.friends-panel[data-v-77c0eba7]{pointer-events:auto;-webkit-backdrop-filter:blur(6px)saturate(120%);backdrop-filter:blur(6px)saturate(120%);z-index:100;transform-origin:100% 0;background:#82879138;border:1px solid #ffffff4d;border-radius:16px;flex-direction:column;gap:.6rem;width:340px;max-width:min(340px,90vw);max-height:70vh;padding:.8rem;animation:.15s ease-out forwards slideDown-77c0eba7;display:flex;position:absolute;top:calc(100% + .6rem);right:0;overflow-y:auto;box-shadow:0 8px 28px #0000001f,0 2px 8px #0000000a}:root.dark-theme .friends-panel[data-v-77c0eba7],html.dark-theme .friends-panel[data-v-77c0eba7],.dark-theme .friends-panel[data-v-77c0eba7]{background:#2d323c94;border-color:#ffffff26;box-shadow:0 8px 28px #0006,0 2px 8px #0003}@keyframes slideDown-77c0eba7{0%{opacity:0;transform:scale(.95)}to{opacity:1;transform:scale(1)}}.glass-badge[data-v-77c0eba7]{-webkit-backdrop-filter:blur(6px)saturate(120%);backdrop-filter:blur(6px)saturate(120%);box-sizing:border-box;height:28px;font-family:var(--font-mono);letter-spacing:.06em;color:var(--text-primary);cursor:pointer;background:#82879138;border:1px solid #ffffff4d;border-radius:9999px;justify-content:center;align-items:center;padding:0 .8rem;font-size:.68rem;transition:border-color .2s,background-color .2s,color .2s;display:inline-flex;box-shadow:0 8px 28px #0000001f,0 2px 8px #0000000a}:root.dark-theme .glass-badge[data-v-77c0eba7],html.dark-theme .glass-badge[data-v-77c0eba7],.dark-theme .glass-badge[data-v-77c0eba7]{background:#2d323c94;border-color:#ffffff26}.glass-badge[data-v-77c0eba7]:hover{background:#6e737d2e}.glass-badge[data-v-77c0eba7]:disabled{opacity:.5;cursor:default}.glass-badge.on[data-v-77c0eba7]{color:var(--text-primary);border-color:#000}:root.dark-theme .glass-badge.on[data-v-77c0eba7],html.dark-theme .glass-badge.on[data-v-77c0eba7],.dark-theme .glass-badge.on[data-v-77c0eba7]{border-color:#fff}.glass-badge.danger[data-v-77c0eba7]{color:#ef4444}.glass-badge.icon-btn[data-v-77c0eba7]{border-radius:50%;flex-shrink:0;width:28px;height:28px;padding:0}.glass-badge.icon-btn svg[data-v-77c0eba7]{width:14px;height:14px;display:block}.invite-badge[data-v-77c0eba7]{width:100%;height:32px}.invite-code[data-v-77c0eba7]{letter-spacing:.1em;font-weight:700}.mono-label[data-v-77c0eba7]{font-family:var(--font-mono);letter-spacing:.08em;color:var(--text-primary);font-size:.7rem;font-weight:700}.mono-text[data-v-77c0eba7]{font-family:var(--font-mono);letter-spacing:.05em;color:var(--text-secondary);font-size:.72rem}.center[data-v-77c0eba7]{text-align:center}.empty[data-v-77c0eba7]{text-align:center;padding:.4rem 0}.text-danger[data-v-77c0eba7]{color:#ef4444}.req-block[data-v-77c0eba7]{flex-direction:column;gap:.4rem;display:flex}.req-block .friend-row[data-v-77c0eba7]{-webkit-backdrop-filter:blur(6px)saturate(120%);backdrop-filter:blur(6px)saturate(120%);background:#ffffff38;border:1px solid #ffffff4d;border-radius:12px;padding:.4rem .6rem;box-shadow:0 2px 10px #0000000f}:root.dark-theme .req-block .friend-row[data-v-77c0eba7],html.dark-theme .req-block .friend-row[data-v-77c0eba7],.dark-theme .req-block .friend-row[data-v-77c0eba7]{background:#ffffff12;border-color:#ffffff26}.row-head[data-v-77c0eba7]{justify-content:space-between;align-items:center;gap:.5rem;padding:.2rem 0;display:flex}.icon-group[data-v-77c0eba7]{align-items:center;gap:.4rem;display:inline-flex}.add-row[data-v-77c0eba7]{gap:.4rem;display:flex}.username-input[data-v-77c0eba7]{border:1px solid var(--border-medium);background-color:var(--bg-primary);min-width:0;height:28px;color:var(--text-primary);font-family:var(--font-mono);border-radius:9999px;flex:1;padding:0 .7rem;font-size:.75rem}.friend-block[data-v-77c0eba7]{-webkit-backdrop-filter:blur(6px)saturate(120%);backdrop-filter:blur(6px)saturate(120%);background:#ffffff38;border:1px solid #ffffff4d;border-radius:12px;flex-direction:column;gap:.4rem;padding:.5rem .6rem;display:flex;position:relative;overflow:visible;box-shadow:0 2px 10px #0000000f}:root.dark-theme .friend-block[data-v-77c0eba7],html.dark-theme .friend-block[data-v-77c0eba7],.dark-theme .friend-block[data-v-77c0eba7]{background:#ffffff12;border-color:#ffffff26}.friend-row[data-v-77c0eba7]{justify-content:space-between;align-items:center;gap:.5rem;display:flex}.friend-name[data-v-77c0eba7]{font-family:var(--font-mono);text-overflow:ellipsis;white-space:nowrap;font-size:.85rem;font-weight:700;overflow:hidden}.kebab-btn[data-v-77c0eba7]{letter-spacing:0;font-size:.85rem;font-weight:700;line-height:1;padding-bottom:7px!important}.friend-menu-wrap[data-v-77c0eba7]{flex-shrink:0;display:inline-flex;position:relative}.friend-menu[data-v-77c0eba7]{-webkit-backdrop-filter:blur(6px)saturate(120%);backdrop-filter:blur(6px)saturate(120%);white-space:nowrap;background:#82879138;border:1px solid #ffffff4d;border-radius:12px;flex-direction:column;gap:.15rem;min-width:110px;padding:.3rem;display:flex;box-shadow:0 8px 28px #0000001f,0 2px 8px #0000000a}.friend-menu-teleported[data-v-77c0eba7]{z-index:2000;transform-origin:100% 0;margin:0;animation:.12s ease-out forwards slideDown-77c0eba7;position:fixed}:root.dark-theme .friend-menu[data-v-77c0eba7],html.dark-theme .friend-menu[data-v-77c0eba7],.dark-theme .friend-menu[data-v-77c0eba7]{background:#2d323c94;border-color:#ffffff26;box-shadow:0 8px 28px #0006,0 2px 8px #0003}.friend-menu-item[data-v-77c0eba7]{text-align:left;font-family:var(--font-mono);letter-spacing:.06em;color:var(--text-primary);cursor:pointer;background:0 0;border:none;border-radius:8px;padding:.45rem .7rem;font-size:.7rem;transition:background-color .15s,color .15s,opacity .15s}.friend-menu-item[data-v-77c0eba7]:hover{background:#8080802e}.friend-menu-item[data-v-77c0eba7]:disabled{cursor:default;opacity:.5}.friend-menu-item.off[data-v-77c0eba7]{color:var(--text-secondary);opacity:.55;text-decoration:line-through}.friend-menu-item.danger[data-v-77c0eba7]{color:#ef4444}.refresh-icon[data-v-3a1136cd]{width:1em;height:1em;display:block}.mailbox-panel[data-v-8ea5e7cc]{width:380px;max-width:min(380px,92vw)}.compose-block[data-v-8ea5e7cc]{border-bottom:1px solid #ffffff26;flex-direction:column;gap:.4rem;padding-bottom:.6rem;display:flex}.compose-row[data-v-8ea5e7cc]{gap:.4rem;display:flex}.send-badge[data-v-8ea5e7cc]{width:100%;height:30px}.draft-badges[data-v-8ea5e7cc]{flex-wrap:wrap;gap:.3rem;display:flex}.msg-card[data-v-8ea5e7cc]{-webkit-backdrop-filter:blur(6px)saturate(120%);backdrop-filter:blur(6px)saturate(120%);background:#ffffff38;border:1px solid #ffffff4d;border-radius:12px;flex-direction:column;gap:.45rem;padding:.6rem .7rem;display:flex;box-shadow:0 2px 10px #0000000f}:root.dark-theme .msg-card[data-v-8ea5e7cc],html.dark-theme .msg-card[data-v-8ea5e7cc],.dark-theme .msg-card[data-v-8ea5e7cc]{background:#ffffff12;border-color:#ffffff26}.msg-card.grey[data-v-8ea5e7cc]{opacity:.55}.msg-head[data-v-8ea5e7cc]{align-items:center;gap:.5rem;display:flex}.msg-user[data-v-8ea5e7cc]{font-family:var(--font-mono);text-overflow:ellipsis;white-space:nowrap;flex:1;font-size:.8rem;font-weight:700;overflow:hidden}.msg-time[data-v-8ea5e7cc]{font-family:var(--font-mono);color:var(--text-secondary);font-size:.62rem}.print-btn[data-v-8ea5e7cc]{height:24px;font-size:.62rem}.print-icon-btn svg[data-v-8ea5e7cc]{width:14px;height:14px;display:block}.msg-badges[data-v-8ea5e7cc]{flex-wrap:wrap;gap:.3rem;display:flex}.q-badge[data-v-8ea5e7cc]{-webkit-backdrop-filter:blur(6px)saturate(120%);backdrop-filter:blur(6px)saturate(120%);cursor:pointer;color:var(--text-primary);background:#82879138;border:1px solid #ffffff4d;border-radius:6px;align-items:center;gap:.35rem;padding:.25rem .5rem;font-size:.72rem;display:inline-flex;box-shadow:0 8px 28px #0000001f,0 2px 8px #0000000a}.q-badge .badge[data-v-8ea5e7cc]{font-size:.62rem}.q-badge .paper-title[data-v-8ea5e7cc]{margin:0;font-size:.72rem}.q-badge.grey[data-v-8ea5e7cc]{opacity:.45;filter:grayscale()}:root.dark-theme .q-badge[data-v-8ea5e7cc],html.dark-theme .q-badge[data-v-8ea5e7cc],.dark-theme .q-badge[data-v-8ea5e7cc]{background:#2d323c94;border-color:#ffffff26}.msg-badge[data-v-8ea5e7cc]{padding:.3rem .5rem}.q-badge .x[data-v-8ea5e7cc]{color:#ef4444;cursor:pointer;background:0 0;border:none;padding:0 0 0 .2rem;font-size:.9rem;line-height:1}.friends-panel[data-v-8ea5e7cc]{pointer-events:auto;-webkit-backdrop-filter:blur(6px)saturate(120%);backdrop-filter:blur(6px)saturate(120%);z-index:100;transform-origin:100% 0;background:#82879138;border:1px solid #ffffff4d;border-radius:16px;flex-direction:column;gap:.6rem;width:340px;max-width:min(340px,90vw);max-height:70vh;padding:.8rem;animation:.15s ease-out forwards slideDown-8ea5e7cc;display:flex;position:absolute;top:calc(100% + .6rem);right:0;overflow-y:auto;box-shadow:0 8px 28px #0000001f,0 2px 8px #0000000a}:root.dark-theme .friends-panel[data-v-8ea5e7cc],html.dark-theme .friends-panel[data-v-8ea5e7cc],.dark-theme .friends-panel[data-v-8ea5e7cc]{background:#2d323c94;border-color:#ffffff26}@keyframes slideDown-8ea5e7cc{0%{opacity:0;transform:scale(.95)}to{opacity:1;transform:scale(1)}}.glass-badge[data-v-8ea5e7cc]{height:28px;font-family:var(--font-mono);letter-spacing:.06em;color:var(--text-primary);cursor:pointer;background:#82879138;border:1px solid #ffffff4d;border-radius:9999px;justify-content:center;align-items:center;padding:0 .8rem;font-size:.68rem;display:inline-flex}.glass-badge.on[data-v-8ea5e7cc]{color:var(--text-primary);border-color:#000}:root.dark-theme .glass-badge.on[data-v-8ea5e7cc],html.dark-theme .glass-badge.on[data-v-8ea5e7cc],.dark-theme .glass-badge.on[data-v-8ea5e7cc]{border-color:#fff}.refresh-btn[data-v-8ea5e7cc]{font-size:14px}.refresh-btn .refresh-icon[data-v-8ea5e7cc]{stroke-width:1.8px}.glass-badge[data-v-8ea5e7cc]:disabled{opacity:.5;cursor:default}.glass-badge.icon-btn[data-v-8ea5e7cc]{border-radius:50%;width:28px;height:28px;padding:0}.row-head[data-v-8ea5e7cc]{justify-content:space-between;align-items:center;gap:.5rem;padding:.2rem 0;display:flex}.icon-group[data-v-8ea5e7cc]{align-items:center;gap:.4rem;display:inline-flex}.mono-label[data-v-8ea5e7cc]{font-family:var(--font-mono);letter-spacing:.08em;font-size:.7rem;font-weight:700}.mono-text[data-v-8ea5e7cc]{font-family:var(--font-mono);color:var(--text-secondary);font-size:.72rem}.center[data-v-8ea5e7cc]{text-align:center}.empty[data-v-8ea5e7cc]{text-align:center;padding:.4rem 0}.text-danger[data-v-8ea5e7cc]{color:#ef4444}.username-input[data-v-8ea5e7cc]{border:1px solid var(--border-medium);background-color:var(--bg-primary);min-width:0;height:28px;color:var(--text-primary);font-family:var(--font-mono);border-radius:9999px;flex:1;padding:0 .7rem;font-size:.75rem}.recv-wrap[data-v-8ea5e7cc]{flex:1;min-width:0;display:flex;position:relative}.recv-menu[data-v-8ea5e7cc]{z-index:20;-webkit-backdrop-filter:blur(12px)saturate(140%);backdrop-filter:blur(12px)saturate(140%);background:#fff9;border:1px solid #ffffff80;border-radius:12px;flex-direction:column;gap:.25rem;max-height:160px;padding:.35rem;display:flex;position:absolute;top:calc(100% + .3rem);left:0;right:0;overflow-y:auto;box-shadow:0 8px 28px #0000001f,0 2px 8px #0000000a}:root.dark-theme .recv-menu[data-v-8ea5e7cc],html.dark-theme .recv-menu[data-v-8ea5e7cc],.dark-theme .recv-menu[data-v-8ea5e7cc]{background:#414855d9;border-color:#fff3}.recv-item[data-v-8ea5e7cc]{text-align:left;font-family:var(--font-mono);color:var(--text-primary);cursor:pointer;text-overflow:ellipsis;white-space:nowrap;background:0 0;border:1px solid #0000;border-radius:8px;padding:.35rem .6rem;font-size:.75rem;overflow:hidden}.recv-item[data-v-8ea5e7cc]:hover{background:#8080802e}.recv-item.sel[data-v-8ea5e7cc]{border-color:#000;font-weight:700}:root.dark-theme .recv-item.sel[data-v-8ea5e7cc],html.dark-theme .recv-item.sel[data-v-8ea5e7cc],.dark-theme .recv-item.sel[data-v-8ea5e7cc]{border-color:#fff}.badge-outline[data-v-8ea5e7cc]{border:1px solid var(--border-medium);border-radius:4px;padding:0 .3rem}.app-header[data-v-60e6c3a6]{z-index:1000;pointer-events:none;background:0 0;border-bottom:none;position:fixed;top:1rem;left:0;right:0;transform:translateZ(0)}.header-container[data-v-60e6c3a6]{box-sizing:border-box;justify-content:space-between;align-items:center;gap:1rem;width:100%;max-width:1280px;margin:0 auto;padding:0 1.5rem;transition:padding .3s cubic-bezier(.16,1,.3,1);display:flex;position:static}.header-group-left[data-v-60e6c3a6]{z-index:10;flex:none;align-items:center;gap:.5rem;display:flex;position:relative}.header-group-middle[data-v-60e6c3a6]{pointer-events:none;z-index:5;grid-template-columns:1fr auto 1fr;align-items:center;gap:.4rem;width:max-content;max-width:100%;display:grid;position:absolute;top:50%;left:50%;transform:translate(-50%,-50%)}.header-group-middle[data-v-60e6c3a6]>:first-child{justify-self:end}.header-group-middle[data-v-60e6c3a6]>:last-child{justify-self:start}.header-group-middle-nav-right[data-v-60e6c3a6]{align-items:center;gap:.4rem;display:flex}.header-group-middle-nav-left[data-v-60e6c3a6]{justify-content:flex-end;align-items:center;gap:.4rem;display:flex}.header-group-right[data-v-60e6c3a6]{z-index:10;flex:none;align-items:center;gap:.5rem;display:flex;position:relative}.header-capsule[data-v-60e6c3a6]{pointer-events:auto;-webkit-backdrop-filter:blur(6px)saturate(120%);backdrop-filter:blur(6px)saturate(120%);box-sizing:border-box;background:#82879138;border:1px solid #ffffff4d;border-radius:9999px;align-items:center;height:32px;transition:border-color .2s,background-color .2s;display:flex;box-shadow:0 8px 28px #0000001f,0 2px 8px #0000000a;text-decoration:none!important}:root.dark-theme .header-capsule[data-v-60e6c3a6],html.dark-theme .header-capsule[data-v-60e6c3a6],.dark-theme .header-capsule[data-v-60e6c3a6]{background:#2d323c94;border-color:#ffffff26;box-shadow:0 