<html><head><link rel="stylesheet" href="resource://content-accessible/plaintext.css"><style media="screen" id="__markdown-viewer__md_css">/*
* Copyright (c) Sindre Sorhus <sindresorhus@gmail.com> (https://sindresorhus.com)
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of
* this software and associated documentation files (the "Software"), to deal in
* the Software without restriction, including without limitation the rights to
* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
* of the Software, and to permit persons to whom the Software is furnished to do
* so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
@media (prefers-color-scheme: dark) {
:root {
--color-prettylights-syntax-comment: #8b949e;
--color-prettylights-syntax-constant: #79c0ff;
--color-prettylights-syntax-entity: #d2a8ff;
--color-prettylights-syntax-storage-modifier-import: #c9d1d9;
--color-prettylights-syntax-entity-tag: #7ee787;
--color-prettylights-syntax-keyword: #ff7b72;
--color-prettylights-syntax-string: #a5d6ff;
--color-prettylights-syntax-variable: #ffa657;
--color-prettylights-syntax-brackethighlighter-unmatched: #f85149;
--color-prettylights-syntax-invalid-illegal-text: #f0f6fc;
--color-prettylights-syntax-invalid-illegal-bg: #8e1519;
--color-prettylights-syntax-carriage-return-text: #f0f6fc;
--color-prettylights-syntax-carriage-return-bg: #b62324;
--color-prettylights-syntax-string-regexp: #7ee787;
--color-prettylights-syntax-markup-list: #f2cc60;
--color-prettylights-syntax-markup-heading: #1f6feb;
--color-prettylights-syntax-markup-italic: #c9d1d9;
--color-prettylights-syntax-markup-bold: #c9d1d9;
--color-prettylights-syntax-markup-deleted-text: #ffdcd7;
--color-prettylights-syntax-markup-deleted-bg: #67060c;
--color-prettylights-syntax-markup-inserted-text: #aff5b4;
--color-prettylights-syntax-markup-inserted-bg: #033a16;
--color-prettylights-syntax-markup-changed-text: #ffdfb6;
--color-prettylights-syntax-markup-changed-bg: #5a1e02;
--color-prettylights-syntax-markup-ignored-text: #c9d1d9;
--color-prettylights-syntax-markup-ignored-bg: #1158c7;
--color-prettylights-syntax-meta-diff-range: #d2a8ff;
--color-prettylights-syntax-brackethighlighter-angle: #8b949e;
--color-prettylights-syntax-sublimelinter-gutter-mark: #484f58;
--color-prettylights-syntax-constant-other-reference-link: #a5d6ff;
--color-fg-default: #c9d1d9;
--color-fg-muted: #8b949e;
--color-fg-subtle: #484f58;
--color-canvas-default: #0d1117;
--color-canvas-subtle: #161b22;
--color-border-default: #30363d;
--color-border-muted: #21262d;
--color-neutral-muted: rgba(110,118,129,0.4);
--color-accent-fg: #58a6ff;
--color-accent-emphasis: #1f6feb;
--color-danger-fg: #f85149;
}
}
@media (prefers-color-scheme: light) {
:root {
--color-prettylights-syntax-comment: #6e7781;
--color-prettylights-syntax-constant: #0550ae;
--color-prettylights-syntax-entity: #8250df;
--color-prettylights-syntax-storage-modifier-import: #24292f;
--color-prettylights-syntax-entity-tag: #116329;
--color-prettylights-syntax-keyword: #cf222e;
--color-prettylights-syntax-string: #0a3069;
--color-prettylights-syntax-variable: #953800;
--color-prettylights-syntax-brackethighlighter-unmatched: #82071e;
--color-prettylights-syntax-invalid-illegal-text: #f6f8fa;
--color-prettylights-syntax-invalid-illegal-bg: #82071e;
--color-prettylights-syntax-carriage-return-text: #f6f8fa;
--color-prettylights-syntax-carriage-return-bg: #cf222e;
--color-prettylights-syntax-string-regexp: #116329;
--color-prettylights-syntax-markup-list: #3b2300;
--color-prettylights-syntax-markup-heading: #0550ae;
--color-prettylights-syntax-markup-italic: #24292f;
--color-prettylights-syntax-markup-bold: #24292f;
--color-prettylights-syntax-markup-deleted-text: #82071e;
--color-prettylights-syntax-markup-deleted-bg: #FFEBE9;
--color-prettylights-syntax-markup-inserted-text: #116329;
--color-prettylights-syntax-markup-inserted-bg: #dafbe1;
--color-prettylights-syntax-markup-changed-text: #953800;
--color-prettylights-syntax-markup-changed-bg: #ffd8b5;
--color-prettylights-syntax-markup-ignored-text: #eaeef2;
--color-prettylights-syntax-markup-ignored-bg: #0550ae;
--color-prettylights-syntax-meta-diff-range: #8250df;
--color-prettylights-syntax-brackethighlighter-angle: #57606a;
--color-prettylights-syntax-sublimelinter-gutter-mark: #8c959f;
--color-prettylights-syntax-constant-other-reference-link: #0a3069;
--color-fg-default: #24292f;
--color-fg-muted: #57606a;
--color-fg-subtle: #6e7781;
--color-canvas-default: #ffffff;
--color-canvas-subtle: #f6f8fa;
--color-border-default: #d0d7de;
--color-border-muted: hsla(210,18%,87%,1);
--color-neutral-muted: rgba(175,184,193,0.2);
--color-accent-fg: #0969da;
--color-accent-emphasis: #0969da;
--color-danger-fg: #cf222e;
}
}
:root {
color: var(--color-fg-default);
background-color: var(--color-canvas-default);
}
.markdownroot {
-ms-text-size-adjust: 100%;
-webkit-text-size-adjust: 100%;
margin: 0;
font-family: -apple-system,BlinkMacSystemFont,"Segoe UI",Helvetica,Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji";
font-size: 16px;
line-height: 1.5;
word-wrap: break-word;
}
.markdownroot .octicon {
display: inline-block;
fill: currentColor;
vertical-align: text-bottom;
}
.markdownroot h1:hover .anchor .octicon-link:before,
.markdownroot h2:hover .anchor .octicon-link:before,
.markdownroot h3:hover .anchor .octicon-link:before,
.markdownroot h4:hover .anchor .octicon-link:before,
.markdownroot h5:hover .anchor .octicon-link:before,
.markdownroot h6:hover .anchor .octicon-link:before {
width: 16px;
height: 16px;
content: ' ';
display: inline-block;
background-color: currentColor;
-webkit-mask-image: url("data:image/svg+xml,<svg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' version='1.1' aria-hidden='true'><path fill-rule='evenodd' d='M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z'></path></svg>");
mask-image: url("data:image/svg+xml,<svg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' version='1.1' aria-hidden='true'><path fill-rule='evenodd' d='M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z'></path></svg>");
}
.markdownroot details,
.markdownroot figcaption,
.markdownroot figure {
display: block;
}
.markdownroot summary {
display: list-item;
}
.markdownroot a {
background-color: transparent;
color: var(--color-accent-fg);
text-decoration: none;
}
.markdownroot a:active,
.markdownroot a:hover {
outline-width: 0;
}
.markdownroot abbr[title] {
border-bottom: none;
-webkit-text-decoration: underline dotted;
text-decoration: underline dotted;
}
.markdownroot b,
.markdownroot strong {
font-weight: 600;
}
.markdownroot dfn {
font-style: italic;
}
.markdownroot h1 {
margin: .67em 0;
font-weight: 600;
padding-bottom: .3em;
font-size: 2em;
border-bottom: 1px solid var(--color-border-muted);
}
.markdownroot mark {
background-color: #ff0;
color: var(--color-text-primary);
}
.markdownroot small {
font-size: 90%;
}
.markdownroot sub,
.markdownroot sup {
font-size: 75%;
line-height: 0;
position: relative;
vertical-align: baseline;
}
.markdownroot sub {
bottom: -0.25em;
}
.markdownroot sup {
top: -0.5em;
}
.markdownroot img {
border-style: none;
max-width: 100%;
box-sizing: content-box;
background-color: var(--color-canvas-default);
}
.markdownroot code,
.markdownroot kbd,
.markdownroot pre,
.markdownroot samp {
font-family: monospace,monospace;
font-size: 1em;
}
.markdownroot figure {
margin: 1em 40px;
}
.markdownroot hr {
box-sizing: content-box;
overflow: hidden;
background: transparent;
border-bottom: 1px solid var(--color-border-muted);
height: .25em;
padding: 0;
margin: 24px 0;
background-color: var(--color-border-default);
border: 0;
}
.markdownroot html [type=button],
.markdownroot [type=reset],
