/* Pre-rendered MathJax 4.1.0 styles for the three fixed method equations. */
:root {
  --mjx-fg-red: 255, 0, 0;
  --mjx-fg-green: 0, 255, 0;
  --mjx-fg-blue: 0, 0, 255;
  --mjx-fg-yellow: 255, 255, 0;
  --mjx-fg-cyan: 0, 255, 255;
  --mjx-fg-magenta: 255, 0, 255;
  --mjx-fg-white: 255, 255, 255;
  --mjx-fg-black: 0, 0, 0;
  --mjx-bg-red: 255, 0, 0;
  --mjx-bg-green: 0, 255, 0;
  --mjx-bg-blue: 0, 0, 255;
  --mjx-bg-yellow: 255, 255, 0;
  --mjx-bg-cyan: 0, 255, 255;
  --mjx-bg-magenta: 255, 0, 255;
  --mjx-bg-white: 255, 255, 255;
  --mjx-bg-black: 0, 0, 0;
  --mjx-live-bg-color: white;
  --mjx-live-shadow-color: #888;
  --mjx-live-border-color: #CCCCCC;
  --mjx-bg1-color: rgba(var(--mjx-bg-blue), var(--mjx-bg-alpha));
  --mjx-fg1-color: rgba(var(--mjx-fg-black), 1);
  --mjx-bg2-color: rgba(var(--mjx-bg-red), 1);
  --mjx-fg2-color: rgba(var(--mjx-fg-black), 1);
  --mjx-bg1-alpha: 0.2;
  --mjx-fg1-alpha: 1;
  --mjx-bg2-alpha: 1;
  --mjx-fg2-alpha: 1;
}

@media (prefers-color-scheme: dark) {
  :root {
    --mjx-bg-blue: 132, 132, 255;
      --mjx-bg-white: 0, 0, 0;
      --mjx-bg-black: 255, 255, 255;
      --mjx-fg-white: 0, 0, 0;
      --mjx-fg-black: 255, 255, 255;
      --mjx-live-bg-color: #222025;
      --mjx-live-shadow-color: black;
      --mjx-live-border-color: #7C7C7C;
      --mjx-bg1-alpha: 0.3;
      --mjx-fg1-alpha: 1;
      --mjx-bg2-alpha: 1;
      --mjx-fg2-alpha: 1;
  }
}

.MJX_LiveRegion {
  position: absolute;
  top: 0;
  display: none;
  width: auto;
  height: auto;
  padding: 0;
  opacity: 1;
  z-index: 202;
  left: 0;
  right: 0;
  margin: 0 auto;
  background-color: var(--mjx-live-bg-color);
  box-shadow: 0px 5px 20px var(--mjx-live-shadow-color);
  border: 2px solid var(--mjx-live-border-color);
}

.MJX_LiveRegion_Show {
  display: block;
}

.MJX_LiveRegion > div {
  color: var(--mjx-fg1-color);
  background-color: var(--mjx-bg1-color);
}

mjx-container [data-sre-highlight-1]:not([data-mjx-collapsed], rect) {
  color: var(--mjx-fg1-color) ! important;
  fill: var(--mjx-fg1-color) ! important;
}

mjx-container:not([data-mjx-clone-container]) [data-sre-highlight-1]:not([data-sre-enclosed], rect) {
  background-color: var(--mjx-bg1-color) ! important;
}

mjx-container rect[data-sre-highlight-1]:not([data-sre-enclosed]) {
  fill: var(--mjx-bg1-color) ! important;
}

mjx-container [data-sre-highlight-2] {
  color: var(--mjx-fg2-color) ! important;
  background-color: var(--mjx-bg2-color) ! important;
  fill: var(--mjx-fg2-color) ! important;
}

mjx-container rect[data-sre-highlight-2] {
  fill: var(--mjx-bg2-color) ! important;
}
.MJX_HoverRegion {
  display: block;
  position: absolute;
  width: max-content;
  height: auto;
  padding: 0;
  opacity: 1;
  z-index: 202;
  margin: 0 auto;
  background-color: white;
  line-height: 0;
  box-shadow: 0px 10px 20px #888;
  border: 2px solid #CCCCCC;
}

.MJX_HoverRegion > div {
  overflow: hidden;
  color: var(--mjx-fg1-color);
  background-color: var(--mjx-bg1-color);
}