8px 28px #0006,0 2px 8px #0003}.header-capsule[data-v-60e6c3a6]:has(.router-link-active){border:1px solid #000!important}:root.dark-theme .header-capsule[data-v-60e6c3a6]:has(.router-link-active){border:1px solid #fff!important}html.dark-theme .header-capsule[data-v-60e6c3a6]:has(.router-link-active){border:1px solid #fff!important}.dark-theme .header-capsule[data-v-60e6c3a6]:has(.router-link-active){border:1px solid #fff!important}.header-capsule[data-v-60e6c3a6]:hover{background:#6e737d2e}:root.dark-theme .header-capsule[data-v-60e6c3a6]:hover,html.dark-theme .header-capsule[data-v-60e6c3a6]:hover,.dark-theme .header-capsule[data-v-60e6c3a6]:hover{background:#23283266}.capsule-left[data-v-60e6c3a6]{padding:0 .8rem}.capsule-back[data-v-60e6c3a6],.capsule-nav-side[data-v-60e6c3a6]{padding:0}.capsule-nav-circle[data-v-60e6c3a6]{border-radius:50%;justify-content:center;align-items:center;width:40px;height:40px;padding:0}.capsule-btn[data-v-60e6c3a6],.user-greeting-btn[data-v-60e6c3a6]{cursor:pointer!important;-webkit-backdrop-filter:blur(6px)saturate(120%)!important;backdrop-filter:blur(6px)saturate(120%)!important;box-sizing:border-box!important;height:32px!important;font-family:var(--font-sans)!important;color:var(--text-primary)!important;background:#82879138!important;border:1px solid #ffffff4d!important;border-radius:9999px!important;justify-content:center!important;align-items:center!important;padding:0 .8rem!important;font-size:.75rem!important;font-weight:500!important;text-decoration:none!important;transition:border-color .2s,background-color .2s!important;display:inline-flex!important;box-shadow:0 8px 28px #0000001f,0 2px 8px #0000000a!important}:root.dark-theme .capsule-btn[data-v-60e6c3a6],:root.dark-theme .user-greeting-btn[data-v-60e6c3a6],html.dark-theme .capsule-btn[data-v-60e6c3a6],html.dark-theme .user-greeting-btn[data-v-60e6c3a6],.dark-theme .capsule-btn[data-v-60e6c3a6],.dark-theme .user-greeting-btn[data-v-60e6c3a6]{background:#2d323c94!important;border-color:#ffffff26!important}.capsule-btn[data-v-60e6c3a6]:hover,.user-greeting-btn[data-v-60e6c3a6]:hover{background:#6e737d2e!important}:root.dark-theme .capsule-btn[data-v-60e6c3a6]:hover,:root.dark-theme .user-greeting-btn[data-v-60e6c3a6]:hover,html.dark-theme .capsule-btn[data-v-60e6c3a6]:hover,html.dark-theme .user-greeting-btn[data-v-60e6c3a6]:hover,.dark-theme .capsule-btn[data-v-60e6c3a6]:hover,.dark-theme .user-greeting-btn[data-v-60e6c3a6]:hover{background:#23283266!important}.logo-row[data-v-60e6c3a6]{align-items:center;gap:.6rem;display:flex}.logo[data-v-60e6c3a6]{font-family:var(--font-sans);letter-spacing:.06em;color:var(--text-primary);border:none;font-size:1.05rem;font-weight:700;text-decoration:none!important}.back-capsule[data-v-60e6c3a6]{height:100%;font-family:var(--font-mono);letter-spacing:.04em;color:var(--text-secondary);transition:var(--transition);white-space:nowrap;align-items:center;gap:.3rem;padding:0 .45rem;font-size:.68rem;font-weight:600;display:inline-flex;text-decoration:none!important}.back-capsule .back-arrow[data-v-60e6c3a6]{width:12px;height:12px;display:block}.back-capsule[data-v-60e6c3a6]:hover{color:var(--text-primary)}.home-link[data-v-60e6c3a6]{color:var(--text-secondary);justify-content:center;align-items:center;width:100%;height:100%;transition:color .2s;display:flex;text-decoration:none!important}.home-link[data-v-60e6c3a6]:hover{color:var(--text-primary)}.nav-item[data-v-60e6c3a6]{color:var(--text-secondary);white-space:nowrap;border:none;border-radius:9999px;align-items:center;height:100%;padding:0 1.2rem;font-size:.8rem;font-weight:400;transition:all .2s;display:inline-flex;text-decoration:none!important}.nav-item[data-v-60e6c3a6]:hover{color:var(--text-primary);background:0 0!important}.router-link-active.nav-item[data-v-60e6c3a6]{color:var(--text-primary);font-weight:500;background:0 0!important}#toolbar-dock[data-v-60e6c3a6]{pointer-events:none;opacity:0;align-items:center;gap:6px;height:32px;transition:opacity .18s ease-in-out;display:flex;overflow:visible}#toolbar-dock.dock-active[data-v-60e6c3a6]{pointer-events:auto;opacity:1;transition:opacity .18s ease-in-out .18s}#toolbar-dock .handwriting-toolbar{pointer-events:auto!important;-webkit-backdrop-filter:blur(6px)saturate(120%)!important;backdrop-filter:blur(6px)saturate(120%)!important;box-sizing:border-box!important;background:#82879138!important;border:1px solid #ffffff4d!important;border-radius:9999px!important;justify-content:center!important;align-items:center!important;gap:1px!important;width:auto!important;height:40px!important;padding:0 4px!important;display:flex!important;box-shadow:0 8px 28px #0000001f,0 2px 8px #0000000a!important}:root.dark-theme #toolbar-dock .handwriting-toolbar,html.dark-theme #toolbar-dock .handwriting-toolbar,.dark-theme #toolbar-dock .handwriting-toolbar{background:#2d323c94!important;border-color:#ffffff26!important;box-shadow:0 8px 28px #0006,0 2px 8px #0003!important}#toolbar-dock .toolbar-btn{width:30px!important;height:30px!important;color:var(--text-secondary)!important;background:0 0!important;border:none!important;border-radius:50%!important;transition:all .2s!important}#toolbar-dock .toolbar-btn:hover{color:var(--text-primary)!important;background:#8080801f!important}#toolbar-dock .toolbar-btn.btn-active,#toolbar-dock .toolbar-btn.eraser-active{color:var(--text-primary)!important;background:#80808038!important}.dropdown-container[data-v-60e6c3a6]{align-items:center;display:flex;position:relative}.chevron-icon[data-v-60e6c3a6]{stroke:currentColor;flex-shrink:0;width:12px;height:12px;margin-left:.35rem;transition:transform .2s;display:inline-block}.chevron-icon.open[data-v-60e6c3a6]{transform:rotate(180deg)}.dropdown-menu[data-v-60e6c3a6]{pointer-events:auto;z-index:100;transform-origin:100% 0;flex-direction:column;gap:.2rem;min-width:170px;padding:.35rem;animation:.15s ease-out forwards slideDown-60e6c3a6;display:flex;position:absolute;top:calc(100% + .6rem);right:0;overflow:hidden;-webkit-backdrop-filter:blur(6px)saturate(120%)!important;backdrop-filter:blur(6px)saturate(120%)!important;background:#82879138!important;border:1px solid #ffffff4d!important;border-radius:16px!important;box-shadow:0 8px 28px #0000001f,0 2px 8px #0000000a!important}:root.dark-theme .dropdown-menu[data-v-60e6c3a6],html.dark-theme .dropdown-menu[data-v-60e6c3a6],.dark-theme .dropdown-menu[data-v-60e6c3a6]{background:#2d323c94!important;border-color:#ffffff26!important;box-shadow:0 8px 28px #0006,0 2px 8px #0003!important}@keyframes slideDown-60e6c3a6{0%{opacity:0;transform:scale(.95)}to{opacity:1;transform:scale(1)}}.dropdown-item[data-v-60e6c3a6]{text-align:left;font-family:var(--font-sans);color:var(--text-primary);cursor:pointer;background:0 0;border:none;border-radius:10px;justify-content:space-between;align-items:center;padding:.5rem .8rem;font-size:.78rem;font-weight:500;transition:all .2s;display:flex}.dropdown-item[data-v-60e6c3a6]:hover{background:#8080802e!important}.dropdown-divider[data-v-60e6c3a6]{background-color:#ffffff26;height:1px;margin:.2rem 0}.text-danger[data-v-60e6c3a6]{color:#ef4444}.text-danger[data-v-60e6c3a6]:hover{background-color:#ef44441a}.theme-toggle-btn[data-v-60e6c3a6]{gap:.3rem}.theme-icon[data-v-60e6c3a6]{font-size:.85rem;line-height:1}.theme-label[data-v-60e6c3a6]{font-size:.65rem}.modal-overlay{-webkit-backdrop-filter:blur(8px);backdrop-filter:blur(8px);z-index:2000;pointer-events:auto;background-color:#0006;justify-content:center;align-items:center;width:100%;height:100%;animation:.2s ease-out forwards fadeIn-60e6c3a6;display:flex;position:fixed;top:0;left:0}.modal-content{-webkit-backdrop-filter:blur(20px)saturate(160%);backdrop-filter:blur(20px)saturate(160%);color:var(--text-primary);text-align:center;font-family:var(--font-mono);letter-spacing:.05em;background:#f0f2f5b8;border:1px solid #ffffff8c;border-radius:20px;flex-direction:column;align-items:center;gap:1.5rem;padding:2rem 2.5rem;font-size:1rem;font-weight:600;display:flex;box-shadow:0 16px 48px #00000024,0 4px 16px #00000014}.modal-content.error{border-color:#ef4444}.confirm-btn{min-width:100px;padding:.6rem 1rem;font-size:.9rem}@keyframes fadeIn-60e6c3a6{0%{opacity:0}to{opacity:1}}.playground-tab[data-v-60e6c3a6]{color:#10b981}.playground-tab[data-v-60e6c3a6]:hover{color:#059669}.router-link-active.playground-tab[data-v-60e6c3a6]{color:#10b981}.playground-stack[data-v-60e6c3a6]{width:max-content;display:flex;position:relative}.playground-capsule[data-v-60e6c3a6]{padding-right:.35rem}.playground-capsule .nav-item[data-v-60e6c3a6]{padding-right:.4rem}.playground-x[data-v-60e6c3a6]{cursor:pointer;width:20px;height:20px;color:var(--text-secondary);background:0 0;border:none;border-radius:50%;flex-shrink:0;justify-content:center;align-items:center;padding:0;transition:color .2s,background-color .2s;display:inline-flex}.playground-x svg[data-v-60e6c3a6]{width:10px;height:10px;display:block}.playground-x[data-v-60e6c3a6]:hover{color:#ef4444;background:#8080802e}.playground-x[data-v-60e6c3a6]:disabled{opacity:.5;cursor:default}.send-btn[data-v-60e6c3a6]{white-space:nowrap;z-index:1001;gap:.3rem;position:absolute;top:calc(100% + .3rem);left:50%;transform:translate(-50%);height:28px!important;font-size:.7rem!important}.send-btn[data-v-60e6c3a6]:disabled{opacity:.7;cursor:default!important}.send-arrow[data-v-60e6c3a6]{flex-shrink:0;width:12px;height:12px;display:block}.btn-friends-icon[data-v-60e6c3a6]{flex-shrink:0;width:32px;position:relative;padding:0!important}.friends-icon[data-v-60e6c3a6]{width:16px;height:16px;display:block}.friends-badge[data-v-60e6c3a6]{color:#fff;background:#ef4444;border-radius:9999px;justify-content:center;align-items:center;min-width:16px;height:16px;padding:0 4px;font-size:.6rem;font-weight:700;display:inline-flex;position:absolute;top:-6px;right:-6px}@keyframes tabPulse-60e6c3a6{0%{opacity:1}50%{opacity:.6}to{opacity:1}}.pulse-tab[data-v-60e6c3a6]{animation:2s infinite tabPulse-60e6c3a6}.header-group-nav-mobile[data-v-60e6c3a6]{display:none}@media (width<=768px){.header-container[data-v-60e6c3a6]{flex-wrap:wrap;gap:.5rem;padding:0 .75rem}.nav-item[data-v-60e6c3a6]{padding:0 1.1rem;font-size:.75rem}.capsule-nav-circle[data-v-60e6c3a6]{width:34px;height:34px}.header-group-middle[data-v-60e6c3a6]{display:none}.header-group-nav-mobile[data-v-60e6c3a6]{flex-direction:column;flex:1 0 100%;order:10;gap:.5rem;margin-top:.25rem;display:flex}.nav-mobile-row[data-v-60e6c3a6]{justify-content:flex-start;align-items:center;gap:.5rem;width:100%;display:flex}.nav-expand-row[data-v-60e6c3a6]{flex-direction:column;align-items:flex-start;gap:.5rem;padding:.4rem 0;display:flex}#toolbar-dock[data-v-60e6c3a6]:not(.dock-active){width:0}.logo[data-v-60e6c3a6]{font-size:.85rem}.capsule-left[data-v-60e6c3a6]{padding:0 .6rem}.header-group-left[data-v-60e6c3a6],.header-group-right[data-v-60e6c3a6]{gap:.4rem;min-width:0}.capsule-btn[data-v-60e6c3a6],.user-greeting-btn[data-v-60e6c3a6]{padding:0 .6rem!important}.user-greeting-btn span[data-v-60e6c3a6]{text-overflow:ellipsis;white-space:nowrap;max-width:90px;overflow:hidden}}.app-header a,.app-header a:hover{border-bottom:none!important;text-decoration:none!important}.left-group-content[data-v-60e6c3a6]{align-items:center;gap:.5rem;display:flex}.nav-toggle-btn[data-v-60e6c3a6]{flex-shrink:0;width:34px;height:34px!important;padding:0!important}.nav-toggle-icon[data-v-60e6c3a6]{width:16px;height:16px;display:block}.nav-toggle-btn.toggle-active[data-v-60e6c3a6]{background:#6e737d59!important}.nav-expand-enter-active[data-v-60e6c3a6],.nav-expand-leave-active[data-v-60e6c3a6]{transition:opacity .18s}.nav-expand-enter-from[data-v-60e6c3a6],.nav-expand-leave-to[data-v-60e6c3a6]{opacity:0}.header-transition-enter-active[data-v-60e6c3a6],.header-transition-leave-active[data-v-60e6c3a6]{transition:opacity .18s ease-in-out}.header-transition-enter-from[data-v-60e6c3a6],.header-transition-leave-to[data-v-60e6c3a6]{opacity:0}.app-footer[data-v-0bf20916]{border-top:1px solid var(--border-light);background-color:var(--bg-secondary);margin-top:auto;padding:2rem 1.5rem}.footer-container[data-v-0bf20916]{max-width:1200px;color:var(--text-muted);letter-spacing:.05em;justify-content:space-between;align-items:center;margin:0 auto;font-size:.8rem;display:flex}.mono-tag[data-v-0bf20916]{font-family:var(--font-mono)}@media (width<=600px){.footer-container[data-v-0bf20916]{text-align:center;flex-direction:column;gap:1rem}}.beian-container[data-v-0bf20916]{text-align:center;margin-top:3000px}.beian-link[data-v-0bf20916]{color:var(--text-muted);font-family:var(--font-mono);font-size:.8rem;text-decoration:none;transition:color .2s}.beian-link[data-v-0bf20916]:hover{color:var(--text-primary)}.pwa-update-modal[data-v-788af449]{z-index:9999;-webkit-backdrop-filter:blur(4px);backdrop-filter:blur(4px);background-color:#00000080;justify-content:center;align-items:center;width:100%;height:100svh;display:flex;position:fixed;top:0;left:0}.pwa-update-content[data-v-788af449]{text-align:center;background:var(--bg-primary,#fff);border:2px solid var(--text-primary,#000);width:90%;max-width:400px;box-shadow:var(--shadow-lg,0 12px 24px #0000000f);padding:2.5rem 2rem}.pwa-update-content h3[data-v-788af449]{letter-spacing:.15em;color:var(--text-primary,#000);margin-bottom:.5rem;font-size:1.4rem}.subtitle[data-v-788af449]{color:var(--text-secondary,#555);margin-bottom:1.5rem;font-size:.85rem}.version-info[data-v-788af449]{background-color:var(--bg-secondary,#fafafa);border:1px solid var(--border-light,#e5e5e5);font-family:var(--font-mono,monospace);border-radius:8px;margin:1.5rem 0;padding:1rem;font-size:.85rem}.version-row[data-v-788af449]{justify-content:space-between;margin:.25rem 