.markdownroot [type=submit] {
-webkit-appearance: button;
}
.markdownroot [type=button]::-moz-focus-inner,
.markdownroot [type=reset]::-moz-focus-inner,
.markdownroot [type=submit]::-moz-focus-inner {
border-style: none;
padding: 0;
}
.markdownroot [type=button]:-moz-focusring,
.markdownroot [type=reset]:-moz-focusring,
.markdownroot [type=submit]:-moz-focusring {
outline: 1px dotted ButtonText;
}
.markdownroot [type=checkbox],
.markdownroot [type=radio] {
box-sizing: border-box;
padding: 0;
}
.markdownroot [type=number]::-webkit-inner-spin-button,
.markdownroot [type=number]::-webkit-outer-spin-button {
height: auto;
}
.markdownroot [type=search] {
-webkit-appearance: textfield;
outline-offset: -2px;
}
.markdownroot [type=search]::-webkit-search-cancel-button,
.markdownroot [type=search]::-webkit-search-decoration {
-webkit-appearance: none;
}
.markdownroot ::-webkit-input-placeholder {
color: inherit;
opacity: .54;
}
.markdownroot ::-webkit-file-upload-button {
-webkit-appearance: button;
font: inherit;
}
.markdownroot a:hover {
text-decoration: underline;
}
.markdownroot hr::before {
display: table;
content: "";
}
.markdownroot hr::after {
display: table;
clear: both;
content: "";
}
.markdownroot table {
border-spacing: 0;
border-collapse: collapse;
display: block;
width: max-content;
max-width: 100%;
overflow: auto;
}
.markdownroot td,
.markdownroot th {
padding: 0;
}
.markdownroot details summary {
cursor: pointer;
}
.markdownroot details:not([open])>*:not(summary) {
display: none !important;
}
.markdownroot kbd {
display: inline-block;
padding: 3px 5px;
font: 11px ui-monospace,SFMono-Regular,SF Mono,Menlo,Consolas,Liberation Mono,monospace;
line-height: 10px;
color: var(--color-fg-default);
vertical-align: middle;
background-color: var(--color-canvas-subtle);
border: solid 1px var(--color-neutral-muted);
border-bottom-color: var(--color-neutral-muted);
border-radius: 6px;
box-shadow: inset 0 -1px 0 var(--color-neutral-muted);
}
.markdownroot h1,
.markdownroot h2,
.markdownroot h3,
.markdownroot h4,
.markdownroot h5,
.markdownroot h6 {
margin-top: 24px;
margin-bottom: 16px;
font-weight: 600;
line-height: 1.25;
}
.markdownroot h2 {
font-weight: 600;
padding-bottom: .3em;
font-size: 1.5em;
border-bottom: 1px solid var(--color-border-muted);
}
.markdownroot h3 {
font-weight: 600;
font-size: 1.25em;
}
.markdownroot h4 {
font-weight: 600;
font-size: 1em;
}
.markdownroot h5 {
font-weight: 600;
font-size: .875em;
}
.markdownroot h6 {
font-weight: 600;
font-size: .85em;
color: var(--color-fg-muted);
}
.markdownroot p {
margin-top: 0;
margin-bottom: 10px;
}
.markdownroot blockquote {
margin: 0;
padding: 0 1em;
color: var(--color-fg-muted);
border-left: .25em solid var(--color-border-default);
}
.markdownroot ul,
.markdownroot ol {
margin-top: 0;
margin-bottom: 0;
padding-left: 2em;
}
.markdownroot ol ol,
.markdownroot ul ol {
list-style-type: lower-roman;
}
.markdownroot ul ul ol,
.markdownroot ul ol ol,
.markdownroot ol ul ol,
.markdownroot ol ol ol {
list-style-type: lower-alpha;
}
.markdownroot dd {
margin-left: 0;
}
.markdownroot tt,
.markdownroot code {
font-family: ui-monospace,SFMono-Regular,SF Mono,Menlo,Consolas,Liberation Mono,monospace;
font-size: 12px;
}
.markdownroot pre {
margin-top: 0;
margin-bottom: 0;
font-family: ui-monospace,SFMono-Regular,SF Mono,Menlo,Consolas,Liberation Mono,monospace;
font-size: 12px;
word-wrap: normal;
}
.markdownroot :-ms-input-placeholder {
color: var(--color-fg-subtle);
opacity: 1;
}
.markdownroot ::-ms-input-placeholder {
color: var(--color-fg-subtle);
opacity: 1;
}
.markdownroot ::placeholder {
color: var(--color-fg-subtle);
opacity: 1;
}
.markdownroot .pl-c {
color: var(--color-prettylights-syntax-comment);
}
.markdownroot .pl-c1,
.markdownroot .pl-s .pl-v {
color: var(--color-prettylights-syntax-constant);
}
.markdownroot .pl-e,
.markdownroot .pl-en {
color: var(--color-prettylights-syntax-entity);
}
.markdownroot .pl-smi,
.markdownroot .pl-s .pl-s1 {
color: var(--color-prettylights-syntax-storage-modifier-import);
}
.markdownroot .pl-ent {
color: var(--color-prettylights-syntax-entity-tag);
}
.markdownroot .pl-k {
color: var(--color-prettylights-syntax-keyword);
}
.markdownroot .pl-s,
.markdownroot .pl-pds,
.markdownroot .pl-s .pl-pse .pl-s1,
.markdownroot .pl-sr,
.markdownroot .pl-sr .pl-cce,
.markdownroot .pl-sr .pl-sre,
.markdownroot .pl-sr .pl-sra {
color: var(--color-prettylights-syntax-string);
}
.markdownroot .pl-v,
.markdownroot .pl-smw {
color: var(--color-prettylights-syntax-variable);
}
.markdownroot .pl-bu {
color: var(--color-prettylights-syntax-brackethighlighter-unmatched);
}
.markdownroot .pl-ii {
color: var(--color-prettylights-syntax-invalid-illegal-text);
background-color: var(--color-prettylights-syntax-invalid-illegal-bg);
}
.markdownroot .pl-c2 {
color: var(--color-prettylights-syntax-carriage-return-text);
background-color: var(--color-prettylights-syntax-carriage-return-bg);
}
.markdownroot .pl-sr .pl-cce {
font-weight: bold;
color: var(--color-prettylights-syntax-string-regexp);
}
.markdownroot .pl-ml {
color: var(--color-prettylights-syntax-markup-list);
}
.markdownroot .pl-mh,
.markdownroot .pl-mh .pl-en,
.markdownroot .pl-ms {
font-weight: bold;
color: var(--color-prettylights-syntax-markup-heading);
}
.markdownroot .pl-mi {
font-style: italic;
color: var(--color-prettylights-syntax-markup-italic);
}
.markdownroot .pl-mb {
font-weight: bold;
color: var(--color-prettylights-syntax-markup-bold);
}
.markdownroot .pl-md {
color: var(--color-prettylights-syntax-markup-deleted-text);
background-color: var(--color-prettylights-syntax-markup-deleted-bg);
}
.markdownroot .pl-mi1 {
color: var(--color-prettylights-syntax-markup-inserted-text);
background-color: var(--color-prettylights-syntax-markup-inserted-bg);
}
.markdownroot .pl-mc {
color: var(--color-prettylights-syntax-markup-changed-text);
background-color: var(--color-prettylights-syntax-markup-changed-bg);
}
.markdownroot .pl-mi2 {
color: var(--color-prettylights-syntax-markup-ignored-text);
background-color: var(--color-prettylights-syntax-markup-ignored-bg);
}
.markdownroot .pl-mdr {
font-weight: bold;
color: var(--color-prettylights-syntax-meta-diff-range);
}
.markdownroot .pl-ba {
color: var(--color-prettylights-syntax-brackethighlighter-angle);
}
.markdownroot .pl-sg {
color: var(--color-prettylights-syntax-sublimelinter-gutter-mark);
}
.markdownroot .pl-corl {
text-decoration: underline;
color: var(--color-prettylights-syntax-constant-other-reference-link);
}
.markdownroot [data-catalyst] {
display: block;
}
.markdownroot g-emoji {
font-family: "Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol";
font-size: 1em;
font-style: normal !important;
font-weight: 400;
line-height: 1;
vertical-align: -0.075em;
}
.markdownroot g-emoji img {
width: 1em;
height: 1em;
}
.markdownroot::before {
display: table;
content: "";
}
.markdownroot::after {
display: table;
clear: both;
content: "";
}
.markdownroot>*:first-child {
margin-top: 0 !important;
}
.markdownroot>*:last-child {
margin-bottom: 0 !important;
}
.markdownroot a:not([href]) {
color: inherit;
text-decoration: none;
}
.markdownroot .absent {
color: var(--color-danger-fg);
}
.markdownroot .anchor {
float: left;
padding-right: 4px;
margin-left: -20px;
line-height: 1;
}
.markdownroot .anchor:focus {
outline: none;
}
.markdownroot p,
.markdownroot blockquote,
.markdownroot ul,
.markdownroot ol,
.markdownroot dl,
.markdownroot table,
.markdownroot pre,
.markdownroot details {
margin-top: 0;
margin-bottom: 16px;
}
.markdownroot blockquote>:first-child {
margin-top: 0;
}
.markdownroot blockquote>:last-child {
margin-bottom: 0;
}
.markdownroot sup>a::before {
content: "[";
}
.markdownroot sup>a::after {
