My \(\LaTeX\) Package
Click here to download the zip file that contains 'natsirt.cls'.
I have modified the MIT Course 6 LaTeX Package to one that is suited for my convenience and purposes. For an example of a product of this package, see my Real Analysis Notes and Topology Notes.
To use the package on Overleaf, upload the .cls file onto your project, and type the following into your .tex file:
\documentclass{natsirt}
\title{...}
\author{...}
\subtitle{...} % optional
\begin{document}
...
\end{document}
Extra Features
New Chapter and Subchapters
\chapter{} and \chapterpart{} will create chapter titles. \chapter{} will create a page break for every subsequent chapter.
New Problem and Subproblems (for Psets)
\problem{Num}{Collaborators} and \problempart{} will create problem titles. \problem{} will create a page break for every subsequent problem.
Blue, Green, Red and White Boxes
The environment commands \begin{bluebox}, \begin{greenbox}, \begin{redbox} and \begin{whitebox} create a colored box in which you can type paragraphs.
Brackets
These brackets support automatic size correction. E.g. \pr{\sum} will be $\left(\displaystyle\sum\right)$ instead of $(\displaystyle\sum)$
| \pr{...} | \br{...} | \ar{...} | \set{...} | \abs{...} | \norm{...} | \fl{...} | \ce{...} |
|---|---|---|---|---|---|---|---|
| $(...)$ | $[...]$ | $\langle ... \rangle$ | $\\{...\\}$ | $\mid ... \mid$ | $\Vert ... \Vert$ | $\lfloor...\rfloor$ | $\lceil...\rceil$ |
Function Shorthands
| \prb{...} | \epv{...} | \var{...} | \Re{...} | \Im{...} |
|---|---|---|---|---|
| $\mathbb{P}[...]$ | $\mathbb{E}[...]$ | $\mathbb{V}[...]$ | $\mathfrak{Re}[...]$ | $\mathfrak{Im}[...]$ |
| \under{abc}{x} | \od{a}{b} | \pd{a}{b} |
|---|---|---|
| $\underset{x}{\mathrm{abc}}$ | $\frac{\mathrm{d}a}{\mathrm{d}b}$ | $\frac{\partial a}{\partial b}$ |
Symbols
| \emp | \A,\B,...,\Z | \eps | \phi | \\> |
|---|---|---|---|---|
| $\varnothing$ | $\mathbb{A},\mathbb{B},\cdots,\mathbb{Z}$ | $\varepsilon$ | $\varphi$ | $\rightarrow$ |
| \imply | \Imply | \iff | \Iff | \qed | \QED | \mod{...} | \df |
|---|---|---|---|---|---|---|---|
| $\Rightarrow$ | $\Longrightarrow$ | $\Leftrightarrow$ | $\Longleftrightarrow$ | $\square$ | $\blacksquare$ | $(\mathrm{mod} \ ...)$ | $\mathrm{d}$ |
Others
| \DS | \TS | \cases{abc\\\ xyz\\\ ...} | \ol{abc} | \td{abc} | \emph{text} | \scr{ABC} |
|---|---|---|---|---|---|---|
| \displaystyle | \textstyle | $\begin{cases}abc \\\ xyz\\\ \vdots \end{cases}$ | $\overline{abc}$ | $\widetilde{abc}$ | text | $\mathscr{ABC}$ |
Example
f_X(x) = \od{}{t}\prb{X\leq t} = \cases{1, & 0\leq x \leq 1 \\ 0, & \text{otherwise}}
$$ f_X(x) = \frac{\mathrm{d}}{\mathrm{d}t}\mathbb{P}[X\leq t] = \begin{cases}1, & 0\leq x \leq 1\\ 0, & \text{otherwise}\end{cases} $$
f \in \mathcal{R}(a,b) \iff \under{inf}{a=x_0<\cdots<x_N=b} \sum_{i=1}^{N} (x_i - x_{i-1}) \under{osc}{[x_{i-1}, x_i]} f = 0
$$f \in \mathcal{R}(a,b) \ \Leftrightarrow \ \underset{a=x_0 \lt \cdots\lt x_N=b}{\mathrm{inf}} \sum_{i=1}^{N} (x_i - x_{i-1}) \underset{[x_{i-1}, x_i]}{\mathrm{osc}} f = 0 $$
Pakej \(\LaTeX\) Saya
Click here to download the zip file that contains 'natsirt.cls'.