@media (prefers-color-scheme: dark) {
  .MJX_HoverRegion {
    background-color: #222025;
      box-shadow: 0px 5px 20px #000;
      border: 1px solid #7C7C7C;
  }
}

mjx-container[data-mjx-clone-container] {
  padding: 2px ! important;
}

mjx-math > mjx-mlabeledtr {
  display: inline-block;
  margin-right: .5em ! important;
}

mjx-math > mjx-mtd {
  float: right;
}
.MJX_ToolTip {
  width: auto;
  height: auto;
  opacity: 1;
  text-align: center;
  border-radius: 4px;
  padding: 0;
  border-bottom: 1px dotted black;
  position: absolute;
  display: inline-block;
  background-color: white;
  z-index: 202;
}

.MJX_ToolTip > div {
  border-radius: inherit;
  padding: 0 2px;
}

@media (prefers-color-scheme: dark) {
  .MJX_ToolTip {
    background-color: #222025;
      box-shadow: 0px 5px 20px #000;
      border: 1px solid #7C7C7C;
  }
}
.CtxtMenu_Menu {
  position: absolute;
  background-color: white;
  color: black;
  width: auto;
  padding: 5px 0px;
  border: 1px solid #CCCCCC;
  margin: 0;
  cursor: default;
  font: menu;
  text-align: left;
  text-indent: 0;
  text-transform: none;
  line-height: normal;
  letter-spacing: normal;
  word-spacing: normal;
  word-wrap: normal;
  white-space: nowrap;
  float: none;
  z-index: 1001;
  border-radius: 5px;
  box-shadow: 0px 10px 20px #808080;
}
.CtxtMenu_MenuItem {
  padding: 1px 2em;
  background: transparent;
}
.CtxtMenu_MenuArrow {
  position: absolute;
  right: 0.5em;
  padding-top: 0.25em;
  color: #666666;
  font-family: null;
  font-size: 0.75em;
}
.CtxtMenu_MenuActive .CtxtMenu_MenuArrow {
  color: white;
}
.CtxtMenu_MenuArrow.CtxtMenu_RTL {
  left: 0.5em;
  right: auto;
}
.CtxtMenu_MenuCheck {
  position: absolute;
  left: 0.7em;
  font-family: null;
}
.CtxtMenu_MenuCheck.CtxtMenu_RTL {
  right: 0.7em;
  left: auto;
}
.CtxtMenu_MenuRadioCheck {
  position: absolute;
  left: 0.7em;
}
.CtxtMenu_MenuRadioCheck.CtxtMenu_RTL {
  right: 0.7em;
  left: auto;
}
.CtxtMenu_MenuInputBox {
  padding-left: 1em;
  right: 0.5em;
  color: #666666;
  font-family: null;
}
.CtxtMenu_MenuInputBox.CtxtMenu_RTL {
  left: 0.1em;
}
.CtxtMenu_MenuComboBox {
  left: 0.1em;
  padding-bottom: 0.5em;
}
.CtxtMenu_MenuSlider {
  left: 0.1em;
}
.CtxtMenu_SliderValue {
  position: absolute;
  right: 0.1em;
  padding-top: 0.25em;
  color: #333333;
  font-size: 0.75em;
}
.CtxtMenu_MenuActive .CtxtMenu_SliderValue {
  color: #DDDDDD;
}
.CtxtMenu_SliderBar {
  outline: none;
  background: #D3D3D3;
}
.CtxtMenu_MenuLabel {
  padding: 1px 2em 3px 1.33em;
  font-style: italic;
}
.CtxtMenu_MenuRule {
  border-top: 1px solid #DDDDDD;
  margin: 4px 3px;
}
.CtxtMenu_MenuDisabled {
  color: #999;
}
.CtxtMenu_MenuActive {
  background-color: #606872;
  color: white;
}
.CtxtMenu_MenuDisabled:focus {
  background-color: #E8E8E8;
}
.CtxtMenu_MenuLabel:focus {
  background-color: #E8E8E8;
}
.CtxtMenu_ContextMenu:focus {
  outline: none;
}
.CtxtMenu_ContextMenu .CtxtMenu_MenuItem:focus {
  outline: none;
}
.CtxtMenu_SelectionMenu {
  position: relative;
  float: left;
  border-bottom: none;
  box-shadow: none ! important;
  border-radius: 0px !important;
}
.CtxtMenu_SelectionItem {
  padding-right: 1em;
}
.CtxtMenu_Selection {
  right: 40%;
  width: 50%;
}
.CtxtMenu_SelectionBox {
  padding: 0em;
  max-height: 20em;
  max-width: none;
  background-color: #FFFFFF;
}
.CtxtMenu_SelectionDivider {
  clear: both;
  border-top: 2px solid #000000;
}
.CtxtMenu_Menu .CtxtMenu_MenuClose {
  top: -10px;
  left: -10px;
}
@media (prefers-color-scheme: dark) /* menu */ {
  .CtxtMenu_Menu {
  color: #E0E0E0;
  background-color: #242436;
  box-shadow: 0px 10px 20px #000;
  border: 1px solid #808080;
}
  .CtxtMenu_SliderValue {
  color: #D0D0D0;
}
  .CtxtMenu_MenuDisabled:focus {
  background-color: #383838;
}
  .CtxtMenu_MenuLabel:focus {
  background-color: #585858;
}
  .CtxtMenu_MenuRule {
  border-top: 1px solid #808080;
}
  .CtxtMenu_SelectionDivider {
  border-top: 2px solid #808080;
};
}
.CtxtMenu_MenuClose {
  position: absolute;
  cursor: pointer;
  display: inline-block;
  border: 2px solid #AAA;
  border-radius: 18px;
  font-family:  "Courier New", Courier;
  font-size: 24px;
  color: #F0F0F0;
}
.CtxtMenu_MenuClose span {
  display: block;
  background-color: #AAA;
  border: 1.5px solid;
  border-radius: 18px;
  line-height: 0;
  padding: 8px 0 6px;
}
.CtxtMenu_MenuClose:hover {
  color: white !important;
  border: 2px solid #CCC !important;
}
.CtxtMenu_MenuClose:hover span {
  background-color: #CCC !important;
}
.CtxtMenu_MenuClose:hover:focus {
  outline: none;
}