content: "]";
}
.markdownroot h1 .octicon-link,
.markdownroot h2 .octicon-link,
.markdownroot h3 .octicon-link,
.markdownroot h4 .octicon-link,
.markdownroot h5 .octicon-link,
.markdownroot h6 .octicon-link {
color: var(--color-fg-default);
vertical-align: middle;
visibility: hidden;
}
.markdownroot h1:hover .anchor,
.markdownroot h2:hover .anchor,
.markdownroot h3:hover .anchor,
.markdownroot h4:hover .anchor,
.markdownroot h5:hover .anchor,
.markdownroot h6:hover .anchor {
text-decoration: none;
}
.markdownroot h1:hover .anchor .octicon-link,
.markdownroot h2:hover .anchor .octicon-link,
.markdownroot h3:hover .anchor .octicon-link,
.markdownroot h4:hover .anchor .octicon-link,
.markdownroot h5:hover .anchor .octicon-link,
.markdownroot h6:hover .anchor .octicon-link {
visibility: visible;
}
.markdownroot h1 tt,
.markdownroot h1 code,
.markdownroot h2 tt,
.markdownroot h2 code,
.markdownroot h3 tt,
.markdownroot h3 code,
.markdownroot h4 tt,
.markdownroot h4 code,
.markdownroot h5 tt,
.markdownroot h5 code,
.markdownroot h6 tt,
.markdownroot h6 code {
padding: 0 .2em;
font-size: inherit;
}
.markdownroot ul.no-list,
.markdownroot ol.no-list {
padding: 0;
list-style-type: none;
}
.markdownroot ol[type="1"] {
list-style-type: decimal;
}
.markdownroot ol[type=a] {
list-style-type: lower-alpha;
}
.markdownroot ol[type=i] {
list-style-type: lower-roman;
}
.markdownroot div>ol:not([type]) {
list-style-type: decimal;
}
.markdownroot ul ul,
.markdownroot ul ol,
.markdownroot ol ol,
.markdownroot ol ul {
margin-top: 0;
margin-bottom: 0;
}
.markdownroot li>p {
margin-top: 16px;
}
.markdownroot li+li {
margin-top: .25em;
}
.markdownroot dl {
padding: 0;
}
.markdownroot dl dt {
padding: 0;
margin-top: 16px;
font-size: 1em;
font-style: italic;
font-weight: 600;
}
.markdownroot dl dd {
padding: 0 16px;
margin-bottom: 16px;
}
.markdownroot table th {
font-weight: 600;
}
.markdownroot table th,
.markdownroot table td {
padding: 6px 13px;
border: 1px solid var(--color-border-default);
}
.markdownroot table tr {
background-color: var(--color-canvas-default);
border-top: 1px solid var(--color-border-muted);
}
.markdownroot table tr:nth-child(2n) {
background-color: var(--color-canvas-subtle);
}
.markdownroot table img {
background-color: transparent;
}
.markdownroot img[align=right] {
padding-left: 20px;
}
.markdownroot img[align=left] {
padding-right: 20px;
}
.markdownroot .emoji {
max-width: none;
vertical-align: text-top;
background-color: transparent;
}
.markdownroot span.frame {
display: block;
overflow: hidden;
}
.markdownroot span.frame>span {
display: block;
float: left;
width: auto;
padding: 7px;
margin: 13px 0 0;
overflow: hidden;
border: 1px solid var(--color-border-default);
}
.markdownroot span.frame span img {
display: block;
float: left;
}
.markdownroot span.frame span span {
display: block;
padding: 5px 0 0;
clear: both;
color: var(--color-fg-default);
}
.markdownroot span.align-center {
display: block;
overflow: hidden;
clear: both;
}
.markdownroot span.align-center>span {
display: block;
margin: 13px auto 0;
overflow: hidden;
text-align: center;
}
.markdownroot span.align-center span img {
margin: 0 auto;
text-align: center;
}
.markdownroot span.align-right {
display: block;
overflow: hidden;
clear: both;
}
.markdownroot span.align-right>span {
display: block;
margin: 13px 0 0;
overflow: hidden;
text-align: right;
}
.markdownroot span.align-right span img {
margin: 0;
text-align: right;
}
.markdownroot span.float-left {
display: block;
float: left;
margin-right: 13px;
overflow: hidden;
}
.markdownroot span.float-left span {
margin: 13px 0 0;
}
.markdownroot span.float-right {
display: block;
float: right;
margin-left: 13px;
overflow: hidden;
}
.markdownroot span.float-right>span {
display: block;
margin: 13px auto 0;
overflow: hidden;
text-align: right;
}
.markdownroot code,
.markdownroot tt {
padding: .2em .4em;
margin: 0;
font-size: 85%;
background-color: var(--color-neutral-muted);
border-radius: 6px;
}
.markdownroot code br,
.markdownroot tt br {
display: none;
}
.markdownroot del code {
text-decoration: inherit;
}
.markdownroot pre code {
font-size: 100%;
}
.markdownroot pre>code {
padding: 0;
margin: 0;
word-break: normal;
white-space: pre;
background: transparent;
border: 0;
}
.markdownroot .highlight {
margin-bottom: 16px;
}
.markdownroot .highlight pre {
margin-bottom: 0;
word-break: normal;
}
.markdownroot .highlight pre,
.markdownroot pre {
padding: 16px;
overflow: auto;
font-size: 85%;
line-height: 1.45;
background-color: var(--color-canvas-subtle);
border-radius: 6px;
}
.markdownroot pre code,
.markdownroot pre tt {
display: inline;
max-width: auto;
padding: 0;
margin: 0;
overflow: visible;
line-height: inherit;
word-wrap: normal;
background-color: transparent;
border: 0;
}
.markdownroot .csv-data td,
.markdownroot .csv-data th {
padding: 5px;
overflow: hidden;
font-size: 12px;
line-height: 1;
text-align: left;
white-space: nowrap;
}
.markdownroot .csv-data .blob-num {
padding: 10px 8px 9px;
text-align: right;
background: var(--color-canvas-default);
border: 0;
}
.markdownroot .csv-data tr {
border-top: 0;
}
.markdownroot .csv-data th {
font-weight: 600;
background: var(--color-canvas-subtle);
border-top: 0;
}
.markdownroot .footnotes {
font-size: 12px;
color: var(--color-fg-muted);
border-top: 1px solid var(--color-border-default);
}
.markdownroot .footnotes ol {
padding-left: 16px;
}
.markdownroot .footnotes li {
position: relative;
}
.markdownroot .footnotes li:target::before {
position: absolute;
top: -8px;
right: -8px;
bottom: -8px;
left: -24px;
pointer-events: none;
content: "";
border: 2px solid var(--color-accent-emphasis);
border-radius: 6px;
}
.markdownroot .footnotes li:target {
color: var(--color-fg-default);
}
.markdownroot .footnotes .data-footnote-backref g-emoji {
font-family: monospace;
}
.markdownroot [hidden] {
display: none !important;
}
.markdownroot ::-webkit-calendar-picker-indicator {
filter: invert(50%);
}
</style><style media="print" id="__markdown-viewer__md_print_css">:root {
background: white;
color: black;
font: 8pt serif;
line-height: 1.5;
vertical-align: baseline;
}
body, .markdownRoot {
max-width: 100%;
margin: 0;
padding: 0;
}
* {
margin: 0;
padding: 0;
}
p {
margin: 0 0 .3rem 0;
}
ul, ol {
padding-left: 2em
}
a {
color: #666;
text-decoration: underline;
}
a[href]:after {
content: ' (' attr(href) ')';
font-size: 1rem;
}
img {
max-width: 100%;
}
h1, h2, h3, h4, h5, h6 {
padding: 0 0 .2em 0;
}
h1, h2, h3, h4, h5, h6, dt {
/* break-after: avoid; */
break-inside: avoid;
}
/* Hack to fix break-after: https://stackoverflow.com/a/53742871 */
h1:after, h2:after, h3:after, h4:after, h5:after, h6:after, dt:after {
content: "";
display: block;
/* .2em of padding + 3em for 2 full lines */
height: 3.2em;
margin-bottom: -3.2em;
}
blockquote, pre, li, dt, dd {
break-inside: avoid;
}