I have modified the MIT Course 6 LaTeX Package to one that is suited for my convenience and purposes. For an example of a product of this package, see my Real Analysis Notes and Topology Notes.
To use the package on Overleaf, upload the .cls file onto your project, and type the following into your .tex file:
\documentclass{natsirt}
\title{...}
\author{...}
\subtitle{...} % optional
\begin{document}
...
\end{document}
Extra Features
New Chapter and Subchapters
\chapter{} and \chapterpart{} will create chapter titles. \chapter{} will create a page break for every subsequent chapter.
New Problem and Subproblems (for Psets)
\problem{Num}{Collaborators} and \problempart{} will create problem titles. \problem{} will create a page break for every subsequent problem.
Blue, Green, Red and White Boxes
The environment commands \begin{bluebox}, \begin{greenbox}, \begin{redbox} and \begin{whitebox} create a colored box in which you can type paragraphs.
Brackets
These brackets support automatic size correction. E.g. \pr{\sum} will be $\left(\displaystyle\sum\right)$ instead of $(\displaystyle\sum)$
| \pr{...} | \br{...} | \ar{...} | \set{...} | \abs{...} | \norm{...} | \fl{...} | \ce{...} |
|---|---|---|---|---|---|---|---|
| $(...)$ | $[...]$ | $\langle ... \rangle$ | $\\{...\\}$ | $\mid ... \mid$ | $\Vert ... \Vert$ | $\lfloor...\rfloor$ | $\lceil...\rceil$ |
Function Shorthands
| \prb{...} | \epv{...} | \var{...} | \Re{...} | \Im{...} |
|---|---|---|---|---|
| $\mathbb{P}[...]$ | $\mathbb{E}[...]$ | $\mathbb{V}[...]$ | $\mathfrak{Re}[...]$ | $\mathfrak{Im}[...]$ |
| \under{abc}{x} | \od{a}{b} | \pd{a}{b} |
|---|---|---|
| $\underset{x}{\mathrm{abc}}$ | $\frac{\mathrm{d}a}{\mathrm{d}b}$ | $\frac{\partial a}{\partial b}$ |
Symbols
| \emp | \A,\B,...,\Z | \eps | \phi | \\> |
|---|---|---|---|---|
| $\varnothing$ | $\mathbb{A},\mathbb{B},\cdots,\mathbb{Z}$ | $\varepsilon$ | $\varphi$ | $\rightarrow$ |
| \imply | \Imply | \iff | \Iff | \qed | \QED | \mod{...} | \df |
|---|---|---|---|---|---|---|---|
| $\Rightarrow$ | $\Longrightarrow$ | $\Leftrightarrow$ | $\Longleftrightarrow$ | $\square$ | $\blacksquare$ | $(\mathrm{mod} \ ...)$ | $\mathrm{d}$ |
Others
| \DS | \TS | \cases{abc\\\ xyz\\\ ...} | \ol{abc} | \td{abc} | \emph{text} | \scr{ABC} |
|---|---|---|---|---|---|---|
| \displaystyle | \textstyle | $\begin{cases}abc \\\ xyz\\\ \vdots \end{cases}$ | $\overline{abc}$ | $\widetilde{abc}$ | text | $\mathscr{ABC}$ |
Example
f_X(x) = \od{}{t}\prb{X\leq t} = \cases{1, & 0\leq x \leq 1 \\ 0, & \text{otherwise}}
$$ f_X(x) = \frac{\mathrm{d}}{\mathrm{d}t}\mathbb{P}[X\leq t] = \begin{cases}1, & 0\leq x \leq 1\\ 0, & \text{otherwise}\end{cases} $$
f \in \mathcal{R}(a,b) \iff \under{inf}{a=x_0<\cdots<x_N=b} \sum_{i=1}^{N} (x_i - x_{i-1}) \under{osc}{[x_{i-1}, x_i]} f = 0
$$f \in \mathcal{R}(a,b) \ \Leftrightarrow \ \underset{a=x_0 \lt \cdots\lt x_N=b}{\mathrm{inf}} \sum_{i=1}^{N} (x_i - x_{i-1}) \underset{[x_{i-1}, x_i]}{\mathrm{osc}} f = 0 $$
我的\(\LaTeX\)宏包
Click here to download the zip file that contains 'natsirt.cls'.
