.MathJax_Hover_Frame { border-radius: 0.25em; box-shadow: rgb(136, 51, 170) 0px 0px 15px; display: inline-block; position: absolute; border: 1px solid rgb(170, 102, 221) !important; }
.MathJax_Menu_Button .MathJax_Hover_Arrow { position: absolute; cursor: pointer; display: inline-block; border: 2px solid rgb(170, 170, 170); border-radius: 4px; font-family: "Courier New", Courier; font-size: 9px; color: rgb(240, 240, 240); }
.MathJax_Menu_Button .MathJax_Hover_Arrow span { display: block; background-color: rgb(170, 170, 170); border: 1px solid; border-radius: 3px; line-height: 0; padding: 4px; }
.MathJax_Hover_Arrow:hover { color: white !important; border: 2px solid rgb(204, 204, 204) !important; }
.MathJax_Hover_Arrow:hover span { background-color: rgb(204, 204, 204) !important; }
#MathJax_About { position: fixed; left: 50%; width: auto; text-align: center; border: 3px outset; padding: 1em 2em; background-color: rgb(221, 221, 221); color: black; cursor: default; font-family: message-box; font-size: 120%; font-style: normal; text-indent: 0px; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; z-index: 201; border-radius: 15px; box-shadow: rgb(128, 128, 128) 0px 10px 20px; }
#MathJax_About.MathJax_MousePost { outline: none; }
.MathJax_Menu { position: absolute; background-color: white; color: black; width: auto; padding: 2px; border: 1px solid rgb(204, 204, 204); margin: 0px; cursor: default; font-variant: normal; text-align: left; text-indent: 0px; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; z-index: 201; box-shadow: rgb(128, 128, 128) 0px 10px 20px; }
.MathJax_MenuItem { padding: 2px 2em; background: transparent; }
.MathJax_MenuArrow { position: absolute; right: 0.5em; padding-top: 0.25em; color: rgb(102, 102, 102); font-size: 0.75em; }
.MathJax_MenuActive .MathJax_MenuArrow { color: white; }
.MathJax_MenuArrow.RTL { left: 0.5em; right: auto; }
.MathJax_MenuCheck { position: absolute; left: 0.7em; }
.MathJax_MenuCheck.RTL { right: 0.7em; left: auto; }
.MathJax_MenuRadioCheck { position: absolute; left: 1em; }
.MathJax_MenuRadioCheck.RTL { right: 1em; left: auto; }
.MathJax_MenuLabel { padding: 2px 2em 4px 1.33em; font-style: italic; }
.MathJax_MenuRule { border-top: 1px solid rgb(204, 204, 204); margin: 4px 1px 0px; }
.MathJax_MenuDisabled { color: graytext; }
.MathJax_MenuActive { background-color: highlight; color: highlighttext; }
.MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus { background-color: rgb(232, 232, 232); }
.MathJax_ContextMenu:focus { outline: none; }
.MathJax_ContextMenu .MathJax_MenuItem:focus { outline: none; }
#MathJax_AboutClose { top: 0.2em; right: 0.2em; }
.MathJax_Menu .MathJax_MenuClose { top: -10px; left: -10px; }
.MathJax_MenuClose { position: absolute; cursor: pointer; display: inline-block; border: 2px solid rgb(170, 170, 170); border-radius: 18px; font-family: "Courier New", Courier; font-size: 24px; color: rgb(240, 240, 240); }
.MathJax_MenuClose span { display: block; background-color: rgb(170, 170, 170); border: 1.5px solid; border-radius: 18px; line-height: 0; padding: 8px 0px 6px; }
.MathJax_MenuClose:hover { color: white !important; border: 2px solid rgb(204, 204, 204) !important; }
.MathJax_MenuClose:hover span { background-color: rgb(204, 204, 204) !important; }
.MathJax_MenuClose:hover:focus { outline: none; }
.MathJax_Preview .MJXf-math { color: inherit !important; }
.MJX_Assistive_MathML { top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); user-select: none; position: absolute !important; padding: 1px 0px 0px !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important; }
.MJX_Assistive_MathML.MJX_Assistive_MathML_Block { width: 100% !important; }
#MathJax_Zoom { position: absolute; background-color: rgb(240, 240, 240); overflow: auto; display: block; z-index: 301; padding: 0.5em; border: 1px solid black; margin: 0px; font-weight: normal; font-style: normal; text-align: left; text-indent: 0px; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; box-sizing: content-box; box-shadow: rgb(170, 170, 170) 5px 5px 15px; }
