can comment somewhere else tho, this note is dead, Lam, Srijan, Katniss have been offline for 1-2 months and Frisk and Nscs are rarely online. Pall deleted hiss account. Only I'm here.

Percy Jackson - 2 months, 1 week ago

Log in to reply

@Percy Jackson Sad\pmb{\text{Sad}}

Jason Gomez - 2 months, 1 week ago

Log in to reply

@Jason Gomez lol I'm happy, bcoz I don't need to open this note anymore, all the latex causes lag

Percy Jackson - 2 months, 1 week ago

Log in to reply

@Percy Jackson im not online cus u dont mention me in interesting stuff anymore

NSCS 747 - 2 months, 1 week ago

Log in to reply

@Nscs 747 Well...Brilliant's not a gossip site, its for learning. Have you seen any solutions in the daily problems lately? I've got 1-2 top solutions in the last week.

Percy Jackson - 2 months, 1 week ago

Log in to reply

@Percy Jackson Yes yes whatever wit your fancy latex and diagram stuff I want wo wind back a few months where we had fun with comments in daily challenges

NSCS 747 - 2 months, 1 week ago

Log in to reply

@Nscs 747 None of that nowadays. I guess we won't be meeting much then. I'm going offline after May...

Percy Jackson - 2 months, 1 week ago

Log in to reply

@Percy Jackson why

NSCS 747 - 2 months, 1 week ago

Log in to reply

@Percy Jackson That’s quite sad to hear, my fate also will mostly be the same

Jason Gomez - 2 months, 1 week ago

Log in to reply

@Percy Jackson Maybe we can trade usernames to join some server idk

Frisk Dreemurr - 2 months, 1 week ago

Log in to reply

@Frisk Dreemurr Myusrname is NSCS_737#2887

NSCS 747 - 2 months, 1 week ago

Log in to reply

@Percy Jackson Anyone use discord?

Frisk Dreemurr - 2 months, 1 week ago

Log in to reply

@Frisk Dreemurr I say you guys are rarely online...and then you just show up...of course.

Yeah, I use discord but only while gaming, so unless you're suggesting chatting while gaming, I can't join. I'm also active until May end, I'll probably go inactive for a long time after June.

Percy Jackson - 2 months, 1 week ago

Log in to reply

Nice!

Percy Jackson - 2 months, 1 week ago

Log in to reply

[[123456789]10]\begin{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} & 1 & 0 \end{bmatrix}

Lâm Lê - 6 months ago

Log in to reply

@Percy Jackson, @NSCS 747, @Frisk Dreemurr How do you do a matrix with LaTeX\LaTeX?

Lâm Lê - 6 months ago

Log in to reply

[Percy: the awesomeNSCS: the “cyberman”SRIJAN: the irritatingFrisk: the flirtatiousLaˆm: the innovativeHalf: the childishKatniss: strong girl on fire]\begin{bmatrix} \text{Percy: the awesome} & \text{NSCS: the “cyberman”} & \text{SRIJAN: the irritating} \\ \text{Frisk: the flirtatious} & \text{Lâm: the innovative} & \text{Half: the childish} \\ \text{∆} & \text{Katniss: strong girl on fire} & \text{∆} \end{bmatrix}

Frisk Dreemurr - 6 months ago

Log in to reply

Mine, Srijan's, NSCS' and HalfPass3's descriptions are accurate, but Lam the innovative...I guess that's partially correct. Frisk the flirtatious is true, but still eww...and Katniss' description is...wrong...totally...wrong....She is supposed to be a battle-hardened warrior!!! Its the whole point of writing a novel series bout her!!! Suzzanne Collins' work on Hunger Games is to signify that, not make here a cute, fire girl!!!

Percy Jackson - 6 months ago

Log in to reply

@Percy Jackson I

don't

care

I am not meant to be cute, but here we are. She is cute, whether you admit it or not... lol

Frisk Dreemurr - 6 months ago

Log in to reply

@Frisk Dreemurr Nope...you might say Jennifer Lawrence is cute, but not Katniss Everdeen(fictional character). Saying she is cute is a violation to my 3rd favorite book series(The Hunger Games)!!!

Percy Jackson - 6 months ago

Log in to reply

@Percy Jackson You sound like someone else in this comment lol

Frisk Dreemurr - 6 months ago

Log in to reply

@Frisk Dreemurr Nope...no sound, only text :)

Percy Jackson - 6 months ago

Log in to reply

@Frisk Dreemurr @Katniss Everdeen, you are cute. Take the compliment, don't blush :)

@Percy Jackson, there, I made myself clear lmao

Frisk Dreemurr - 6 months ago

Log in to reply

@Frisk Dreemurr Take...that...back...right..now...or...else...I...will...make...you..wish...you...were...dead...

Percy Jackson - 6 months ago

Log in to reply

@Percy Jackson lmao ok

Frisk Dreemurr - 6 months ago

Log in to reply

@Frisk Dreemurr good...lol

Percy Jackson - 6 months ago

Log in to reply

@Percy Jackson But what to take back?