I have modified the MIT Course 6 LaTeX Package to one that is suited for my convenience and purposes. For an example of a product of this package, see my Real Analysis Notes and Topology Notes.
To use the package on Overleaf, upload the .cls file onto your project, and type the following into your .tex file:
\documentclass{natsirt}
\title{...}
\author{...}
\subtitle{...} % optional
\begin{document}
...
\end{document}
Extra Features
New Chapter and Subchapters
\chapter{} and \chapterpart{} will create chapter titles. \chapter{} will create a page break for every subsequent chapter.
New Problem and Subproblems (for Psets)
\problem{Num}{Collaborators} and \problempart{} will create problem titles. \problem{} will create a page break for every subsequent problem.
Blue, Green, Red and White Boxes
The environment commands \begin{bluebox}, \begin{greenbox}, \begin{redbox} and \begin{whitebox} create a colored box in which you can type paragraphs.
Brackets
These brackets support automatic size correction. E.g. \pr{\sum} will be $\left(\displaystyle\sum\right)$ instead of $(\displaystyle\sum)$
| \pr{...} | \br{...} | \ar{...} | \set{...} | \abs{...} | \norm{...} | \fl{...} | \ce{...} |
|---|---|---|---|---|---|---|---|
| $(...)$ | $[...]$ | $\langle ... \rangle$ | $\\{...\\}$ | $\mid ... \mid$ | $\Vert ... \Vert$ | $\lfloor...\rfloor$ | $\lceil...\rceil$ |
Function Shorthands
| \prb{...} | \epv{...} | \var{...} | \Re{...} | \Im{...} |
|---|---|---|---|---|
| $\mathbb{P}[...]$ | $\mathbb{E}[...]$ | $\mathbb{V}[...]$ | $\mathfrak{Re}[...]$ | $\mathfrak{Im}[...]$ |
| \under{abc}{x} | \od{a}{b} | \pd{a}{b} |
|---|---|---|
| $\underset{x}{\mathrm{abc}}$ | $\frac{\mathrm{d}a}{\mathrm{d}b}$ | $\frac{\partial a}{\partial b}$ |
Symbols
| \emp | \A,\B,...,\Z | \eps | \phi | \\> |
|---|---|---|---|---|
| $\varnothing$ | $\mathbb{A},\mathbb{B},\cdots,\mathbb{Z}$ | $\varepsilon$ | $\varphi$ | $\rightarrow$ |
| \imply | \Imply | \iff | \Iff | \qed | \QED | \mod{...} | \df |
|---|---|---|---|---|---|---|---|
| $\Rightarrow$ | $\Longrightarrow$ | $\Leftrightarrow$ | $\Longleftrightarrow$ | $\square$ | $\blacksquare$ | $(\mathrm{mod} \ ...)$ | $\mathrm{d}$ |
Others
| \DS | \TS | \cases{abc\\\ xyz\\\ ...} | \ol{abc} | \td{abc} | \emph{text} | \scr{ABC} |
|---|---|---|---|---|---|---|
| \displaystyle | \textstyle | $\begin{cases}abc \\\ xyz\\\ \vdots \end{cases}$ | $\overline{abc}$ | $\widetilde{abc}$ | text | $\mathscr{ABC}$ |
Example
f_X(x) = \od{}{t}\prb{X\leq t} = \cases{1, & 0\leq x \leq 1 \\ 0, & \text{otherwise}}
$$ f_X(x) = \frac{\mathrm{d}}{\mathrm{d}t}\mathbb{P}[X\leq t] = \begin{cases}1, & 0\leq x \leq 1\\ 0, & \text{otherwise}\end{cases} $$
f \in \mathcal{R}(a,b) \iff \under{inf}{a=x_0<\cdots<x_N=b} \sum_{i=1}^{N} (x_i - x_{i-1}) \under{osc}{[x_{i-1}, x_i]} f = 0
$$f \in \mathcal{R}(a,b) \ \Leftrightarrow \ \underset{a=x_0 \lt \cdots\lt x_N=b}{\mathrm{inf}} \sum_{i=1}^{N} (x_i - x_{i-1}) \underset{[x_{i-1}, x_i]}{\mathrm{osc}} f = 0 $$
我嘅\(\LaTeX\)宏包
Click here to download the zip file that contains 'natsirt.cls'.