</style><style id="__markdown-viewer__hljs_css">.hljs-comment,.hljs-quote{color:#d4d0ab}.hljs-deletion,.hljs-name,.hljs-regexp,.hljs-selector-class,.hljs-selector-id,.hljs-tag,.hljs-template-variable,.hljs-variable{color:#ffa07a}.hljs-built_in,.hljs-builtin-name,.hljs-link,.hljs-literal,.hljs-meta,.hljs-number,.hljs-params,.hljs-type{color:#f5ab35}.hljs-attribute{color:gold}.hljs-addition,.hljs-bullet,.hljs-string,.hljs-symbol{color:#abe338}.hljs-section,.hljs-title{color:#00e0e0}.hljs-keyword,.hljs-selector-tag{color:#dcc6e0}.hljs{display:block;overflow-x:auto;background:#2b2b2b;color:#f8f8f2;padding:.5em}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:700}@media screen and (-ms-high-contrast:active){.hljs-addition,.hljs-attribute,.hljs-built_in,.hljs-builtin-name,.hljs-bullet,.hljs-comment,.hljs-link,.hljs-literal,.hljs-meta,.hljs-number,.hljs-params,.hljs-quote,.hljs-string,.hljs-symbol,.hljs-type{color:highlight}.hljs-keyword,.hljs-selector-tag{font-weight:700}}</style><style id="__markdown-viewer__katex_css">@font-face{font-family:KaTeX_AMS;font-style:normal;font-weight:400}@font-face{font-family:KaTeX_Caligraphic;font-style:normal;font-weight:700}@font-face{font-family:KaTeX_Caligraphic;font-style:normal;font-weight:400}@font-face{font-family:KaTeX_Fraktur;font-style:normal;font-weight:700}@font-face{font-family:KaTeX_Fraktur;font-style:normal;font-weight:400}@font-face{font-family:KaTeX_Main;font-style:normal;font-weight:700}@font-face{font-family:KaTeX_Main;font-style:italic;font-weight:700}@font-face{font-family:KaTeX_Main;font-style:italic;font-weight:400}@font-face{font-family:KaTeX_Main;font-style:normal;font-weight:400}@font-face{font-family:KaTeX_Math;font-style:italic;font-weight:700}@font-face{font-family:KaTeX_Math;font-style:italic;font-weight:400}@font-face{font-family:"KaTeX_SansSerif";font-style:normal;font-weight:700}@font-face{font-family:"KaTeX_SansSerif";font-style:italic;font-weight:400}@font-face{font-family:"KaTeX_SansSerif";font-style:normal;font-weight:400}@font-face{font-family:KaTeX_Script;font-style:normal;font-weight:400}@font-face{font-family:KaTeX_Size1;font-style:normal;font-weight:400}@font-face{font-family:KaTeX_Size2;font-style:normal;font-weight:400}@font-face{font-family:KaTeX_Size3;font-style:normal;font-weight:400}@font-face{font-family:KaTeX_Size4;font-style:normal;font-weight:400}@font-face{font-family:KaTeX_Typewriter;font-style:normal;font-weight:400}.katex{text-rendering:auto;font:normal 1.21em KaTeX_Main,Times New Roman,serif;line-height:1.2;text-indent:0}.katex *{-ms-high-contrast-adjust:none!important;border-color:currentColor}.katex .katex-version:after{content:"0.13.13"}.katex .katex-mathml{clip:rect(1px,1px,1px,1px);border:0;height:1px;overflow:hidden;padding:0;position:absolute;width:1px}.katex .katex-html>.newline{display:block}.katex .base{position:relative;white-space:nowrap;width:-webkit-min-content;width:-moz-min-content;width:min-content}.katex .base,.katex .strut{display:inline-block}.katex .textbf{font-weight:700}.katex .textit{font-style:italic}.katex .textrm{font-family:KaTeX_Main}.katex .textsf{font-family:KaTeX_SansSerif}.katex .texttt{font-family:KaTeX_Typewriter}.katex .mathnormal{font-family:KaTeX_Math;font-style:italic}.katex .mathit{font-family:KaTeX_Main;font-style:italic}.katex .mathrm{font-style:normal}.katex .mathbf{font-family:KaTeX_Main;font-weight:700}.katex .boldsymbol{font-family:KaTeX_Math;font-style:italic;font-weight:700}.katex .amsrm,.katex .mathbb,.katex .textbb{font-family:KaTeX_AMS}.katex .mathcal{font-family:KaTeX_Caligraphic}.katex .mathfrak,.katex .textfrak{font-family:KaTeX_Fraktur}.katex .mathtt{font-family:KaTeX_Typewriter}.katex .mathscr,.katex .textscr{font-family:KaTeX_Script}.katex .mathsf,.katex .textsf{font-family:KaTeX_SansSerif}.katex .mathboldsf,.katex .textboldsf{font-family:KaTeX_SansSerif;font-weight:700}.katex .mathitsf,.katex .textitsf{font-family:KaTeX_SansSerif;font-style:italic}.katex .mainrm{font-family:KaTeX_Main;font-style:normal}.katex .vlist-t{border-collapse:collapse;display:inline-table;table-layout:fixed}.katex .vlist-r{display:table-row}.katex .vlist{display:table-cell;position:relative;vertical-align:bottom}.katex .vlist>span{display:block;height:0;position:relative}.katex .vlist>span>span{display:inline-block}.katex .vlist>span>.pstrut{overflow:hidden;width:0}.katex .vlist-t2{margin-right:-2px}.katex .vlist-s{display:table-cell;font-size:1px;min-width:2px;vertical-align:bottom;width:2px}.katex .vbox{align-items:baseline;display:inline-flex;flex-direction:column}.katex .hbox{width:100%}.katex .hbox,.katex .thinbox{display:inline-flex;flex-direction:row}.katex .thinbox{max-width:0;width:0}.katex .msupsub{text-align:left}.katex .mfrac>span>span{text-align:center}.katex .mfrac .frac-line{border-bottom-style:solid;display:inline-block;width:100%}.katex .hdashline,.katex .hline,.katex .mfrac .frac-line,.katex .overline .overline-line,.katex .rule,.katex .underline .underline-line{min-height:1px}.katex .mspace{display:inline-block}.katex .clap,.katex .llap,.katex .rlap{position:relative;width:0}.katex .clap>.inner,.katex .llap>.inner,.katex .rlap>.inner{position:absolute}.katex .clap>.fix,.katex .llap>.fix,.katex .rlap>.fix{display:inline-block}.katex .llap>.inner{right:0}.katex .clap>.inner,.katex .rlap>.inner{left:0}.katex .clap>.inner>span{margin-left:-50%;margin-right:50%}.katex .rule{border:0 solid;display:inline-block;position:relative}.katex .hline,.katex .overline .overline-line,.katex .underline .underline-line{border-bottom-style:solid;display:inline-block;width:100%}.katex .hdashline{border-bottom-style:dashed;display:inline-block;width:100%}.katex .sqrt>.root{margin-left:.27777778em;margin-right:-.55555556em}.katex .fontsize-ensurer.reset-size1.size1,.katex .sizing.reset-size1.size1{font-size:1em}.katex .fontsize-ensurer.reset-size1.size2,.katex .sizing.reset-size1.size2{font-size:1.2em}.katex .fontsize-ensurer.reset-size1.size3,.katex .sizing.reset-size1.size3{font-size:1.4em}.katex .fontsize-ensurer.reset-size1.size4,.katex .sizing.reset-size1.size4{font-size:1.6em}.katex .fontsize-ensurer.reset-size1.size5,.katex .sizing.reset-size1.size5{font-size:1.8em}.katex .fontsize-ensurer.reset-size1.size6,.katex .sizing.reset-size1.size6{font-size:2em}.katex .fontsize-ensurer.reset-size1.size7,.katex .sizing.reset-size1.size7{font-size:2.4em}.katex .fontsize-ensurer.reset-size1.size8,.katex .sizing.reset-size1.size8{font-size:2.88em}.katex .fontsize-ensurer.reset-size1.size9,.katex .sizing.reset-size1.size9{font-size:3.456em}.katex .fontsize-ensurer.reset-size1.size10,.katex .sizing.reset-size1.size10{font-size:4.148em}.katex .fontsize-ensurer.reset-size1.size11,.katex .sizing.reset-size1.size11{font-size:4.976em}.katex .fontsize-ensurer.reset-size2.size1,.katex .sizing.reset-size2.size1{font-size:.83333333em}.katex .fontsize-ensurer.reset-size2.size2,.katex .sizing.reset-size2.size2{font-size:1em}.katex .fontsize-ensurer.reset-size2.size3,.katex .sizing.reset-size2.size3{font-size:1.16666667em}.katex .fontsize-ensurer.reset-size2.size4,.katex .sizing.reset-size2.size4{font-size:1.33333333em}.katex .fontsize-ensurer.reset-size2.size5,.katex .sizing.reset-size2.size5{font-size:1.5em}.katex .fontsize-ensurer.reset-size2.size6,.katex .sizing.reset-size2.size6{font-size:1.66666667em}.katex .fontsize-ensurer.reset-size2.size7,.katex .sizing.reset-size2.size7{font-size:2em}.katex .fontsize-ensurer.reset-size2.size8,.katex .sizing.reset-size2.size8{font-size:2.4em}.katex .fontsize-ensurer.reset-size2.size9,.katex .sizing.reset-size2.size9{font-size:2.88em}.katex .fontsize-ensurer.reset-size2.size10,.katex .sizing.reset-size2.size10{font-size:3.45666667em}.katex .fontsize-ensurer.reset-size2.size11,.katex .sizing.reset-size2.size11{font-size:4.14666667em}.katex .fontsize-ensurer.reset-size3.size1,.katex .sizing.reset-size3.size1{font-size:.71428571em}.katex .fontsize-ensurer.reset-size3.size2,.katex .sizing.reset-size3.size2{font-size:.85714286em}.katex .fontsize-ensurer.reset-size3.size3,.katex .sizing.reset-size3.size3{font-size:1em}.katex .fontsize-ensurer.reset-size3.size4,.katex .sizing.reset-size3.size4{font-size:1.14285714em}.katex .fontsize-ensurer.reset-size3.size5,.katex .sizing.reset-size3.size5{font-size:1.28571429em}.katex .fontsize-ensurer.reset-size3.size6,.katex .sizing.reset-size3.size6{font-size:1.42857143em}.katex .fontsize-ensurer.reset-size3.size7,.katex .sizing.reset-size3.size7{font-size:1.71428571em}.katex .fontsize-ensurer.reset-size3.size8,.katex .sizing.reset-size3.size8{font-size:2.05714286em}.katex .fontsize-ensurer.reset-size3.size9,.katex .sizing.reset-size3.size9{font-size:2.46857143em}.katex .fontsize-ensurer.reset-size3.size10,.katex .sizing.reset-size3.size10{font-size:2.96285714em}.katex .fontsize-ensurer.reset-size3.size11,.katex .sizing.reset-size3.size11{font-size:3.55428571em}.katex .fontsize-ensurer.reset-size4.size1,.katex .sizing.reset-size4.size1{font-size:.625em}.katex .fontsize-ensurer.reset-size4.size2,.katex .sizing.reset-size4.size2{font-size:.75em}.katex .fontsize-ensurer.reset-size4.size3,.katex .sizing.reset-size4.size3{font-size:.875em}.katex .fontsize-ensurer.reset-size4.size4,.katex .sizing.reset-size4.size4{font-size:1em}.katex .fontsize-ensurer.reset-size4.size5,.katex .sizing.reset-size4.size5{font-size:1.125em}.katex .fontsize-ensurer.reset-size4.size6,.katex .sizing.reset-size4.size6{font-size:1.25em}.katex .fontsize-ensurer.reset-size4.size7,.katex .sizing.reset-size4.size7{font-size:1.5em}.katex .fontsize-ensurer.reset-size4.size8,.katex .sizing.reset-size4.size8{font-size:1.8em}.katex .fontsize-ensurer.reset-size4.size9,.katex .sizing.reset-size4.size9{font-size:2.16em}.katex .fontsize-ensurer.reset-size4.size10,.katex .sizing.reset-size4.size10{font-size:2.5925em}.katex .fontsize-ensurer.reset-size4.size11,.katex .sizing.reset-size4.size11{font-size:3.11em}.katex .fontsize-ensurer.reset-size5.size1,.katex .sizing.reset-size5.size1{font-size:.55555556em}.katex .fontsize-ensurer.reset-size5.size2,.katex .sizing.reset-size5.size2{font-size:.66666667em}.katex .fontsize-ensurer.reset-size5.size3,.katex .sizing.reset-size5.size3{font-size:.77777778em}.katex .fontsize-ensurer.reset-size5.size4,.katex .sizing.reset-size5.size4{font-size:.88888889em}.katex .fontsize-ensurer.reset-size5.size5,.katex .sizing.reset-size5.size5{font-size:1em}.katex .fontsize-ensurer.reset-size5.size6,.katex .sizing.reset-size5.size6{font-size:1.11111111em}.katex .fontsize-ensurer.reset-size5.size7,.katex .sizing.reset-size5.size7{font-size:1.33333333em}.katex .fontsize-ensurer.reset-size5.size8,.katex .sizing.reset-size5.size8{font-size:1.6em}.katex .fontsize-ensurer.reset-size5.size9,.katex .sizing.reset-size5.size9{font-size:1.92em}.katex .fontsize-ensurer.reset-size5.size10,.katex .sizing.reset-size5.size10{font-size:2.30444444em}.katex .fontsize-ensurer.reset-size5.size11,.katex .sizing.reset-size5.size11{font-size:2.76444444em}.katex .fontsize-ensurer.reset-size6.size1,.katex .sizing.reset-size6.size1{font-size:.5em}.katex .fontsize-ensurer.reset-size6.size2,.katex .sizing.reset-size6.size2{font-size:.6em}.katex .fontsize-ensurer.reset-size6.size3,.katex .sizing.reset-size6.size3{font-size:.7em}.katex .fontsize-ensurer.reset-size6.size4,.katex .sizing.reset-size6.size4{font-size:.8em}.katex .fontsize-ensurer.reset-size6.size5,.katex .sizing.reset-size6.size5{font-size:.9em}.katex .fontsize-ensurer.reset-size6.size6,.katex .sizing.reset-size6.size6{font-size:1em}.katex .fontsize-ensurer.reset-size6.size7,.katex .sizing.reset-size6.size7{font-size:1.2em}.katex .fontsize-ensurer.reset-size6.size8,.katex .sizing.reset-size6.size8{font-size:1.44em}.katex .fontsize-ensurer.reset-size6.size9,.katex .sizing.reset-size6.size9{font-size:1.728em}.katex .fontsize-ensurer.reset-size6.size10,.katex .sizing.reset-size6.size10{font-size:2.074em}.katex .fontsize-ensurer.reset-size6.size11,.katex .sizing.reset-size6.size11{font-size:2.488em}.katex .fontsize-ensurer.reset-size7.size1,.katex .sizing.reset-size7.size1{font-size:.41666667em}.katex .fontsize-ensurer.reset-size7.size2,.katex .sizing.reset-size7.size2{font-size:.5em}.katex .fontsize-ensurer.reset-size7.size3,.katex .sizing.reset-size7.size3{font-size:.58333333em}.katex .fontsize-ensurer.reset-size7.size4,.katex .sizing.reset-size7.size4{font-size:.66666667em}.katex .fontsize-ensurer.reset-size7.size5,.katex .sizing.reset-size7.size5{font-size:.75em}.katex .fontsize-ensurer.reset-size7.size6,.katex .sizing.reset-size7.size6{font-size:.83333333em}.katex .fontsize-ensurer.reset-size7.size7,.katex .sizing.reset-size7.size7{font-size:1em}.katex .fontsize-ensurer.reset-size7.size8,.katex .sizing.reset-size7.size8{font-size:1.2em}.katex .fontsize-ensurer.reset-size7.size9,.katex .sizing.reset-size7.size9{font-size:1.44em}.katex .fontsize-ensurer.reset-size7.size10,.katex .sizing.reset-size7.size10{font-size:1.72833333em}.katex .fontsize-ensurer.reset-size7.size11,.katex .sizing.reset-size7.size11{font-size:2.07333333em}.katex .fontsize-ensurer.reset-size8.size1,.katex .sizing.reset-size8.size1{font-size:.34722222em}.katex .fontsize-ensurer.reset-size8.size2,.katex .sizing.reset-size8.size2{font-size:.41666667em}.katex .fontsize-ensurer.reset-size8.size3,.katex .sizing.reset-size8.size3{font-size:.48611111em}.katex .fontsize-ensurer.reset-size8.size4,.katex .sizing.reset-size8.size4{font-size:.55555556em}.katex .fontsize-ensurer.reset-size8.size5,.katex .sizing.reset-size8.size5{font-size:.625em}.katex .fontsize-ensurer.reset-size8.size6,.katex .sizing.reset-size8.size6{font-size:.69444444em}.katex .fontsize-ensurer.reset-size8.size7,.katex .sizing.reset-size8.size7{font-size:.83333333em}.katex .fontsize-ensurer.reset-size8.size8,.katex .sizing.reset-size8.size8{font-size:1em}.katex .fontsize-ensurer.reset-size8.size9,.katex .sizing.reset-size8.size9{font-size:1.2em}.katex .fontsize-ensurer.reset-size8.size10,.katex .sizing.reset-size8.size10{font-size:1.44027778em}.katex .fontsize-ensurer.reset-size8.size11,.katex .sizing.reset-size8.size11{font-size:1.72777778em}.katex .fontsize-ensurer.reset-size9.size1,.katex .sizing.reset-size9.size1{font-size:.28935185em}.katex .fontsize-ensurer.reset-size9.size2,.katex .sizing.reset-size9.size2{font-size:.34722222em}.katex .fontsize-ensurer.reset-size9.size3,.katex .sizing.reset-size9.size3{font-size:.40509259em}.katex .fontsize-ensurer.reset-size9.size4,.katex .sizing.reset-size9.size4{font-size:.46296296em}.katex .fontsize-ensurer.reset-size9.size5,.katex .sizing.reset-size9.size5{font-size:.52083333em}.katex .fontsize-ensurer.reset-size9.size6,.katex .sizing.reset-size9.size6{font-size:.5787037em}.katex .fontsize-ensurer.reset-size9.size7,.katex .sizing.reset-size9.size7{font-size:.69444444em}.katex .fontsize-ensurer.reset-size9.size8,.katex .sizing.reset-size9.size8{font-size:.83333333em}.katex .fontsize-ensurer.reset-size9.size9,.katex .sizing.reset-size9.size9{font-size:1em}.katex .fontsize-ensurer.reset-size9.size10,.katex .sizing.reset-size9.size10{font-size:1.20023148em}.katex .fontsize-ensurer.reset-size9.size11,.katex .sizing.reset-size9.size11{font-size:1.43981481em}.katex .fontsize-ensurer.reset-size10.size1,.katex .sizing.reset-size10.size1{font-size:.24108004em}.katex .fontsize-ensurer.reset-size10.size2,.katex .sizing.reset-size10.size2{font-size:.28929605em}.katex .fontsize-ensurer.reset-size10.size3,.katex .sizing.reset-size10.size3{font-size:.33751205em}.katex .fontsize-ensurer.reset-size10.size4,.katex .sizing.reset-size10.size4{font-size:.38572806em}.katex .fontsize-ensurer.reset-size10.size5,.katex .sizing.reset-size10.size5{font-size:.43394407em}.katex .fontsize-ensurer.reset-size10.size6,.katex .sizing.reset-size10.size6{font-size:.48216008em}.katex .fontsize-ensurer.reset-size10.size7,.katex .sizing.reset-size10.size7{font-size:.57859209em}.katex .fontsize-ensurer.reset-size10.size8,.katex .sizing.reset-size10.size8{font-size:.69431051em}.katex .fontsize-ensurer.reset-size10.size9,.katex .sizing.reset-size10.size9{font-size:.83317261em}.katex .fontsize-ensurer.reset-size10.size10,.katex .sizing.reset-size10.size10{font-size:1em}.katex .fontsize-ensurer.reset-size10.size11,.katex .sizing.reset-size10.size11{font-size:1.19961427em}.katex .fontsize-ensurer.reset-size11.size1,.katex .sizing.reset-size11.size1{font-size:.20096463em}.katex .fontsize-ensurer.reset-size11.size2,.katex .sizing.reset-size11.size2{font-size:.24115756em}.katex .fontsize-ensurer.reset-size11.size3,.katex .sizing.reset-size11.size3{font-size:.28135048em}.katex .fontsize-ensurer.reset-size11.size4,.katex .sizing.reset-size11.size4{font-size:.32154341em}.katex .fontsize-ensurer.reset-size11.size5,.katex .sizing.reset-size11.size5{font-size:.36173633em}.katex .fontsize-ensurer.reset-size11.size6,.katex .sizing.reset-size11.size6{font-size:.40192926em}.katex .fontsize-ensurer.reset-size11.size7,.katex .sizing.reset-size11.size7{font-size:.48231511em}.katex .fontsize-ensurer.reset-size11.size8,.katex .sizing.reset-size11.size8{font-size:.57877814em}.katex .fontsize-ensurer.reset-size11.size9,.katex .sizing.reset-size11.size9{font-size:.69453376em}.katex .fontsize-ensurer.reset-size11.size10,.katex .sizing.reset-size11.size10{font-size:.83360129em}.katex .fontsize-ensurer.reset-size11.size11,.katex .sizing.reset-size11.size11{font-size:1em}.katex .delimsizing.size1{font-family:KaTeX_Size1}.katex .delimsizing.size2{font-family:KaTeX_Size2}.katex .delimsizing.size3{font-family:KaTeX_Size3}.katex .delimsizing.size4{font-family:KaTeX_Size4}.katex .delimsizing.mult .delim-size1>span{font-family:KaTeX_Size1}.katex .delimsizing.mult .delim-size4>span{font-family:KaTeX_Size4}.katex .nulldelimiter{display:inline-block;width:.12em}.katex .delimcenter,.katex .op-symbol{position:relative}.katex .op-symbol.small-op{font-family:KaTeX_Size1}.katex .op-symbol.large-op{font-family:KaTeX_Size2}.katex .accent>.vlist-t,.katex .op-limits>.vlist-t{text-align:center}.katex .accent .accent-body{position:relative}.katex .accent .accent-body:not(.accent-full){width:0}.katex .overlay{display:block}.katex .mtable .vertical-separator{display:inline-block;min-width:1px}.katex .mtable .arraycolsep{display:inline-block}.katex .mtable .col-align-c>.vlist-t{text-align:center}.katex .mtable .col-align-l>.vlist-t{text-align:left}.katex .mtable .col-align-r>.vlist-t{text-align:right}.katex .svg-align{text-align:left}.katex svg{fill:currentColor;stroke:currentColor;fill-rule:nonzero;fill-opacity:1;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;display:block;height:inherit;position:absolute;width:100%}.katex svg path{stroke:none}.katex img{border-style:none;max-height:none;max-width:none;min-height:0;min-width:0}.katex .stretchy{display:block;overflow:hidden;position:relative;width:100%}.katex .stretchy:after,.katex .stretchy:before{content:""}.katex .hide-tail{overflow:hidden;position:relative;width:100%}.katex .halfarrow-left{left:0;overflow:hidden;position:absolute;width:50.2%}.katex .halfarrow-right{overflow:hidden;position:absolute;right:0;width:50.2%}.katex .brace-left{left:0;overflow:hidden;position:absolute;width:25.1%}.katex .brace-center{left:25%;overflow:hidden;position:absolute;width:50%}.katex .brace-right{overflow:hidden;position:absolute;right:0;width:25.1%}.katex .x-arrow-pad{padding:0 .5em}.katex .cd-arrow-pad{padding:0 .55556em 0 .27778em}.katex .mover,.katex .munder,.katex .x-arrow{text-align:center}.katex .boxpad{padding:0 .3em}.katex .fbox,.katex .fcolorbox{border:.04em solid;box-sizing:border-box}.katex .cancel-pad{padding:0 .2em}.katex .cancel-lap{margin-left:-.2em;margin-right:-.2em}.katex .sout{border-bottom-style:solid;border-bottom-width:.08em}.katex .angl{border-right:.049em solid;border-top:.049em solid;box-sizing:border-box;margin-right:.03889em}.katex .anglpad{padding:0 .03889em}.katex .eqn-num:before{content:"(" counter(katexEqnNo) ")";counter-increment:katexEqnNo}.katex .mml-eqn-num:before{content:"(" counter(mmlEqnNo) ")";counter-increment:mmlEqnNo}.katex .mtr-glue{width:50%}.katex .cd-vert-arrow{display:inline-block;position:relative}.katex .cd-label-left{display:inline-block;position:absolute;right:calc(50% + .3em);text-align:left}.katex .cd-label-right{display:inline-block;left:calc(50% + .3em);position:absolute;text-align:right}.katex-display{display:block;margin:1em 0;text-align:center}.katex-display>.katex{display:block;text-align:center;white-space:nowrap}.katex-display>.katex>.katex-html{display:block;position:relative}.katex-display>.katex>.katex-html>.tag{position:absolute;right:0}.katex-display.leqno>.katex>.katex-html>.tag{left:0;right:auto}.katex-display.fleqn>.katex{padding-left:2em;text-align:left}body{counter-reset:katexEqnNo mmlEqnNo}
</style><style id="__markdown-viewer__texmath_css">/* style for html inside of browsers */
.katex { font-size: 1em !important; } /* align KaTeX font-size to surrounding text */
eq { display: inline-block; }
eqn { display: block}
section.eqno {
display: flex;
flex-direction: row;
align-content: space-between;
align-items: center;
}
section.eqno > eqn {
width: 100%;
margin-left: 3em;
}
section.eqno > span {
width:3em;
text-align:right;
}
</style><style id="__markdown-viewer__menu_css">/* Style for the menu, possible positions/visibility */
#__markdown-viewer__tools {
margin:0;
padding:0;
background:#555;
color:#eee;
box-shadow:0 -1px rgba(0,0,0,.5) inset;
border-radius: .5em;
max-width: 25%;
min-width: 2.8em;
min-height: 3em;
z-index: 2147483647;
position: relative;
}
#__markdown-viewer__tools.floating {
float:right;
margin: 0 0 .5em .5em;
}
#__markdown-viewer__tools.fixed {
max-height: calc(100vh - 1em);
overflow-y: auto;
position:fixed;
top:.5em;
right:1em;
}
#__markdown-viewer__tools.hidden {
display:none;
}
@media print {
#__markdown-viewer__tools {
display: none;
}
}
#__markdown-viewer__tools a[href]:after {
content: "";
}
/* Style for the menu top */
label[for=__markdown-viewer__show-tools] {
display:block;
padding:0 18px 0 12px;
line-height:3em;
background:#333;
cursor:pointer;
border-radius: .5em;
min-height: 3em;
width: .9em;
position: absolute;
right: 0;
}
input#__markdown-viewer__show-tools:not(:checked) ~ label {
margin-left: -.9em;
}
input#__markdown-viewer__show-tools:checked ~ label {
}
label[for=__markdown-viewer__show-tools]:before{
}
label[for=__markdown-viewer__show-tools]:after {
content:"";
display:inline-block;
float:right;
margin-top:1.5em;
right:5px;
width:0;
height:0;
border-style: solid;
border-color: rgba(255,255,255,.5) transparent;
border-width: 4px 4px 0 4px;
transition:border-bottom .1s, border-top .1s .1s;
}
input#__markdown-viewer__show-tools:checked ~ label:after {
border-top-width:0;
border-bottom-width:4px;
transition:border-top .1s, border-bottom .1s .1s;
}
/* hide the input that tracks the menu's visibility */
input#__markdown-viewer__show-tools {
display:none;
}
/* style, and hide/show menu items based on the input being checked */
#__markdown-viewer__tools > .toggleable {
overflow:hidden;
transition-property:max-height, max-width, padding-top, padding-bottom, margin-top, margin-bottom;
transition-duration:0.5s;
}
input#__markdown-viewer__show-tools:checked ~ .toggleable {
/* maxes should be 'none' or infinite values, however those are not aniimatable, so just put something big enough. */
max-width: 2000px;
max-height: 2000px;
overflow-y: auto;
transition-timing-function:ease-in;
}
input#__markdown-viewer__show-tools:not(:checked) ~ .toggleable {
max-height:0;
max-width:0;
transition-timing-function:ease-out;
padding-top:0;
padding-bottom:0;
margin-top:0;
margin-bottom:0;
}
/* style the table of contents and its items */
#__markdown-viewer__toc {
display:block;
padding: .5em;
border:0;
}
#__markdown-viewer__toc::before {
content: "Table of Contents";
text-align: center;
display: block;
font-weight: bold;
text-decoration: underline;
}
#__markdown-viewer__toc {
margin-top: 2em;
}