Frisk Dreemurr - 6 months ago

Log in to reply

@Frisk Dreemurr I don't remember...leave it be lol

Percy Jackson - 6 months ago

Log in to reply

@Percy Jackson lol (some text)

NSCS 747 - 6 months ago

Log in to reply

@Percy Jackson what do you think my discription means?

NSCS 747 - 6 months ago

Log in to reply

i emailed brilliant and tried to get my name changed but they don't support changing for fictitious names... nvm just have to wait till next year

NSCS 747 - 6 months ago

Log in to reply

@Nscs 747 You wanna roleplay, roleplay as someone awesome. Cybermen don't have much of a personality. Hell, they don't even have a personality. Free walking EXP

Frisk Dreemurr - 6 months ago

Log in to reply

@Frisk Dreemurr thats what i like about them their cold personality

NSCS 747 - 5 months, 4 weeks ago

Log in to reply

@Nscs 747 It ain't cold, it's lifeless(quite literally) and not very interesting. Cold is like one of those cold-hearted assassin commanders they turn Percy into in one of those Chaos Fanfics.

Percy Jackson - 5 months, 4 weeks ago

Log in to reply

@Percy Jackson cybermen have no mercy i mean being cold as in being emotionless and also we do have living organisms inside

NSCS 747 - 5 months, 4 weeks ago

Log in to reply

@Nscs 747 Sure, your Cybermen are nothing but big, rusty buckets.

Percy Jackson - 5 months, 4 weeks ago

Log in to reply

@Nscs 747 Or you might just call your self "heartless", more like "body less", get it?

ba dumm tiss\tiny\color{#FFFFFF}\text{ba dumm tiss}

Frisk Dreemurr - 5 months, 4 weeks ago

Log in to reply

@Nscs 747 You sure you want to be a human with no emotions and natural parts? Cold, metallic, and aggressive, with no free will? Always controlled by another stronger one? (talking about cyber controllers here...)

Even Mettaton is better than a cyberman, and he is a ghost in a robot. He too has a personality, though he is metallic. You need to choose another person for the play Nathan... And definitely not a cyberman

Frisk Dreemurr - 5 months, 4 weeks ago

Log in to reply

@Frisk Dreemurr gimme some ideas then

NSCS 747 - 5 months, 4 weeks ago

Log in to reply

@Nscs 747 One of those orange trains lol

Percy Jackson - 5 months, 4 weeks ago

Log in to reply

@Percy Jackson a proper idea god damn it

NSCS 747 - 5 months, 4 weeks ago

Log in to reply

@Nscs 747 How about the Doctor himself you doofus?

Percy Jackson - 5 months, 4 weeks ago

Log in to reply

@Percy Jackson which one :)

NSCS 747 - 5 months, 4 weeks ago

Log in to reply

@Nscs 747 Darn you to heck Nathan Soliman...you know what I mean...or rather Who I mean...

Percy Jackson - 5 months, 4 weeks ago

Log in to reply

@Percy Jackson ik that but which incarnation lmao i am deciding 11th or 12th

NSCS 747 - 5 months, 4 weeks ago

Log in to reply

@Nscs 747 I haven't watched, so I dunno whatcha talkin bout...

Percy Jackson - 5 months, 4 weeks ago

Log in to reply

@Percy Jackson THESE ARE ATTACK EYEBROWS YOU CAN TAKE BOTTLE TOPS OFF WITH THESE ps. search up the quote on youtube for a funny scene it doesnt spoil anything its just funny

NSCS 747 - 5 months, 4 weeks ago

Log in to reply

@Frisk Dreemurr and people ask me why I have a crush on Mettaton, but not on Cybermen. I will have a crush on anything that has a true personality

Frisk Dreemurr - 5 months, 4 weeks ago

Log in to reply

@Frisk Dreemurr cyberman do not care for your human love we only care aboit universal domination

NSCS 747 - 5 months, 4 weeks ago

Log in to reply

@Frisk Dreemurr Yes

Percy Jackson - 6 months ago

Log in to reply

its not cyberbot it is CYBERMAN like the discription of srijan tho

NSCS 747 - 6 months ago

Log in to reply

Code - \(\begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}\)

Output - [123456789]\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}

Percy Jackson - 6 months ago

Log in to reply

Like that?

Percy Jackson - 6 months ago

Log in to reply

[PercyFriskNscsLamKatnissSrijan(prick)]\begin{bmatrix}\text{Percy} & \text{Frisk} & \text{Nscs} \\ \text{Lam} & \text{Katniss} & \text{Srijan(prick)} \end{bmatrix}

Percy Jackson - 6 months ago

Log in to reply

https://brilliant.org/discussions/thread/testing-19

I remade it!\text{I remade it!}

Or did I...\color{#FFFFFF}\text{Or did I...}

Lâm Lê - 6 months, 3 weeks ago

Log in to reply

does not work the link

NSCS 747 - 6 months, 3 weeks ago

Log in to reply

@NSCS 747 Where does it come up? It goes to the main Brilliant page, right?😜

Lâm Lê - 6 months, 2 weeks ago

Log in to reply

∈≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡∋

NSCS 747 - 7 months ago

Log in to reply

\in\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\equiv\ni