{"_id":"640daeaaff3d6dd51bac04e5","createdAt":"2023-03-12T10:51:22.071Z","updatedAt":"2023-03-12T10:51:22.071Z","views":8,"isActive":true,"sourcedFromGithub":false,"hasLatex":false,"popularity":5991.2685,"enableToc":false,"type":"story","partOfPublication":true,"responseCount":0,"replyCount":0,"isFeatured":false,"isEngaging":false,"isDelisted":false,"isNotified":false,"numCollapsed":0,"reactions":[],"totalReactions":0,"totalReactionsByCurrentUser":0,"isPinnedToBlog":false,"disableComments":false,"commentsPaused":false,"syncAlgolia":false,"numUniqueUsersWhoReacted":0,"slugOverridden":false,"tweetOptions":{"enabled":false},"title":"Session 7 - Revisiting Analysis of algorithm","cuid":"clf59zfx0000009mg925iepto","dateAdded":"2023-03-12T10:51:22.069Z","hasCustomDate":null,"isCoverAttributionHidden":false,"coverImageAttribution":"https://unsplash.com/@lazycreekimages","coverImagePhotographer":"Michael Dziedzic","slug":"session-7-revisiting-analysis-of-algorithm","content":"\n\n

Topics Covered

Bounding
\n
Upper/Lower Bound
\n
Big O
\n
Omega
\n
Theta
\n

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var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg:transparent;--bs-alert-padding-x:1rem;--bs-alert-padding-y:1rem;--bs-alert-margin-bottom:1rem;--bs-alert-color:inherit;--bs-alert-border-color:transparent;--bs-alert-border:1px solid var(--bs-alert-border-color);--bs-alert-border-radius:0.375rem;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-primary{--bs-alert-color:#084298;--bs-alert-bg:#cfe2ff;--bs-alert-border-color:#b6d4fe}.alert-primary .alert-link{color:#06357a}.alert-secondary{--bs-alert-color:#41464b;--bs-alert-bg:#e2e3e5;--bs-alert-border-color:#d3d6d8}.alert-secondary .alert-link{color:#34383c}.alert-success{--bs-alert-color:#0f5132;--bs-alert-bg:#d1e7dd;--bs-alert-border-color:#badbcc}.alert-success .alert-link{color:#0c4128}.alert-info{--bs-alert-color:#055160;--bs-alert-bg:#cff4fc;--bs-alert-border-color:#b6effb}.alert-info .alert-link{color:#04414d}.alert-warning{--bs-alert-color:#664d03;--bs-alert-bg:#fff3cd;--bs-alert-border-color:#ffecb5}.alert-warning .alert-link{color:#523e02}.alert-danger{--bs-alert-color:#842029;--bs-alert-bg:#f8d7da;--bs-alert-border-color:#f5c2c7}.alert-danger .alert-link{color:#6a1a21}.alert-light{--bs-alert-color:#636464;--bs-alert-bg:#fefefe;--bs-alert-border-color:#fdfdfe}.alert-light .alert-link{color:#4f5050}.alert-dark{--bs-alert-color:#141619;--bs-alert-bg:#d3d3d4;--bs-alert-border-color:#bcbebf}.alert-dark .alert-link{color:#101214}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress{--bs-progress-height:1rem;--bs-progress-font-size:0.75rem;--bs-progress-bg:#e9ecef;--bs-progress-border-radius:0.375rem;--bs-progress-box-shadow:inset 0 1px 2px rgba(0, 0, 0, 0.075);--bs-progress-bar-color:#fff;--bs-progress-bar-bg:#0d6efd;--bs-progress-bar-transition:width 0.6s ease;display:flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;flex-direction:column;justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media 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\";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:focus,.list-group-item-action:hover{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid var(--bs-list-group-border-color)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1 * var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media (min-width:576px){.list-group-horizontal-sm{flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width:768px){.list-group-horizontal-md{flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width:992px){.list-group-horizontal-lg{flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width:1200px){.list-group-horizontal-xl{flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media 