0;display:flex}.version-label[data-v-788af449]{color:var(--text-secondary,#555)}.version-val[data-v-788af449]{color:var(--text-primary,#000);font-weight:600}.version-val.highlight[data-v-788af449]{color:var(--text-primary,#000);text-decoration:underline}.update-loader-container[data-v-788af449]{flex-direction:column;align-items:center;margin:1.5rem 0 .5rem;display:flex}.spinner[data-v-788af449]{border:3px solid var(--border-light,#e5e5e5);border-left-color:var(--text-primary,#000);border-radius:50%;width:32px;height:32px;margin-bottom:.75rem;animation:.8s linear infinite spin-788af449}.updating-text[data-v-788af449]{color:var(--text-secondary,#555);font-size:.8rem}.update-success-container[data-v-788af449]{flex-direction:column;align-items:center;margin:1.5rem 0 .5rem;display:flex}.success-icon[data-v-788af449]{stroke-width:3px;width:52px;height:52px;stroke:var(--success,#4caf50);stroke-miterlimit:10;box-shadow:inset 0px 0px 0px var(--success,#4caf50);border-radius:50%;animation:.4s ease-in-out .4s forwards fill-788af449,.3s ease-in-out both scale-788af449;display:block}.success-icon-circle[data-v-788af449]{stroke-dasharray:166;stroke-dashoffset:166px;stroke-width:3px;stroke-miterlimit:10;stroke:var(--success,#4caf50);fill:none;animation:.6s cubic-bezier(.65,0,.45,1) forwards stroke-788af449}.success-icon-check[data-v-788af449]{transform-origin:50%;stroke-dasharray:48;stroke-dashoffset:48px;stroke:var(--success,#4caf50);animation:.3s cubic-bezier(.65,0,.45,1) .6s forwards stroke-788af449}.success-text[data-v-788af449]{color:var(--success,#4caf50);letter-spacing:.05em;margin-top:.75rem;font-size:.95rem;font-weight:700}.update-error-container[data-v-788af449]{border-top:1px solid var(--border-light,#e5e5e5);margin-top:1.5rem;padding-top:1.25rem}.error-text[data-v-788af449]{color:var(--error,#ff4949);margin-bottom:.75rem;font-size:.85rem}.manual-update-btn[data-v-788af449]{font-weight:700;text-decoration:none;display:block}.mt-4[data-v-788af449]{margin-top:1.25rem}.w-full[data-v-788af449]{width:100%}@keyframes stroke-788af449{to{stroke-dashoffset:0}}@keyframes scale-788af449{0%,to{transform:none}50%{transform:scale(1.1)}}@keyframes fill-788af449{to{box-shadow:inset 0 0 0 30px #4caf501a}}@keyframes spin-788af449{0%{transform:rotate(0)}to{transform:rotate(360deg)}}.animate-fade-in[data-v-788af449]{animation:.3s ease-out forwards fadeIn-788af449}.animate-scale-in[data-v-788af449]{animation:.3s ease-out forwards scaleIn-788af449}@keyframes fadeIn-788af449{0%{opacity:0;transform:scale(.95)}to{opacity:1;transform:scale(1)}}@keyframes scaleIn-788af449{0%{opacity:0;transform:scale(.9)}to{opacity:1;transform:scale(1)}}.view-fade[data-v-a261f0c2]{z-index:1499;pointer-events:none;position:fixed;inset:0;box-shadow:inset 0 0 80px #2d2d2dd9}:root.dark-theme .view-fade[data-v-a261f0c2],html.dark-theme .view-fade[data-v-a261f0c2],.dark-theme .view-fade[data-v-a261f0c2]{box-shadow:inset 0 0 80px #e5e5e5bf}.view-pill[data-v-a261f0c2]{bottom:calc(14px + env(safe-area-inset-bottom,0px));z-index:1600;-webkit-backdrop-filter:blur(6px)saturate(120%);backdrop-filter:blur(6px)saturate(120%);box-sizing:border-box;height:32px;font-family:var(--font-mono);letter-spacing:.06em;color:var(--text-primary);white-space:nowrap;background:#82879138;border:1px solid #ffffff4d;border-radius:9999px;align-items:center;gap:.5rem;max-width:min(92vw,480px);padding:0 .55rem 0 .8rem;font-size:.68rem;font-weight:700;display:flex;position:fixed;left:50%;transform:translate(-50%);box-shadow:0 8px 28px #0000001f,0 2px 8px #0000000a}:root.dark-theme .view-pill[data-v-a261f0c2],html.dark-theme .view-pill[data-v-a261f0c2],.dark-theme .view-pill[data-v-a261f0c2]{background:#2d323c94;border-color:#ffffff26;box-shadow:0 8px 28px #0006,0 2px 8px #0003}.view-eye[data-v-a261f0c2]{flex-shrink:0;width:14px;height:14px;display:block}.view-pill-name[data-v-a261f0c2]{text-overflow:ellipsis;white-space:nowrap;max-width:160px;overflow:hidden}.view-pill-sep[data-v-a261f0c2]{opacity:.4;flex-shrink:0}.view-pill-perms[data-v-a261f0c2]{flex-shrink:0;align-items:center;gap:.35rem;display:inline-flex}.perm[data-v-a261f0c2]{font-size:.62rem;font-weight:700}.perm.off[data-v-a261f0c2]{opacity:.35;text-decoration:line-through}.perm.shake[data-v-a261f0c2]{color:#ef4444;animation:.6s cubic-bezier(.36,.07,.19,.97) perm-shake-a261f0c2}@keyframes perm-shake-a261f0c2{10%,90%{transform:translate(-2px)}20%,80%{transform:translate(3px)}30%,50%,70%{transform:translate(-5px)}40%,60%{transform:translate(5px)}}.view-pill-exit[data-v-a261f0c2]{color:inherit;letter-spacing:.06em;cursor:pointer;background:0 0;border:1px solid;border-radius:9999px;flex-shrink:0;padding:.15rem .6rem;font-family:inherit;font-size:.62rem;font-weight:700}.view-pill-exit[data-v-a261f0c2]:hover{background:#8080802e}.markdown-body{color:var(--text-primary);max-width:100%;font-size:16px;line-height:1.7;overflow:auto hidden}.markdown-body .katex-display{text-align:center;padding:8px 0;display:block;overflow:auto hidden;margin:0 auto!important}.markdown-body .katex{white-space:normal;word-break:break-word;font-size:1.1em;line-height:1.2}.markdown-body .katex-display::-webkit-scrollbar{height:4px}.markdown-body .katex-display::-webkit-scrollbar-thumb{background:var(--border-light);border-radius:2px}.markdown-body table{border-collapse:collapse;border-spacing:0;empty-cells:show;table-layout:fixed;word-wrap:break-word;width:100%;margin:16px 0;font-size:14px}.markdown-body th,.markdown-body td{border:1px solid var(--border-light);text-align:left;vertical-align:top;word-break:break-word;-webkit-hyphens:manual;hyphens:manual;min-width:48px;padding:4px 8px}.markdown-body th{background-color:var(--border-light);color:var(--text-primary);text-transform:uppercase;letter-spacing:.8px;font-size:13px;font-weight:600}.markdown-body img{max-width:100%;height:auto;margin:1rem auto;display:block}.dark-theme .markdown-body img{filter:invert()hue-rotate(180deg)}.qp-stem[data-v-b040e3c2]{margin-bottom:.5rem}.qp-stem[data-v-b040e3c2] p,.subquestion-content[data-v-b040e3c2] p,.subquestion-context[data-v-b040e3c2] p{margin-bottom:.25rem}.subquestion-context[data-v-b040e3c2]{margin-bottom:2px}.subquestion-row[data-v-b040e3c2],.compound-line[data-v-b040e3c2]{align-items:flex-start;width:100%;display:flex}.subquestion-row[data-v-b040e3c2]{margin-bottom:.2rem}.subquestion-tag[data-v-b040e3c2],.compound-parent-tag[data-v-b040e3c2]{flex-shrink:0;min-width:1.8em;display:inline-block}.compound-parent-tag[data-v-b040e3c2],.subquestion-tag[data-v-b040e3c2]{font-weight:500}.subquestion-content[data-v-b040e3c2]{flex-grow:1;min-width:0;display:inline-block}.subquestion-mark[data-v-b040e3c2]{text-align:right;margin:0;font-weight:700;line-height:1.2}.compound-group[data-v-b040e3c2]{margin-bottom:.3rem}.compound-child[data-v-b040e3c2]{margin-bottom:2px;padding-left:1.5em}.qp-paper[data-v-13673066]{width:100%}.qp-paper-body[data-v-13673066]{color:var(--text-primary,#111);opacity:.9;font-size:1.05rem;line-height:1.7}.qp-paper-number[data-v-13673066]{width:1.5em;color:var(--text-primary,#111);line-height:1.7;position:absolute;top:0;left:0}.mailbox-print-root[data-v-8dc7ffb9]{visibility:hidden;pointer-events:none;width:210mm;display:block;position:fixed;top:0;left:-10000px}.fade-enter-active,.fade-leave-active{transition:opacity .15s}.fade-enter-from,.fade-leave-to{opacity:0}.question-page{height:100vh;overflow:hidden}.question-page .main-content{max-width:100%!important;min-height:0!important;padding:0!important}@font-face{font-family:Inter;font-style:normal;font-weight:300 700;font-display:swap;src:url(/fonts/Inter-latin-ext.woff2)format("woff2");unicode-range:U+100-2BA,U+2BD-2C5,U+2C7-2CC,U+2CE-2D7,U+2DD-2FF,U+304,U+308,U+329,U+1D00-1DBF,U+1E00-1E9F,U+1EF2-1EFF,U+2020,U+20A0-20AB,U+20AD-20C0,U+2113,U+2C60-2C7F,U+A720-A7FF}@font-face{font-family:Inter;font-style:normal;font-weight:300 700;font-display:swap;src:url(/fonts/Inter-latin.woff2)format("woff2");unicode-range:U+??,U+131,U+152-153,U+2BB-2BC,U+2C6,U+2DA,U+2DC,U+304,U+308,U+329,U+2000-206F,U+20AC,U+2122,U+2191,U+2193,U+2212,U+2215,U+FEFF,U+FFFD}@font-face{font-family:Outfit;font-style:normal;font-weight:300 700;font-display:swap;src:url(/fonts/Outfit-latin-ext.woff2)format("woff2");unicode-range:U+100-2BA,U+2BD-2C5,U+2C7-2CC,U+2CE-2D7,U+2DD-2FF,U+304,U+308,U+329,U+1D00-1DBF,U+1E00-1E9F,U+1EF2-1EFF,U+2020,U+20A0-20AB,U+20AD-20C0,U+2113,U+2C60-2C7F,U+A720-A7FF}@font-face{font-family:Outfit;font-style:normal;font-weight:300 700;font-display:swap;src:url(/fonts/Outfit-latin.woff2)format("woff2");unicode-range:U+??,U+131,U+152-153,U+2BB-2BC,U+2C6,U+2DA,U+2DC,U+304,U+308,U+329,U+2000-206F,U+20AC,U+2122,U+2191,U+2193,U+2212,U+2215,U+FEFF,U+FFFD}@font-face{font-family:JetBrains Mono;font-style:normal;font-weight:400 600;font-display:swap;src:url(/fonts/JetBrainsMono-latin-ext.woff2)format("woff2");unicode-range:U+100-2BA,U+2BD-2C5,U+2C7-2CC,U+2CE-2D7,U+2DD-2FF,U+304,U+308,U+329,U+1D00-1DBF,U+1E00-1E9F,U+1EF2-1EFF,U+2020,U+20A0-20AB,U+20AD-20C0,U+2113,U+2C60-2C7F,U+A720-A7FF}@font-face{font-family:JetBrains Mono;font-style:normal;font-weight:400 600;font-display:swap;src:url(/fonts/JetBrainsMono-latin.woff2)format("woff2");unicode-range:U+??,U+131,U+152-153,U+2BB-2BC,U+2C6,U+2DA,U+2DC,U+304,U+308,U+329,U+2000-206F,U+20AC,U+2122,U+2191,U+2193,U+2212,U+2215,U+FEFF,U+FFFD}:root{--font-sans:"Outfit", "Inter", -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;--font-mono:"JetBrains Mono", monospace;--bg-primary:#fff;--bg-secondary:#fafafa;--bg-tertiary:#f0f0f0;--text-primary:#000;--text-secondary:#555;--text-muted:#888;--border-light:#e5e5e5;--border-medium:#888;--border-dark:#000;--focus-ring:#00000026;--shadow-sm:0 1px 2px #0000000d;--shadow-md:0 4px 12px #00000008;--shadow-lg:0 12px 24px #0000000f;--transition:all .2s cubic-bezier(.16, 1, .3, 1)}.dark-theme{--bg-primary:#000;--bg-secondary:#0a0a0a;--bg-tertiary:#161616;--text-primary:#fff;--text-secondary:#a0a0a0;--text-muted:#666;--border-light:#222;--border-medium:#666;--border-dark:#fff;--focus-ring:#ffffff40;--shadow-sm:0 1px 2px #00000080;--shadow-md:0 4px 12px #0006;--shadow-lg:0 12px 24px #0009}*{box-sizing:border-box;-webkit-tap-highlight-color:transparent;margin:0;padding:0}html{scrollbar-gutter:stable}body{font-family:var(--font-sans);background-color:var(--bg-primary);color:var(--text-primary);-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;touch-action:pan-y;line-height:1.6}::-webkit-scrollbar{width:6px;height:6px}::-webkit-scrollbar-track{background:var(--bg-primary)}::-webkit-scrollbar-thumb{background:var(--border-light);border-radius:3px}::-webkit-scrollbar-thumb:hover{background:var(--border-medium)}h1,h2,h3,h4,h5,h6{letter-spacing:-.02em;color:var(--text-primary);font-weight:600}a{color:var(--text-primary);transition:var(--transition);border-bottom:1px solid #0000;text-decoration:none}a:hover{border-bottom-color:var(--text-primary)}input[type=text],input[type=email],input[type=password],select{width:100%;font-family:var(--font-sans);background-color:var(--bg-secondary);border:1px solid var(--border-light);color:var(--text-primary);transition:var(--transition);border-radius:12px;outline:none;padding:.75rem 1rem;font-size:.95rem}input[type=password]{-webkit-text-security:disc}input:focus,select:focus{border-color:var(--border-dark);box-shadow:0 0 0 3px var(--focus-ring);background-color:var(--bg-primary)}label{text-transform:uppercase;letter-spacing:.05em;color:var(--text-secondary);margin-bottom:.35rem;font-size:.85rem;font-weight:500;display:block}.btn{font-family:var(--font-sans);cursor:pointer;transition:var(--transition);border:1px solid var(--border-dark);border-radius:12px;justify-content:center;align-items:center;gap:.5rem;padding:.75rem 1.5rem;font-size:.9rem;font-weight:500;display:inline-flex}.btn-primary{background-color:var(--text-primary);color:var(--bg-primary)}.btn-primary:hover,.btn-secondary{color:var(--text-primary);background-color:#0000}.btn-secondary:hover{background-color:var(--text-primary);color:var(--bg-primary)}.btn-text{color:var(--text-secondary);background:0 0;border:none;padding:.5rem}.btn-text:hover{color:var(--text-primary)}.btn:disabled{opacity:.5;cursor:not-allowed}.card{background-color:var(--bg-secondary);border:1px solid var(--border-light);box-shadow:var(--shadow-sm);transition:var(--transition);border-radius:8px;padding:2rem}.card:hover{border-color:var(--border-medium);box-shadow:var(--shadow-md)}.card-stark{border:2px solid var(--text-primary);background-color:var(--bg-primary);border-radius:12px}.app-container{flex-direction:column;min-height:100svh;display:flex}.main-content{flex:1;width:100%;max-width:1200px;min-height:calc(100svh - 80px);margin:0 auto;padding:2rem 1.5rem;transition:padding-top .3s cubic-bezier(.16,1,.3,1);position:relative}.has-thin-header .main-content{padding-top:4rem}@media (width<=768px){.has-nav-row .main-content{padding-top:7.5rem}}.grid-2{grid-template-columns:repeat(2,1fr);gap:2rem;display:grid}@media (width<=768px){.grid-2{grid-template-columns:1fr}}.badge{font-family:var(--font-mono);background-color:var(--bg-tertiary);color:var(--text-secondary);border:1px solid var(--border-light);border-radius:12px;align-items:center;padding:.2rem .6rem;font-size:.75rem;font-weight:500;display:inline-flex}.badge-outline{border-color:var(--text-primary);color:var(--text-primary);background-color:#0000}.markdown-body{font-size:1rem;line-height:1.7}.markdown-body p{margin-bottom:1rem}.markdown-body pre,.markdown-body code{font-family:var(--font-mono);font-size:.9rem}.markdown-body code{background-color:var(--bg-tertiary);border-radius:3px;padding:.15rem .3rem}.markdown-body pre{background-color:var(--bg-secondary);border:1px solid var(--border-light);border-radius:12px;margin-bottom:1.25rem;padding:1rem;overflow-x:auto}.markdown-body