#__markdown-viewer__tools.fixed input#__markdown-viewer__show-tools:checked ~ #__markdown-viewer__toc {
max-height: calc(100vh - 16em);
}
input#__markdown-viewer__show-tools:checked ~ #__markdown-viewer__toc::before {
position: absolute;
top: .5em;
left: 0;
right: 3em;
}
#__markdown-viewer__tools select {
max-width: 40%;
margin: 0 .5em;
}
#__markdown-viewer__tools select,
#__markdown-viewer__toc * {
white-space: nowrap;
overflow-x: hidden;
text-overflow: ellipsis;
}
#__markdown-viewer__tools a {
color: white;
text-decoration: none;
}
#__markdown-viewer__toc ul {
list-style: inside "• ";
padding: 0;
margin: 0;
}
#__markdown-viewer__toc ul ul {
padding-left: 1.5em;
}
/* Style the "Download Source" button at the end of the menu */
#__markdown-viewer__tools > p {
text-align:center;
padding: 0 .5em;
}
#__markdown-viewer__download {
/* appearance: button; */
-moz-appearance: button !important;
display:inline-block;
text-align: center;
text-decoration:none;
margin: .5em auto;
}
</style><style id="__markdown-viewer__custom_css"></style><meta name="viewport" content="width=device-width, initial-scale=1"><title>Generating Bump-Allocated ASTs</title></head><body><div id="__markdown-viewer__tools" class="floating"><input type="checkbox" id="__markdown-viewer__show-tools"><label for="__markdown-viewer__show-tools"></label><div id="__markdown-viewer__toc" class="toggleable"><ul><li><a href="#generating-bump-allocated-asts">Generating Bump-Allocated ASTs</a></li></ul></div><p class="toggleable">Pick a markdown and code style:<br><select id="__markdown-viewer__mdselect"><option value="sss">default</option><option value="github">github</option></select><select id="__markdown-viewer__hlselect"><option value="a11y-dark">a11y-dark</option><option value="a11y-light">a11y-light</option><option value="a11y-auto">a11y-auto</option><option value="agate">agate</option><option value="androidstudio">androidstudio</option><option value="an-old-hope">an-old-hope</option><option value="arduino-light">arduino-light</option><option value="arta">arta</option><option value="ascetic">ascetic</option><option value="atelier-cave-dark">atelier-cave-dark</option><option value="atelier-cave-light">atelier-cave-light</option><option value="atelier-cave-auto">atelier-cave-auto</option><option value="atelier-dune-dark">atelier-dune-dark</option><option value="atelier-dune-light">atelier-dune-light</option><option value="atelier-dune-auto">atelier-dune-auto</option><option value="atelier-estuary-dark">atelier-estuary-dark</option><option value="atelier-estuary-light">atelier-estuary-light</option><option value="atelier-estuary-auto">atelier-estuary-auto</option><option value="atelier-forest-dark">atelier-forest-dark</option><option value="atelier-forest-light">atelier-forest-light</option><option value="atelier-forest-auto">atelier-forest-auto</option><option value="atelier-heath-dark">atelier-heath-dark</option><option value="atelier-heath-light">atelier-heath-light</option><option value="atelier-heath-auto">atelier-heath-auto</option><option value="atelier-lakeside-dark">atelier-lakeside-dark</option><option value="atelier-lakeside-light">atelier-lakeside-light</option><option value="atelier-lakeside-auto">atelier-lakeside-auto</option><option value="atelier-plateau-dark">atelier-plateau-dark</option><option value="atelier-plateau-light">atelier-plateau-light</option><option value="atelier-plateau-auto">atelier-plateau-auto</option><option value="atelier-savanna-dark">atelier-savanna-dark</option><option value="atelier-savanna-light">atelier-savanna-light</option><option value="atelier-savanna-auto">atelier-savanna-auto</option><option value="atelier-seaside-dark">atelier-seaside-dark</option><option value="atelier-seaside-light">atelier-seaside-light</option><option value="atelier-seaside-auto">atelier-seaside-auto</option><option value="atelier-sulphurpool-dark">atelier-sulphurpool-dark</option><option value="atelier-sulphurpool-light">atelier-sulphurpool-light</option><option value="atelier-sulphurpool-auto">atelier-sulphurpool-auto</option><option value="atom-one-dark">atom-one-dark</option><option value="atom-one-dark-reasonable">atom-one-dark-reasonable</option><option value="atom-one-light">atom-one-light</option><option value="brown-paper">brown-paper</option><option value="codepen-embed">codepen-embed</option><option value="color-brewer">color-brewer</option><option value="darcula">darcula</option><option value="dark">dark</option><option value="default">default</option><option value="docco">docco</option><option value="dracula">dracula</option><option value="far">far</option><option value="foundation">foundation</option><option value="github">github</option><option value="github-gist">github-gist</option><option value="gml">gml</option><option value="googlecode">googlecode</option><option value="gradient-dark">gradient-dark</option><option value="grayscale">grayscale</option><option value="gruvbox-dark">gruvbox-dark</option><option value="gruvbox-light">gruvbox-light</option><option value="gruvbox-auto">gruvbox-auto</option><option value="hopscotch">hopscotch</option><option value="hybrid">hybrid</option><option value="idea">idea</option><option value="ir-black">ir-black</option><option value="isbl-editor-dark">isbl-editor-dark</option><option value="isbl-editor-light">isbl-editor-light</option><option value="isbl-editor-auto">isbl-editor-auto</option><option value="kimbie">kimbie</option><option value="kimbie">kimbie</option><option value="lightfair">lightfair</option><option value="lioshi">lioshi</option><option value="magula">magula</option><option value="mono-blue">mono-blue</option><option value="monokai">monokai</option><option value="monokai-sublime">monokai-sublime</option><option value="night-owl">night-owl</option><option value="nnfx">nnfx</option><option value="nnfx-dark">nnfx-dark</option><option value="nord">nord</option><option value="obsidian">obsidian</option><option value="ocean">ocean</option><option value="paraiso-dark">paraiso-dark</option><option value="paraiso-light">paraiso-light</option><option value="paraiso-auto">paraiso-auto</option><option value="pojoaque">pojoaque</option><option value="purebasic">purebasic</option><option value="qtcreator_dark">qtcreator_dark</option><option value="qtcreator_light">qtcreator_light</option><option value="qtcreator_auto">qtcreator_auto</option><option value="railscasts">railscasts</option><option value="rainbow">rainbow</option><option value="routeros">routeros</option><option value="school-book">school-book</option><option value="shades-of-purple">shades-of-purple</option><option value="solarized-dark">solarized-dark</option><option value="solarized-light">solarized-light</option><option value="solarized-auto">solarized-auto</option><option value="srcery">srcery</option><option value="sunburst">sunburst</option><option value="tomorrow">tomorrow</option><option value="tomorrow-night">tomorrow-night</option><option value="tomorrow-night-blue">tomorrow-night-blue</option><option value="tomorrow-night-bright">tomorrow-night-bright</option><option value="tomorrow-night-eighties">tomorrow-night-eighties</option><option value="vs">vs</option><option value="vs2015">vs2015</option><option value="xcode">xcode</option><option value="xt256">xt256</option><option value="zenburn">zenburn</option></select></p><p class="toggleable"><a id="__markdown-viewer__download" download="markdown.html" style="display: none;" href="blob:null/e35bb266-bb12-4772-a6bd-552546116841">Download as HTML</a></p></div><div class="markdownRoot"><h2 id="generating-bump-allocated-asts">Generating <a href="https://docs.rs/bumpalo/latest/bumpalo/index.html">Bump</a>-Allocated ASTs</h2>