I have modified the MIT Course 6 LaTeX Package to one that is suited for my convenience and purposes. For an example of a product of this package, see my Real Analysis Notes and Topology Notes.
To use the package on Overleaf, upload the .cls file onto your project, and type the following into your .tex file:
\documentclass{natsirt}
\title{...}
\author{...}
\subtitle{...} % optional
\begin{document}
...
\end{document}
Extra Features
New Chapter and Subchapters
\chapter{} and \chapterpart{} will create chapter titles. \chapter{} will create a page break for every subsequent chapter.
New Problem and Subproblems (for Psets)
\problem{Num}{Collaborators} and \problempart{} will create problem titles. \problem{} will create a page break for every subsequent problem.
Blue, Green, Red and White Boxes
The environment commands \begin{bluebox}, \begin{greenbox}, \begin{redbox} and \begin{whitebox} create a colored box in which you can type paragraphs.
Brackets
These brackets support automatic size correction. E.g. \pr{\sum} will be $\left(\displaystyle\sum\right)$ instead of $(\displaystyle\sum)$
| \pr{...} | \br{...} | \ar{...} | \set{...} | \abs{...} | \norm{...} | \fl{...} | \ce{...} |
|---|---|---|---|---|---|---|---|
| $(...)$ | $[...]$ | $\langle ... \rangle$ | $\\{...\\}$ | $\mid ... \mid$ | $\Vert ... \Vert$ | $\lfloor...\rfloor$ | $\lceil...\rceil$ |
Function Shorthands
| \prb{...} | \epv{...} | \var{...} | \Re{...} | \Im{...} |
|---|---|---|---|---|
| $\mathbb{P}[...]$ | $\mathbb{E}[...]$ | $\mathbb{V}[...]$ | $\mathfrak{Re}[...]$ | $\mathfrak{Im}[...]$ |
| \under{abc}{x} | \od{a}{b} | \pd{a}{b} |
|---|---|---|
| $\underset{x}{\mathrm{abc}}$ | $\frac{\mathrm{d}a}{\mathrm{d}b}$ | $\frac{\partial a}{\partial b}$ |
Symbols
| \emp | \A,\B,...,\Z | \eps | \phi | \\> |
|---|---|---|---|---|
| $\varnothing$ | $\mathbb{A},\mathbb{B},\cdots,\mathbb{Z}$ | $\varepsilon$ | $\varphi$ | $\rightarrow$ |
| \imply | \Imply | \iff | \Iff | \qed | \QED | \mod{...} | \df |
|---|---|---|---|---|---|---|---|
| $\Rightarrow$ | $\Longrightarrow$ | $\Leftrightarrow$ | $\Longleftrightarrow$ | $\square$ | $\blacksquare$ | $(\mathrm{mod} \ ...)$ | $\mathrm{d}$ |
Others
| \DS | \TS | \cases{abc\\\ xyz\\\ ...} | \ol{abc} | \td{abc} | \emph{text} | \scr{ABC} |
|---|---|---|---|---|---|---|
| \displaystyle | \textstyle | $\begin{cases}abc \\\ xyz\\\ \vdots \end{cases}$ | $\overline{abc}$ | $\widetilde{abc}$ | text | $\mathscr{ABC}$ |
Example
f_X(x) = \od{}{t}\prb{X\leq t} = \cases{1, & 0\leq x \leq 1 \\ 0, & \text{otherwise}}
$$ f_X(x) = \frac{\mathrm{d}}{\mathrm{d}t}\mathbb{P}[X\leq t] = \begin{cases}1, & 0\leq x \leq 1\\ 0, & \text{otherwise}\end{cases} $$
f \in \mathcal{R}(a,b) \iff \under{inf}{a=x_0<\cdots<x_N=b} \sum_{i=1}^{N} (x_i - x_{i-1}) \under{osc}{[x_{i-1}, x_i]} f = 0
$$f \in \mathcal{R}(a,b) \ \Leftrightarrow \ \underset{a=x_0 \lt \cdots\lt x_N=b}{\mathrm{inf}} \sum_{i=1}^{N} (x_i - x_{i-1}) \underset{[x_{i-1}, x_i]}{\mathrm{osc}} f = 0 $$
Mon package \(\LaTeX\)
Click here to download the zip file that contains 'natsirt.cls'.