table{border-collapse:collapse;width:100%;margin-bottom:1.5rem}.markdown-body th,.markdown-body td{border:1px solid var(--border-light);text-align:left;padding:.5rem .75rem}.markdown-body th{background-color:var(--bg-tertiary)}.katex-display{overflow:auto hidden;margin:1.5rem 0!important}@media (pointer:coarse){.handwriting-wrapper,button,.toolbar-btn{-webkit-user-select:none;user-select:none;-webkit-touch-callout:none}input,textarea{-webkit-user-select:text;user-select:text}}@media print{.katex .katex-mathml{display:none!important}.markdown-body img{max-height:12cm;max-width:50%!important}}.mw-pill{background:#82879138}.mw-unattempted{color:#64748b;background:#94a3b826}.mw-correct{color:#065f46;background:#10b98140}.mw-partial{color:#92400e;background:#eab30840}.mw-wrong{color:#991b1b;background:#ef444438}.mw-pending{color:#64748b;background:#94a3b82e}@font-face{font-display:block;font-family:KaTeX_AMS;font-style:normal;font-weight:400;src:url(/assets/KaTeX_AMS-Regular-BQhdFMY1.woff2)format("woff2"),url(/assets/KaTeX_AMS-Regular-DMm9YOAa.woff)format("woff"),url(/assets/KaTeX_AMS-Regular-DRggAlZN.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_Caligraphic;font-style:normal;font-weight:700;src:url(/assets/KaTeX_Caligraphic-Bold-Dq_IR9rO.woff2)format("woff2"),url(/assets/KaTeX_Caligraphic-Bold-BEiXGLvX.woff)format("woff"),url(/assets/KaTeX_Caligraphic-Bold-ATXxdsX0.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_Caligraphic;font-style:normal;font-weight:400;src:url(/assets/KaTeX_Caligraphic-Regular-Di6jR-x-.woff2)format("woff2"),url(/assets/KaTeX_Caligraphic-Regular-CTRA-rTL.woff)format("woff"),url(/assets/KaTeX_Caligraphic-Regular-wX97UBjC.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_Fraktur;font-style:normal;font-weight:700;src:url(/assets/KaTeX_Fraktur-Bold-CL6g_b3V.woff2)format("woff2"),url(/assets/KaTeX_Fraktur-Bold-BsDP51OF.woff)format("woff"),url(/assets/KaTeX_Fraktur-Bold-BdnERNNW.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_Fraktur;font-style:normal;font-weight:400;src:url(/assets/KaTeX_Fraktur-Regular-CTYiF6lA.woff2)format("woff2"),url(/assets/KaTeX_Fraktur-Regular-Dxdc4cR9.woff)format("woff"),url(/assets/KaTeX_Fraktur-Regular-CB_wures.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_Main;font-style:normal;font-weight:700;src:url(/assets/KaTeX_Main-Bold-Cx986IdX.woff2)format("woff2"),url(/assets/KaTeX_Main-Bold-Jm3AIy58.woff)format("woff"),url(/assets/KaTeX_Main-Bold-waoOVXN0.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_Main;font-style:italic;font-weight:700;src:url(/assets/KaTeX_Main-BoldItalic-DxDJ3AOS.woff2)format("woff2"),url(/assets/KaTeX_Main-BoldItalic-SpSLRI95.woff)format("woff"),url(/assets/KaTeX_Main-BoldItalic-DzxPMmG6.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_Main;font-style:italic;font-weight:400;src:url(/assets/KaTeX_Main-Italic-NWA7e6Wa.woff2)format("woff2"),url(/assets/KaTeX_Main-Italic-BMLOBm91.woff)format("woff"),url(/assets/KaTeX_Main-Italic-3WenGoN9.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_Main;font-style:normal;font-weight:400;src:url(/assets/KaTeX_Main-Regular-B22Nviop.woff2)format("woff2"),url(/assets/KaTeX_Main-Regular-Dr94JaBh.woff)format("woff"),url(/assets/KaTeX_Main-Regular-ypZvNtVU.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_Math;font-style:italic;font-weight:700;src:url(/assets/KaTeX_Math-BoldItalic-CZnvNsCZ.woff2)format("woff2"),url(/assets/KaTeX_Math-BoldItalic-iY-2wyZ7.woff)format("woff"),url(/assets/KaTeX_Math-BoldItalic-B3XSjfu4.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_Math;font-style:italic;font-weight:400;src:url(/assets/KaTeX_Math-Italic-t53AETM-.woff2)format("woff2"),url(/assets/KaTeX_Math-Italic-DA0__PXp.woff)format("woff"),url(/assets/KaTeX_Math-Italic-flOr_0UB.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_SansSerif;font-style:normal;font-weight:700;src:url(/assets/KaTeX_SansSerif-Bold-D1sUS0GD.woff2)format("woff2"),url(/assets/KaTeX_SansSerif-Bold-DbIhKOiC.woff)format("woff"),url(/assets/KaTeX_SansSerif-Bold-CFMepnvq.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_SansSerif;font-style:italic;font-weight:400;src:url(/assets/KaTeX_SansSerif-Italic-C3H0VqGB.woff2)format("woff2"),url(/assets/KaTeX_SansSerif-Italic-DN2j7dab.woff)format("woff"),url(/assets/KaTeX_SansSerif-Italic-YYjJ1zSn.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_SansSerif;font-style:normal;font-weight:400;src:url(/assets/KaTeX_SansSerif-Regular-DDBCnlJ7.woff2)format("woff2"),url(/assets/KaTeX_SansSerif-Regular-CS6fqUqJ.woff)format("woff"),url(/assets/KaTeX_SansSerif-Regular-BNo7hRIc.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_Script;font-style:normal;font-weight:400;src:url(/assets/KaTeX_Script-Regular-D3wIWfF6.woff2)format("woff2"),url(/assets/KaTeX_Script-Regular-D5yQViql.woff)format("woff"),url(/assets/KaTeX_Script-Regular-C5JkGWo-.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_Size1;font-style:normal;font-weight:400;src:url(/assets/KaTeX_Size1-Regular-mCD8mA8B.woff2)format("woff2"),url(/assets/KaTeX_Size1-Regular-C195tn64.woff)format("woff"),url(/assets/KaTeX_Size1-Regular-Dbsnue_I.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_Size2;font-style:normal;font-weight:400;src:url(/assets/KaTeX_Size2-Regular-Dy4dx90m.woff2)format("woff2"),url(/assets/KaTeX_Size2-Regular-oD1tc_U0.woff)format("woff"),url(/assets/KaTeX_Size2-Regular-B7gKUWhC.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_Size3;font-style:normal;font-weight:400;src:url(data:font/woff2;base64,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)format("woff2"),url(/assets/KaTeX_Size3-Regular-CTq5MqoE.woff)format("woff"),url(/assets/KaTeX_Size3-Regular-DgpXs0kz.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_Size4;font-style:normal;font-weight:400;src:url(/assets/KaTeX_Size4-Regular-Dl5lxZxV.woff2)format("woff2"),url(/assets/KaTeX_Size4-Regular-BF-4gkZK.woff)format("woff"),url(/assets/KaTeX_Size4-Regular-DWFBv043.ttf)format("truetype")}@font-face{font-display:block;font-family:KaTeX_Typewriter;font-style:normal;font-weight:400;src:url(/assets/KaTeX_Typewriter-Regular-CO6r4hn1.woff2)format("woff2"),url(/assets/KaTeX_Typewriter-Regular-C0xS9mPB.woff)format("woff"),url(/assets/KaTeX_Typewriter-Regular-D3Ib7_Hf.ttf)format("truetype")}.katex{text-indent:0;text-rendering:auto;font:1.21em/1.2 KaTeX_Main,Times New Roman,serif;position:relative}.katex *{border-color:currentColor;-ms-high-contrast-adjust:none!important}.katex .katex-version:after{content:"0.16.47"}.katex .katex-mathml{clip-path:inset(50%);border:0;width:1px;height:1px;padding:0;position:absolute;overflow:hidden}.katex .katex-html>.newline{display:block}.katex .base{white-space:nowrap;width:min-content;position:relative}.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 .mathboldfrak,.katex .textboldfrak{font-family:KaTeX_Fraktur;font-weight:700}.