<p>Abstract syntax trees are usually defined recursively. This normally means
some form of smart pointer is requried to implement them. The problem with
this aspect of Rust is that the smart pointers block <em>nested</em> patterns from
matching against AST expressions. It is possible to define recursive structures
using references (borrows) but all references in an AST structure must have
compatible lifetimes. An "arena" structure is required to hold the values that
they reference. While it's possible to define such an arena manually, rustlr
provides support for using the <a href="https://docs.rs/bumpalo/latest/bumpalo/index.html">bumpalo</a> crate.</p>
<p>A grammar can begin with the declaration</p>
<pre><code><span class="hljs-keyword">auto</span>-bump
</code></pre>
<p>in place of <code>auto</code>, which enables the generation of bump-allocated ASTs.</p>
<p>The disadvantage of bumpalo is that it bipasses some of the memory
safety checks of Rust. Bump-allocation is not recommended if frequent
changes are made to the allocated structures. They are appropriate if
the ASTs remain relatively stable once created, with few changes if
any, until the entire structure can be dropped.</p>
<p>The advantage of bump-allocation, besides an increase in speed, is
that it enables the matching of nested patterns against recursive
types. Consider the following recursive type that tries to avoid
smart pointers:</p>
<pre><code><span class="hljs-class"><span class="hljs-keyword">enum</span> <span class="hljs-title">Expr</span></span><<span class="hljs-symbol">'t</span>> {
Var(&<span class="hljs-symbol">'t</span> <span class="hljs-built_in">str</span>),
Negative(&<span class="hljs-symbol">'t</span> Expr<<span class="hljs-symbol">'t</span>>),
Plus(&<span class="hljs-symbol">'t</span> Expr<<span class="hljs-symbol">'t</span>>, &<span class="hljs-symbol">'t</span> Expr<<span class="hljs-symbol">'t</span>>),
Minus(&<span class="hljs-symbol">'t</span> Expr<<span class="hljs-symbol">'t</span>>, &<span class="hljs-symbol">'t</span> Expr<<span class="hljs-symbol">'t</span>>),
}
</code></pre>
<p>and a function that "pretty-prints" such expressions. The function will print
<code>x</code> instead of <code>--x</code>, <code>x-y</code> instead of <code>x+-y</code>, and <code>x+y</code> instead of <code>x--y</code>.
It also pushes negation inside plus/minus, and only prints parentheses as
required by the non-associative minus symbol.</p>
<pre><code><span class="hljs-function"><span class="hljs-keyword">fn</span> <span class="hljs-title">pprint</span></span><<span class="hljs-symbol">'t</span>>(expr:&<span class="hljs-symbol">'t</span> Expr<<span class="hljs-symbol">'t</span>>,) {
<span class="hljs-keyword">use</span> crate::Expr::*;
<span class="hljs-keyword">match</span> expr {
Negative(Negative(n)) => pprint(n),
Negative(Plus(a,b)) => pprint(&Minus(&Negative(a),b)),
Negative(Minus(a,b)) => pprint(&Plus(&Negative(a),b)),
Negative(n) => {<span class="hljs-built_in">print!</span>(<span class="hljs-string">"-"</span>); pprint(n)},
Plus(a,Negative(b)) => pprint(&Minus(a,b)),
Minus(a,Negative(b)) => pprint(&Plus(a,b)),
Minus(a,p@Minus(_,_)) => { pprint(a); <span class="hljs-built_in">print!</span>(<span class="hljs-string">"-("</span>); pprint(p); <span class="hljs-built_in">print!</span>(<span class="hljs-string">")"</span>)},
Minus(a,p@Plus(_,_)) => { pprint(a); <span class="hljs-built_in">print!</span>(<span class="hljs-string">"+("</span>); pprint(p); <span class="hljs-built_in">print!</span>(<span class="hljs-string">")"</span>)},
Plus(a,b) => {pprint(a); <span class="hljs-built_in">print!</span>(<span class="hljs-string">"+"</span>); pprint(b);},
Minus(a,b) => {pprint(a); <span class="hljs-built_in">print!</span>(<span class="hljs-string">"-"</span>); pprint(b)},
Var(x) => <span class="hljs-built_in">print!</span>(<span class="hljs-string">"{}"</span>,x),
}<span class="hljs-comment">//match expr</span>
}<span class="hljs-comment">//pprint</span>
</code></pre>
<p>Then given</p>
<pre><code> let q = Plus(&Negative(&Negative(&<span class="hljs-keyword">Var</span>(<span class="hljs-string">"x"</span>))),&Negative(&<span class="hljs-keyword">Var</span>(<span class="hljs-string">"y"</span>)));
pprint(&q);
</code></pre>
<p>will print <code>x-y</code>. Such a "declarative" style of programming is not
possible if the type is defined using Box (or <a href="https://docs.rs/rustlr/latest/rustlr/generic_absyn/struct.LBox.html">LBox</a>).</p>
<p>However, allocating such structures temporarily on the stack is impractical.
We would not be able to return references to them.
You may also get the dreaded compiler error <em>"creates a temporary which is freed while still in use"</em> when writing expressions such as <code>Plus(&q,&Negative(&q))</code>.</p>
<p>The <a href="https://docs.rs/bumpalo/latest/bumpalo/index.html">bumpalo</a> crate offers an "arena", a kind of <em>simulated heap</em>,
that allow us to access these structures within the lifetime of the arena:</p>
<pre><code> <span class="hljs-keyword">let</span> bump = bumpalo::Bump::new(); <span class="hljs-comment">// creates new bump arena</span>
<span class="hljs-keyword">let</span> p = bump.alloc(Negative(bump.alloc(Negative(bump.alloc(Var(<span class="hljs-string">"z"</span>))))));
</code></pre>
<p>The <a href="https://docs.rs/bumpalo/latest/bumpalo/struct.Bump.html#method.alloc">Bump::alloc</a> function returns a reference to the allocated memory within
the arena. We can pass a reference to the "bump" to a function, which would
then be able to construct and return bump-allocated structures using references
of the same lifetime.</p>
<p>Rustlr (since version 0.3.93) can now generate such structures automatically.
To use this feature, it is necessary to include <code>bumpalo = "3"</code> in a crate's
dependencies. The easiest way to enable bumpalo is through enhancements to
the <a href="https://docs.rs/rustlr/latest/rustlr/lexer_interface/struct.LexSource.html">Lexsource</a> structure. The following code fragment
demonstrates how to envoke a parser generated from an <code>auto-bump</code> grammar,
<a href="https://cs.hofstra.edu/~cscccl/rustlr_project/bumpcalc/bautocalc.grammar">bautocalc.grammar</a>,</p>
<pre><code> <span class="hljs-keyword">let</span> srcfile = <span class="hljs-string">"test1.txt"</span>; <span class="hljs-comment">// srcfile names file to parse</span>
<span class="hljs-keyword">let</span> source=LexSource::with_bump(srcfile).unwrap();
<span class="hljs-keyword">let</span> <span class="hljs-keyword">mut</span> scanner = bautocalcparser::bautocalclexer::from_source(&source);
<span class="hljs-keyword">let</span> <span class="hljs-keyword">mut</span> parser = bautocalcparser::make_parser();
<span class="hljs-keyword">let</span> result = bautocalcparser::parse_with(&<span class="hljs-keyword">mut</span> parser, &<span class="hljs-keyword">mut</span> scanner);
</code></pre>
<p>A Rustlr Lexsource object containing a <a href="https://docs.rs/bumpalo/latest/bumpalo/struct.Bump.html">Bump</a> is created with <a href="https://docs.rs/rustlr/latest/rustlr/lexer_interface/struct.LexSource.html#method.with_bump">Lexsource::with_bump</a>.
The <code>parse_with</code> function, which is generated for individual parsers, will place
a reference to the bump arena inside the parser. The automatically
generated semantic actions will call <a href="https://docs.rs/bumpalo/latest/bumpalo/struct.Bump.html#method.alloc">Bump::alloc</a> to create ASTS that will have the
same lifetime as the Lexsource structure.</p>
<p>The link to the entire sample crate is <a href="https://cs.hofstra.edu/~cscccl/rustlr_project/bumpcalc/">here</a>.</p>
<hr>
</div></body></html>