#MathJax_ZoomOverlay { position: absolute; left: 0px; top: 0px; z-index: 300; display: inline-block; width: 100%; height: 100%; border: 0px; padding: 0px; margin: 0px; background-color: white; opacity: 0; }
#MathJax_ZoomFrame { position: relative; display: inline-block; height: 0px; width: 0px; }
#MathJax_ZoomEventTrap { position: absolute; left: 0px; top: 0px; z-index: 302; display: inline-block; border: 0px; padding: 0px; margin: 0px; background-color: white; opacity: 0; }
.MathJax_Preview { color: rgb(136, 136, 136); }
#MathJax_Message { position: fixed; left: 1em; bottom: 1.5em; background-color: rgb(230, 230, 230); border: 1px solid rgb(149, 149, 149); margin: 0px; padding: 2px 8px; z-index: 102; color: black; font-size: 80%; width: auto; white-space: nowrap; }
#MathJax_MSIE_Frame { position: absolute; top: 0px; left: 0px; width: 0px; z-index: 101; border: 0px; margin: 0px; padding: 0px; }
.MathJax_Error { color: rgb(204, 0, 0); font-style: italic; }
.MJXp-script { font-size: 0.8em; }
.MJXp-right { transform-origin: right center; }
.MJXp-bold { font-weight: bold; }
.MJXp-italic { font-style: italic; }
.MJXp-scr { font-family: MathJax_Script, "Times New Roman", Times, STIXGeneral, serif; }
.MJXp-frak { font-family: MathJax_Fraktur, "Times New Roman", Times, STIXGeneral, serif; }
.MJXp-sf { font-family: MathJax_SansSerif, "Times New Roman", Times, STIXGeneral, serif; }
.MJXp-cal { font-family: MathJax_Caligraphic, "Times New Roman", Times, STIXGeneral, serif; }
.MJXp-mono { font-family: MathJax_Typewriter, "Times New Roman", Times, STIXGeneral, serif; }
.MJXp-largeop { font-size: 150%; }
.MJXp-largeop.MJXp-int { vertical-align: -0.2em; }
.MJXp-math { display: inline-block; line-height: 1.2; text-indent: 0px; font-family: "Times New Roman", Times, STIXGeneral, serif; white-space: nowrap; border-collapse: collapse; }
.MJXp-display { display: block; text-align: center; margin: 1em 0px; }
.MJXp-math span { display: inline-block; }
.MJXp-box { display: block !important; text-align: center; }
.MJXp-box::after { content: " "; }
.MJXp-rule { display: block !important; margin-top: 0.1em; }
.MJXp-char { display: block !important; }
.MJXp-mo { margin: 0px 0.15em; }
.MJXp-mfrac { margin: 0px 0.125em; vertical-align: 0.25em; }
.MJXp-denom { display: inline-table !important; width: 100%; }
.MJXp-denom > * { display: table-row !important; }
.MJXp-surd { vertical-align: top; }
.MJXp-surd > * { display: block !important; }
.MJXp-script-box > * { display: table !important; height: 50%; }
.MJXp-script-box > * > * { display: table-cell !important; vertical-align: top; }
.MJXp-script-box > :last-child > * { vertical-align: bottom; }
.MJXp-script-box > * > * > * { display: block !important; }
.MJXp-mphantom { visibility: hidden; }
.MJXp-munderover { display: inline-table !important; }
.MJXp-over { display: inline-block !important; text-align: center; }
.MJXp-over > * { display: block !important; }
.MJXp-munderover > * { display: table-row !important; }
.MJXp-mtable { vertical-align: 0.25em; margin: 0px 0.125em; }
.MJXp-mtable > * { display: inline-table !important; vertical-align: middle; }
.MJXp-mtr { display: table-row !important; }
.MJXp-mtd { text-align: center; padding: 0.5em 0px 0px 0.5em; display: table-cell !important; }
.MJXp-mtr > .MJXp-mtd:first-child { padding-left: 0px; }
.MJXp-mtr:first-child > .MJXp-mtd { padding-top: 0px; }
.MJXp-mlabeledtr { display: table-row !important; }
.MJXp-mlabeledtr > .MJXp-mtd:first-child { padding-left: 0px; }
.MJXp-mlabeledtr:first-child > .MJXp-mtd { padding-top: 0px; }
.MJXp-merror { background-color: rgb(255, 255, 136); color: rgb(204, 0, 0); border: 1px solid rgb(204, 0, 0); padding: 1px 3px; font-style: normal; font-size: 90%; }
.MJXp-scale0 { transform: scaleX(0); }
.MJXp-scale1 { transform: scaleX(0.1); }
.MJXp-scale2 { transform: scaleX(0.2); }
.MJXp-scale3 { transform: scaleX(0.3); }
.MJXp-scale4 { transform: scaleX(0.4); }
.MJXp-scale5 { transform: scaleX(0.5); }
.MJXp-scale6 { transform: scaleX(0.6); }
.MJXp-scale7 { transform: scaleX(0.7); }
.MJXp-scale8 { transform: scaleX(0.8); }
.MJXp-scale9 { transform: scaleX(0.9); }
.MathJax_PHTML .noError { font-size: 90%; text-align: left; color: black; padding: 1px 3px; border: 1px solid; }