mjx-container[overflow="scroll"][display] {
  overflow: auto clip;
  min-width: initial !important;
}

mjx-container[overflow="truncate"][display] {
  overflow: hidden clip;
  min-width: initial !important;
}

mjx-container[display] {
  display: block;
  text-align: center;
  justify-content: center;
  margin: .7em 0;
  padding: .3em 2px;
}

mjx-container[display][width="full"] {
  display: flex;
}

mjx-container[justify="left"] {
  text-align: left;
  justify-content: left;
}

mjx-container[justify="right"] {
  text-align: right;
  justify-content: right;
}

mjx-container[jax="SVG"] {
  direction: ltr;
  white-space: nowrap;
}

mjx-container[jax="SVG"] > svg {
  overflow: visible;
  min-height: 1px;
  min-width: 1px;
}

mjx-container[jax="SVG"] > svg a {
  fill: blue;
  stroke: blue;
}

rect[data-sre-highlighter-added]:has(+ .mjx-selected), rect[data-sre-highlighter-bbox].mjx-selected {
  stroke: black;
  stroke-width: 80px;
}

@media (prefers-color-scheme: dark) {
  rect[data-sre-highlighter-added]:has(+ .mjx-selected), rect[data-sre-highlighter-bbox].mjx-selected {
    stroke: #C8C8C8;
  }
}

mjx-container[has-speech="true"] {
  position: relative;
  cursor: default;
}

mjx-speech {
  position: absolute;
  z-index: -1;
  left: 0;
  top: 0;
  bottom: 0;
  right: 0;
}

mjx-speech:focus {
  outline: none;
}

mjx-container .mjx-selected {
  outline: 2px solid black;
}

mjx-container a[data-mjx-href] {
  color: LinkText;
  cursor: pointer;
}

mjx-container a[data-mjx-href].mjx-visited {
  color: VisitedText;
}

mjx-container > mjx-help {
  display: none;
  position: absolute;
  top: -.3em;
  right: -.5em;
  width: .6em;
  height: .6em;
  cursor: pointer;
}

mjx-container[display="true"] > mjx-help {
  position: sticky;
  inset: -100% 0 100% 0;
  margin: -.3em -.5em 0 -.1em;
  right: 0;
  top: initial;
}

mjx-help > svg {
  stroke: black;
  width: 100%;
  height: 100%;
}

mjx-help > svg > circle {
  stroke-width: 1.5px;
  cx: 9px;
  cy: 9px;
  r: 9px;
  fill: white;
}

mjx-help > svg > circle:nth-child(2) {
  fill: var(--mjx-bg1-color);
  r: 7px;
}

mjx-help > svg > line {
  stroke-width: 2.5px;
  stroke-linecap: round;
}

mjx-help:hover > svg > circle:nth-child(2) {
  fill: white;
}

mjx-container.mjx-explorer-active > mjx-help {
  display: inline-flex;
  align-items: center;
}