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var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-primary{color:#084298;background-color:#cfe2ff}.list-group-item-primary.list-group-item-action:focus,.list-group-item-primary.list-group-item-action:hover{color:#084298;background-color:#bacbe6}.list-group-item-primary.list-group-item-action.active{color:#fff;background-color:#084298;border-color:#084298}.list-group-item-secondary{color:#41464b;background-color:#e2e3e5}.list-group-item-secondary.list-group-item-action:focus,.list-group-item-secondary.list-group-item-action:hover{color:#41464b;background-color:#cbccce}.list-group-item-secondary.list-group-item-action.active{color:#fff;background-color:#41464b;border-color:#41464b}.list-group-item-success{color:#0f5132;background-color:#d1e7dd}.list-group-item-success.list-group-item-action:focus,.list-group-item-success.list-group-item-action:hover{color:#0f5132;background-color:#bcd0c7}.list-group-item-success.list-group-item-action.active{color:#fff;background-color:#0f5132;border-color:#0f5132}.list-group-item-info{color:#055160;background-color:#cff4fc}.list-group-item-info.list-group-item-action:focus,.list-group-item-info.list-group-item-action:hover{color:#055160;background-color:#badce3}.list-group-item-info.list-group-item-action.active{color:#fff;background-color:#055160;border-color:#055160}.list-group-item-warning{color:#664d03;background-color:#fff3cd}.list-group-item-warning.list-group-item-action:focus,.list-group-item-warning.list-group-item-action:hover{color:#664d03;background-color:#e6dbb9}.list-group-item-warning.list-group-item-action.active{color:#fff;background-color:#664d03;border-color:#664d03}.list-group-item-danger{color:#842029;background-color:#f8d7da}.list-group-item-danger.list-group-item-action:focus,.list-group-item-danger.list-group-item-action:hover{color:#842029;background-color:#dfc2c4}.list-group-item-danger.list-group-item-action.active{color:#fff;background-color:#842029;border-color:#842029}.list-group-item-light{color:#636464;background-color:#fefefe}.list-group-item-light.list-group-item-action:focus,.list-group-item-light.list-group-item-action:hover{color:#636464;background-color:#e5e5e5}.list-group-item-light.list-group-item-action.active{color:#fff;background-color:#636464;border-color:#636464}.list-group-item-dark{color:#141619;background-color:#d3d3d4}.list-group-item-dark.list-group-item-action:focus,.list-group-item-dark.list-group-item-action:hover{color:#141619;background-color:#bebebf}.list-group-item-dark.list-group-item-action.active{color:#fff;background-color:#141619;border-color:#141619}.btn-close{box-sizing:content-box;width:1em;height:1em;padding:.25em .25em;color:#000;background:transparent url(\"data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23000'%3e%3cpath d='M.293.293a1 1 0 0 1 1.414 0L8 6.586 14.293.293a1 1 0 1 1 1.414 1.414L9.414 8l6.293 6.293a1 1 0 0 1-1.414 1.414L8 9.414l-6.293 6.293a1 1 0 0 1-1.414-1.414L6.586 8 .293 1.707a1 1 0 0 1 0-1.414z'/%3e%3c/svg%3e\") center/1em auto no-repeat;border:0;border-radius:.375rem;opacity:.5}.btn-close:hover{color:#000;text-decoration:none;opacity:.75}.btn-close:focus{outline:0;box-shadow:0 0 0 .25rem rgba(13,110,253,.25);opacity:1}.btn-close.disabled,.btn-close:disabled{pointer-events:none;-webkit-user-select:none;-moz-user-select:none;user-select:none;opacity:.25}.btn-close-white{filter:invert(1) grayscale(100%) brightness(200%)}.toast{--bs-toast-zindex:1090;--bs-toast-padding-x:0.75rem;--bs-toast-padding-y:0.5rem;--bs-toast-spacing:1.5rem;--bs-toast-max-width:350px;--bs-toast-font-size:0.875rem;--bs-toast-color: ;--bs-toast-bg:rgba(255, 255, 255, 