I have modified the MIT Course 6 LaTeX Package to one that is suited for my convenience and purposes. For an example of a product of this package, see my Real Analysis Notes and Topology Notes.
To use the package on Overleaf, upload the .cls file onto your project, and type the following into your .tex file:
\documentclass{natsirt}
\title{...}
\author{...}
\subtitle{...} % optional
\begin{document}
...
\end{document}
Extra Features
New Chapter and Subchapters
\chapter{} and \chapterpart{} will create chapter titles. \chapter{} will create a page break for every subsequent chapter.
New Problem and Subproblems (for Psets)
\problem{Num}{Collaborators} and \problempart{} will create problem titles. \problem{} will create a page break for every subsequent problem.
Blue, Green, Red and White Boxes
The environment commands \begin{bluebox}, \begin{greenbox}, \begin{redbox} and \begin{whitebox} create a colored box in which you can type paragraphs.
Brackets
These brackets support automatic size correction. E.g. \pr{\sum} will be $\left(\displaystyle\sum\right)$ instead of $(\displaystyle\sum)$
| \pr{...} | \br{...} | \ar{...} | \set{...} | \abs{...} | \norm{...} | \fl{...} | \ce{...} |
|---|---|---|---|---|---|---|---|
| $(...)$ | $[...]$ | $\langle ... \rangle$ | $\\{...\\}$ | $\mid ... \mid$ | $\Vert ... \Vert$ | $\lfloor...\rfloor$ | $\lceil...\rceil$ |
Function Shorthands
| \prb{...} | \epv{...} | \var{...} | \Re{...} | \Im{...} |
|---|---|---|---|---|
| $\mathbb{P}[...]$ | $\mathbb{E}[...]$ | $\mathbb{V}[...]$ | $\mathfrak{Re}[...]$ | $\mathfrak{Im}[...]$ |
| \under{abc}{x} | \od{a}{b} | \pd{a}{b} |
|---|---|---|
| $\underset{x}{\mathrm{abc}}$ | $\frac{\mathrm{d}a}{\mathrm{d}b}$ | $\frac{\partial a}{\partial b}$ |
Symbols
| \emp | \A,\B,...,\Z | \eps | \phi | \\> |
|---|---|---|---|---|
| $\varnothing$ | $\mathbb{A},\mathbb{B},\cdots,\mathbb{Z}$ | $\varepsilon$ | $\varphi$ | $\rightarrow$ |
| \imply | \Imply | \iff | \Iff | \qed | \QED | \mod{...} | \df |
|---|---|---|---|---|---|---|---|
| $\Rightarrow$ | $\Longrightarrow$ | $\Leftrightarrow$ | $\Longleftrightarrow$ | $\square$ | $\blacksquare$ | $(\mathrm{mod} \ ...)$ | $\mathrm{d}$ |
Others
| \DS | \TS | \cases{abc\\\ xyz\\\ ...} | \ol{abc} | \td{abc} | \emph{text} | \scr{ABC} |
|---|---|---|---|---|---|---|
| \displaystyle | \textstyle | $\begin{cases}abc \\\ xyz\\\ \vdots \end{cases}$ | $\overline{abc}$ | $\widetilde{abc}$ | text | $\mathscr{ABC}$ |
Example
f_X(x) = \od{}{t}\prb{X\leq t} = \cases{1, & 0\leq x \leq 1 \\ 0, & \text{otherwise}}
$$ f_X(x) = \frac{\mathrm{d}}{\mathrm{d}t}\mathbb{P}[X\leq t] = \begin{cases}1, & 0\leq x \leq 1\\ 0, & \text{otherwise}\end{cases} $$
f \in \mathcal{R}(a,b) \iff \under{inf}{a=x_0<\cdots<x_N=b} \sum_{i=1}^{N} (x_i - x_{i-1}) \under{osc}{[x_{i-1}, x_i]} f = 0
$$f \in \mathcal{R}(a,b) \ \Leftrightarrow \ \underset{a=x_0 \lt \cdots\lt x_N=b}{\mathrm{inf}} \sum_{i=1}^{N} (x_i - x_{i-1}) \underset{[x_{i-1}, x_i]}{\mathrm{osc}} f = 0 $$
私の\(\LaTeX\)のパッケージ
Click here to download the zip file that contains 'natsirt.cls'.