@media (prefers-color-scheme: dark) /* explorer */ {
  mjx-help > svg {
    stroke: #E0E0E0;
  }
  mjx-help > svg > circle {
    fill: #404040;
  }
  mjx-help > svg > circle:nth-child(2) {
    fill: rgba(132, 132, 255, .3);
  }
  mjx-help:hover > svg > circle:nth-child(2) {
    stroke: #AAAAAA;
      fill: #404040;
  }
}

mjx-container[jax="SVG"] mjx-break {
  white-space: normal;
  line-height: 0;
  clip-path: rect(0 0 0 0);
  font-family: MJX-ZERO ! important;
}

mjx-break[size="0"] {
  letter-spacing: -0.999em;
}

mjx-break[size="1"] {
  letter-spacing: -0.889em;
}

mjx-break[size="2"] {
  letter-spacing: -0.833em;
}

mjx-break[size="3"] {
  letter-spacing: -0.778em;
}

mjx-break[size="4"] {
  letter-spacing: -0.722em;
}

mjx-break[size="5"] {
  letter-spacing: -0.667em;
}

mjx-container[jax="SVG"] mjx-break[newline]::before {
  white-space: pre;
  content: "\A";
}

mjx-break[newline] + svg[width="0.054ex"] {
  margin-right: -1px;
}

mjx-break[prebreak] {
  letter-spacing: -.999em;
}

@font-face /* zero */ {
  font-family: MJX-ZERO;
  src: url(data:application/x-font-woff;charset=utf-8;base64,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) format("woff");
}

g[data-mml-node="merror"] > g {
  fill: red;
  stroke: red;
}

g[data-mml-node="merror"] > rect[data-background] {
  fill: yellow;
  stroke: none;
}

g[data-mml-node="mtable"] > line[data-line], svg[data-table] > g > line[data-line] {
  stroke-width: 70px;
  fill: none;
}

g[data-mml-node="mtable"] > rect[data-frame], svg[data-table] > g > rect[data-frame] {
  stroke-width: 70px;
  fill: none;
}

g[data-mml-node="mtable"] > .mjx-dashed, svg[data-table] > g > .mjx-dashed {
  stroke-dasharray: 140;
}

g[data-mml-node="mtable"] > .mjx-dotted, svg[data-table] > g > .mjx-dotted {
  stroke-linecap: round;
  stroke-dasharray: 0,140;
}

g[data-mml-node="mtable"] > g > svg {
  overflow: visible;
}

[jax="SVG"] mjx-tool {
  display: inline-block;
  position: relative;
  width: 0;
  height: 0;
}

[jax="SVG"] mjx-tool > mjx-tip {
  position: absolute;
  top: 0;
  left: 0;
}

mjx-tool > mjx-tip {
  display: inline-block;
  line-height: 0;
  padding: .2em;
  border: 1px solid #888;
  background-color: #F8F8F8;
  color: black;
  box-shadow: 2px 2px 5px #AAAAAA;
}

g[data-mml-node="maction"][data-toggle] {
  cursor: pointer;
}

mjx-status {
  display: block;
  position: fixed;
  left: 1em;
  bottom: 1em;
  min-width: 25%;
  padding: .2em .4em;
  border: 1px solid #888;
  font-size: 90%;
  background-color: #F8F8F8;
  color: black;
}

g[data-mjx-collapsed] {
  fill: #55F;
}

@media (prefers-color-scheme: dark) /* svg maction */ {
  mjx-tool > mjx-tip {
    background-color: #303030;
      color: #E0E0E0;
      box-shadow: 2px 2px 5px #000;
  }
  mjx-status {
    background-color: #303030;
      color: #E0E0E0;
  }
  g[data-mjx-collapsed] {
    fill: #88F;
  }
}

foreignObject[data-mjx-xml] {
  font-family: initial;
  line-height: normal;
  overflow: visible;
}

foreignObject[data-mjx-html] {
  overflow: visible;
}

mjx-measure-xml {
  position: absolute;
  left: 0;
  top: 0;
  display: inline-block;
  line-height: normal;
  white-space: normal;
}

mjx-html {
  display: inline-block;
  line-height: normal;
  text-align: initial;
  white-space: initial;
}

mjx-html-holder {
  display: block;
  position: absolute;
  top: 0;
  left: 0;
  bottom: 0;
  right: 0;
}

mjx-container[jax="SVG"] path[data-c], mjx-container[jax="SVG"] use[data-c] {
  stroke-width: 3;
}