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.nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand-xxl .navbar-nav-scroll{overflow:visible}.navbar-expand-xxl .navbar-collapse{display:flex!important;flex-basis:auto}.navbar-expand-xxl .navbar-toggler{display:none}.navbar-expand-xxl .offcanvas{position:static;z-index:auto;flex-grow:1;width:auto!important;height:auto!important;visibility:visible!important;background-color:transparent!important;border:0!important;transform:none!important;transition:none}.navbar-expand-xxl .offcanvas .offcanvas-header{display:none}.navbar-expand-xxl .offcanvas .offcanvas-body{display:flex;flex-grow:0;padding:0;overflow-y:visible}}.navbar-expand{flex-wrap:nowrap;justify-content:flex-start}.navbar-expand .navbar-nav{flex-direction:row}.navbar-expand .navbar-nav .dropdown-menu{position:absolute}.navbar-expand .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand .navbar-nav-scroll{overflow:visible}.navbar-expand .navbar-collapse{display:flex!important;flex-basis:auto}.navbar-expand .navbar-toggler{display:none}.navbar-expand .offcanvas{position:static;z-index:auto;flex-grow:1;width:auto!important;height:auto!important;visibility:visible!important;background-color:transparent!important;border:0!important;transform:none!important;transition:none}.navbar-expand .offcanvas .offcanvas-header{display:none}.navbar-expand .offcanvas .offcanvas-body{display:flex;flex-grow:0;padding:0;overflow-y:visible}.navbar-dark{--bs-navbar-color:rgba(255, 255, 255, 0.55);--bs-navbar-hover-color:rgba(255, 255, 255, 0.75);--bs-navbar-disabled-color:rgba(255, 255, 255, 0.25);--bs-navbar-active-color:#fff;--bs-navbar-brand-color:#fff;--bs-navbar-brand-hover-color:#fff;--bs-navbar-toggler-border-color:rgba(255, 255, 255, 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var(--bs-card-cap-padding-x))}.card-img-overlay{position:absolute;top:0;right:0;bottom:0;left:0;padding:var(--bs-card-img-overlay-padding);border-radius:var(--bs-card-inner-border-radius)}.card-img,.card-img-bottom,.card-img-top{width:100%}.card-img,.card-img-top{border-top-left-radius:var(--bs-card-inner-border-radius);border-top-right-radius:var(--bs-card-inner-border-radius)}.card-img,.card-img-bottom{border-bottom-right-radius:var(--bs-card-inner-border-radius);border-bottom-left-radius:var(--bs-card-inner-border-radius)}.card-group>.card{margin-bottom:var(--bs-card-group-margin)}@media (min-width:576px){.card-group{display:flex;flex-flow:row wrap}.card-group>.card{flex:1 0 0%;margin-bottom:0}.card-group>.card+.card{margin-left:0;border-left:0}.card-group>.card:not(:last-child){border-top-right-radius:0;border-bottom-right-radius:0}.card-group>.card:not(:last-child) .card-header,.card-group>.card:not(:last-child) 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1px);--bs-accordion-btn-padding-x:1.25rem;--bs-accordion-btn-padding-y:1rem;--bs-accordion-btn-color:#212529;--bs-accordion-btn-bg:var(--bs-accordion-bg);--bs-accordion-btn-icon:url(\"data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23212529'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e\");--bs-accordion-btn-icon-width:1.25rem;--bs-accordion-btn-icon-transform:rotate(-180deg);--bs-accordion-btn-icon-transition:transform 0.2s ease-in-out;--bs-accordion-btn-active-icon:url(\"data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%230c63e4'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e\");--bs-accordion-btn-focus-border-color:#86b7fe;--bs-accordion-btn-focus-box-shadow:0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-accordion-body-padding-x:1.25rem;--bs-accordion-body-padding-y:1rem;--bs-accordion-active-color:#0c63e4;--bs-accordion-active-bg:#e7f1ff}.accordion-button{position:relative;display:flex;align-items:center;width:100%;padding:var(--bs-accordion-btn-padding-y) var(--bs-accordion-btn-padding-x);font-size:1rem;color:var(--bs-accordion-btn-color);text-align:left;background-color:var(--bs-accordion-btn-bg);border:0;border-radius:0;overflow-anchor:none;transition:var(--bs-accordion-transition)}@media (prefers-reduced-motion:reduce){.accordion-button{transition:none}}.accordion-button:not(.collapsed){color:var(--bs-accordion-active-color);background-color:var(--bs-accordion-active-bg);box-shadow:inset 0 calc(-1 * var(--bs-accordion-border-width)) 0 var(--bs-accordion-border-color)}.accordion-button:not(.collapsed)::after{background-image:var(--bs-accordion-btn-active-icon);transform:var(--bs-accordion-btn-icon-transform)}.accordion-button::after{flex-shrink:0;width:var(--bs-accordion-btn-icon-width);height:var(--bs-accordion-btn-icon-width);margin-left:auto;content:\"\";background-image:var(--bs-accordion-btn-icon);background-repeat:no-repeat;background-size:var(--bs-accordion-btn-icon-width);transition:var(--bs-accordion-btn-icon-transition)}@media (prefers-reduced-motion:reduce){.accordion-button::after{transition:none}}.accordion-button:hover{z-index:2}.accordion-button:focus{z-index:3;border-color:var(--bs-accordion-btn-focus-border-color);outline:0;box-shadow:var(--bs-accordion-btn-focus-box-shadow)}.accordion-header{margin-bottom:0}.accordion-item{color:var(--bs-accordion-color);background-color:var(--bs-accordion-bg);border:var(--bs-accordion-border-width) solid var(--bs-accordion-border-color)}.accordion-item:first-of-type{border-top-left-radius:var(--bs-accordion-border-radius);border-top-right-radius:var(--bs-accordion-border-radius)}.accordion-item:first-of-type .accordion-button{border-top-left-radius:var(--bs-accordion-inner-border-radius);border-top-right-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:not(:first-of-type){border-top:0}.accordion-item:last-of-type{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-item:last-of-type .accordion-button.collapsed{border-bottom-right-radius:var(--bs-accordion-inner-border-radius);border-bottom-left-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:last-of-type .accordion-collapse{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-body{padding:var(--bs-accordion-body-padding-y) var(--bs-accordion-body-padding-x)}.accordion-flush .accordion-collapse{border-width:0}.accordion-flush .accordion-item{border-right:0;border-left:0;border-radius:0}.accordion-flush .accordion-item:first-child{border-top:0}.accordion-flush .accordion-item:last-child{border-bottom:0}.accordion-flush .accordion-item .accordion-button,.accordion-flush .accordion-item .accordion-button.collapsed{border-radius:0}.breadcrumb{--bs-breadcrumb-padding-x:0;--bs-breadcrumb-padding-y:0;--bs-breadcrumb-margin-bottom:1rem;--bs-breadcrumb-bg: ;--bs-breadcrumb-border-radius: ;--bs-breadcrumb-divider-color:#6c757d;--bs-breadcrumb-item-padding-x:0.5rem;--bs-breadcrumb-item-active-color:#6c757d;display:flex;flex-wrap:wrap;padding:var(--bs-breadcrumb-padding-y) var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg);border-radius:var(--bs-breadcrumb-border-radius)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, \"/\")}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x:0.75rem;--bs-pagination-padding-y:0.375rem;--bs-pagination-font-size:1rem;--bs-pagination-color:var(--bs-link-color);--bs-pagination-bg:#fff;--bs-pagination-border-width:1px;--bs-pagination-border-color:#dee2e6;--bs-pagination-border-radius:0.375rem;--bs-pagination-hover-color:var(--bs-link-hover-color);--bs-pagination-hover-bg:#e9ecef;--bs-pagination-hover-border-color:#dee2e6;--bs-pagination-focus-color:var(--bs-link-hover-color);--bs-pagination-focus-bg:#e9ecef;--bs-pagination-focus-box-shadow:0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-pagination-active-color:#fff;--bs-pagination-active-bg:#0d6efd;--bs-pagination-active-border-color:#0d6efd;--bs-pagination-disabled-color:#6c757d;--bs-pagination-disabled-bg:#fff;--bs-pagination-disabled-border-color:#dee2e6;display:flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out}@media (prefers-reduced-motion:reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.active>.page-link,.page-link.active{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.disabled>.page-link,.page-link.disabled{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:-1px}.page-item:first-child .page-link{border-top-left-radius:var(--bs-pagination-border-radius);border-bottom-left-radius:var(--bs-pagination-border-radius)}.page-item:last-child .page-link{border-top-right-radius:var(--bs-pagination-border-radius);border-bottom-right-radius:var(--bs-pagination-border-radius)}.pagination-lg{--bs-pagination-padding-x:1.5rem;--bs-pagination-padding-y:0.75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius:0.5rem}.pagination-sm{--bs-pagination-padding-x:0.5rem;--bs-pagination-padding-y:0.25rem;--bs-pagination-font-size:0.875rem;--bs-pagination-border-radius:0.25rem}.badge{--bs-badge-padding-x:0.65em;--bs-badge-padding-y:0.35em;--bs-badge-font-size:0.75em;--bs-badge-font-weight:700;--bs-badge-color:#fff;--bs-badge-border-radius:0.375rem;display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg:transparent;--bs-alert-padding-x:1rem;--bs-alert-padding-y:1rem;--bs-alert-margin-bottom:1rem;--bs-alert-color:inherit;--bs-alert-border-color:transparent;--bs-alert-border:1px solid var(--bs-alert-border-color);--bs-alert-border-radius:0.375rem;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-primary{--bs-alert-color:#084298;--bs-alert-bg:#cfe2ff;--bs-alert-border-color:#b6d4fe}.alert-primary .alert-link{color:#06357a}.alert-secondary{--bs-alert-color:#41464b;--bs-alert-bg:#e2e3e5;--bs-alert-border-color:#d3d6d8}.alert-secondary .alert-link{color:#34383c}.alert-success{--bs-alert-color:#0f5132;--bs-alert-bg:#d1e7dd;--bs-alert-border-color:#badbcc}.alert-success .alert-link{color:#0c4128}.alert-info{--bs-alert-color:#055160;--bs-alert-bg:#cff4fc;--bs-alert-border-color:#b6effb}.alert-info .alert-link{color:#04414d}.alert-warning{--bs-alert-color:#664d03;--bs-alert-bg:#fff3cd;--bs-alert-border-color:#ffecb5}.alert-warning .alert-link{color:#523e02}.alert-danger{--bs-alert-color:#842029;--bs-alert-bg:#f8d7da;--bs-alert-border-color:#f5c2c7}.alert-danger .alert-link{color:#6a1a21}.alert-light{--bs-alert-color:#636464;--bs-alert-bg:#fefefe;--bs-alert-border-color:#fdfdfe}.alert-light .alert-link{color:#4f5050}.alert-dark{--bs-alert-color:#141619;--bs-alert-bg:#d3d3d4;--bs-alert-border-color:#bcbebf}.alert-dark .alert-link{color:#101214}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress{--bs-progress-height:1rem;--bs-progress-font-size:0.75rem;--bs-progress-bg:#e9ecef;--bs-progress-border-radius:0.375rem;--bs-progress-box-shadow:inset 0 1px 2px rgba(0, 0, 0, 0.075);--bs-progress-bar-color:#fff;--bs-progress-bar-bg:#0d6efd;--bs-progress-bar-transition:width 0.6s ease;display:flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;flex-direction:column;justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media (prefers-reduced-motion:reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg,rgba(255,255,255,.15) 25%,transparent 25%,transparent 50%,rgba(255,255,255,.15) 50%,rgba(255,255,255,.15) 75%,transparent 75%,transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media (prefers-reduced-motion:reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color:#212529;--bs-list-group-bg:#fff;--bs-list-group-border-color:rgba(0, 0, 0, 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