I have modified the MIT Course 6 LaTeX Package to one that is suited for my convenience and purposes. For an example of a product of this package, see my Real Analysis Notes and Topology Notes.
To use the package on Overleaf, upload the .cls file onto your project, and type the following into your .tex file:
\documentclass{natsirt}
\title{...}
\author{...}
\subtitle{...} % optional
\begin{document}
...
\end{document}
Extra Features
New Chapter and Subchapters
\chapter{} and \chapterpart{} will create chapter titles. \chapter{} will create a page break for every subsequent chapter.
New Problem and Subproblems (for Psets)
\problem{Num}{Collaborators} and \problempart{} will create problem titles. \problem{} will create a page break for every subsequent problem.
Blue, Green, Red and White Boxes
The environment commands \begin{bluebox}, \begin{greenbox}, \begin{redbox} and \begin{whitebox} create a colored box in which you can type paragraphs.
Brackets
These brackets support automatic size correction. E.g. \pr{\sum} will be $\left(\displaystyle\sum\right)$ instead of $(\displaystyle\sum)$
| \pr{...} | \br{...} | \ar{...} | \set{...} | \abs{...} | \norm{...} | \fl{...} | \ce{...} |
|---|---|---|---|---|---|---|---|
| $(...)$ | $[...]$ | $\langle ... \rangle$ | $\\{...\\}$ | $\mid ... \mid$ | $\Vert ... \Vert$ | $\lfloor...\rfloor$ | $\lceil...\rceil$ |
Function Shorthands
| \prb{...} | \epv{...} | \var{...} | \Re{...} | \Im{...} |
|---|---|---|---|---|
| $\mathbb{P}[...]$ | $\mathbb{E}[...]$ | $\mathbb{V}[...]$ | $\mathfrak{Re}[...]$ | $\mathfrak{Im}[...]$ |
| \under{abc}{x} | \od{a}{b} | \pd{a}{b} |
|---|---|---|
| $\underset{x}{\mathrm{abc}}$ | $\frac{\mathrm{d}a}{\mathrm{d}b}$ | $\frac{\partial a}{\partial b}$ |
Symbols
| \emp | \A,\B,...,\Z | \eps | \phi | \\> |
|---|---|---|---|---|
| $\varnothing$ | $\mathbb{A},\mathbb{B},\cdots,\mathbb{Z}$ | $\varepsilon$ | $\varphi$ | $\rightarrow$ |
| \imply | \Imply | \iff | \Iff | \qed | \QED | \mod{...} | \df |
|---|---|---|---|---|---|---|---|
| $\Rightarrow$ | $\Longrightarrow$ | $\Leftrightarrow$ | $\Longleftrightarrow$ | $\square$ | $\blacksquare$ | $(\mathrm{mod} \ ...)$ | $\mathrm{d}$ |
Others
| \DS | \TS | \cases{abc\\\ xyz\\\ ...} | \ol{abc} | \td{abc} | \emph{text} | \scr{ABC} |
|---|---|---|---|---|---|---|
| \displaystyle | \textstyle | $\begin{cases}abc \\\ xyz\\\ \vdots \end{cases}$ | $\overline{abc}$ | $\widetilde{abc}$ | text | $\mathscr{ABC}$ |
Example
f_X(x) = \od{}{t}\prb{X\leq t} = \cases{1, & 0\leq x \leq 1 \\ 0, & \text{otherwise}}
$$ f_X(x) = \frac{\mathrm{d}}{\mathrm{d}t}\mathbb{P}[X\leq t] = \begin{cases}1, & 0\leq x \leq 1\\ 0, & \text{otherwise}\end{cases} $$
f \in \mathcal{R}(a,b) \iff \under{inf}{a=x_0<\cdots<x_N=b} \sum_{i=1}^{N} (x_i - x_{i-1}) \under{osc}{[x_{i-1}, x_i]} f = 0
$$f \in \mathcal{R}(a,b) \ \Leftrightarrow \ \underset{a=x_0 \lt \cdots\lt x_N=b}{\mathrm{inf}} \sum_{i=1}^{N} (x_i - x_{i-1}) \underset{[x_{i-1}, x_i]}{\mathrm{osc}} f = 0 $$