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 .mathsfit,.katex .textitsf{font-family:KaTeX_SansSerif;font-style:italic}.katex .mainrm{font-family:KaTeX_Main;font-style:normal}.katex .vlist-t{border-collapse:collapse;table-layout:fixed;display:inline-table}.katex .vlist-r{display:table-row}.katex .vlist{vertical-align:bottom;display:table-cell;position:relative}.katex .vlist>span{height:0;display:block;position:relative}.katex .vlist>span>span{display:inline-block}.katex .vlist>span>.pstrut{width:0;overflow:hidden}.katex .vlist-t2{margin-right:-2px}.katex .vlist-s{vertical-align:bottom;width:2px;min-width:2px;font-size:1px;display:table-cell}.katex .vbox{flex-direction:column;align-items:baseline;display:inline-flex}.katex .hbox{width:100%}.katex .hbox,.katex .thinbox{flex-direction:row;display:inline-flex}.katex .thinbox{width:0;max-width:0}.katex .msupsub{text-align:left}.katex .mfrac>span>span{text-align:center}.katex .mfrac .frac-line{border-bottom-style:solid;width:100%;display:inline-block}.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 .smash{line-height:0;display:inline}.katex .clap,.katex .llap,.katex .rlap{width:0;position:relative}.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;width:100%;display:inline-block}.katex .hdashline{border-bottom-style:dashed;width:100%;display:inline-block}.katex .sqrt>.root{margin-left:.277778em;margin-right:-.555556em}.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:.833333em}.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:1.16667em}.katex .fontsize-ensurer.reset-size2.size4,.katex .sizing.reset-size2.size4{font-size:1.33333em}.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:1.66667em}.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:3.45667em}.katex .fontsize-ensurer.reset-size2.size11,.katex .sizing.reset-size2.size11{font-size:4.14667em}.katex .fontsize-ensurer.reset-size3.size1,.katex .sizing.reset-size3.size1{font-size:.714286em}.katex .fontsize-ensurer.reset-size3.size2,.katex .sizing.reset-size3.size2{font-size:.857143em}.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:1.14286em}.katex .fontsize-ensurer.reset-size3.size5,.katex .sizing.reset-size3.size5{font-size:1.28571em}.katex .fontsize-ensurer.reset-size3.size6,.katex .sizing.reset-size3.size6{font-size:1.42857em}.katex .fontsize-ensurer.reset-size3.size7,.katex .sizing.reset-size3.size7{font-size:1.71429em}.katex .fontsize-ensurer.reset-size3.size8,.katex .sizing.reset-size3.size8{font-size:2.05714em}.katex .fontsize-ensurer.reset-size3.size9,.katex .sizing.reset-size3.size9{font-size:2.46857em}.katex .fontsize-ensurer.reset-size3.size10,.katex .sizing.reset-size3.size10{font-size:2.96286em}.katex .fontsize-ensurer.reset-size3.size11,.katex .sizing.reset-size3.size11{font-size:3.55429em}.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:.555556em}.katex .fontsize-ensurer.reset-size5.size2,.katex .sizing.reset-size5.size2{font-size:.666667em}.katex .fontsize-ensurer.reset-size5.size3,.katex .sizing.reset-size5.size3{font-size:.777778em}.katex .fontsize-ensurer.reset-size5.size4,.katex .sizing.reset-size5.size4{font-size:.888889em}.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:1.11111em}.katex .fontsize-ensurer.reset-size5.size7,.katex .sizing.reset-size5.size7{font-size:1.33333em}.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:2.30444em}.katex .fontsize-ensurer.reset-size5.size11,.katex .sizing.reset-size5.size11{font-size:2.76444em}.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:.416667em}.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:.583333em}.katex .fontsize-ensurer.reset-size7.size4,.katex .sizing.reset-size7.size4{font-size:.666667em}.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:.833333em}.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:1.72833em}.katex .fontsize-ensurer.reset-size7.size11,.katex .sizing.reset-size7.size11{font-size:2.07333em}.katex .fontsize-ensurer.reset-size8.size1,.katex .sizing.reset-size8.size1{font-size:.347222em}.katex .fontsize-ensurer.reset-size8.size2,.katex .sizing.reset-size8.size2{font-size:.416667em}.katex .fontsize-ensurer.reset-size8.size3,.katex .sizing.reset-size8.size3{font-size:.486111em}.katex .fontsize-ensurer.reset-size8.size4,.katex .sizing.reset-size8.size4{font-size:.555556em}.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:.694444em}.katex .fontsize-ensurer.reset-size8.size7,.katex .sizing.reset-size8.size7{font-size:.833333em}.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:1.44028em}.katex .fontsize-ensurer.reset-size8.size11,.katex .sizing.reset-size8.size11{font-size:1.72778em}.katex .fontsize-ensurer.reset-size9.size1,.katex .sizing.reset-size9.size1{font-size:.289352em}.katex .fontsize-ensurer.reset-size9.size2,.katex .sizing.reset-size9.size2{font-size:.347222em}.katex .fontsize-ensurer.reset-size9.size3,.katex .sizing.reset-size9.size3{font-size:.405093em}.katex .fontsize-ensurer.reset-size9.size4,.katex .sizing.reset-size9.size4{font-size:.462963em}.katex .fontsize-ensurer.reset-size9.size5,.katex .sizing.reset-size9.size5{font-size:.520833em}.katex .fontsize-ensurer.reset-size9.size6,.katex .sizing.reset-size9.size6{font-size:.578704em}.katex .fontsize-ensurer.reset-size9.size7,.katex .sizing.reset-size9.size7{font-size:.694444em}.katex .fontsize-ensurer.reset-size9.size8,.katex .sizing.reset-size9.size8{font-size:.833333em}.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:1.20023em}.katex .fontsize-ensurer.reset-size9.size11,.katex .sizing.reset-size9.size11{font-size:1.43981em}.katex .fontsize-ensurer.reset-size10.size1,.katex .sizing.reset-size10.size1{font-size:.24108em}.katex .fontsize-ensurer.reset-size10.size2,.katex .sizing.reset-size10.size2{font-size:.289296em}.katex .fontsize-ensurer.reset-size10.size3,.katex .sizing.reset-size10.size3{font-size:.337512em}.katex .fontsize-ensurer.reset-size10.size4,.katex .sizing.reset-size10.size4{font-size:.385728em}.katex .fontsize-ensurer.reset-size10.size5,.katex .sizing.reset-size10.size5{font-size:.433944em}.katex .fontsize-ensurer.reset-size10.size6,.katex .sizing.reset-size10.size6{font-size:.48216em}.katex .fontsize-ensurer.reset-size10.size7,.katex .sizing.reset-size10.size7{font-size:.578592em}.katex .fontsize-ensurer.reset-size10.size8,.katex .sizing.reset-size10.size8{font-size:.694311em}.katex .fontsize-ensurer.reset-size10.size9,.katex .sizing.reset-size10.size9{font-size:.833173em}.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:1.19961em}.katex .fontsize-ensurer.reset-size11.size1,.katex .sizing.reset-size11.size1{font-size:.200965em}.katex .fontsize-ensurer.reset-size11.size2,.katex .sizing.reset-size11.size2{font-size:.241158em}.katex .fontsize-ensurer.reset-size11.size3,.katex .sizing.reset-size11.size3{font-size:.281351em}.katex .fontsize-ensurer.reset-size11.size4,.katex .sizing.reset-size11.size4{font-size:.321543em}.katex .fontsize-ensurer.reset-size11.size5,.katex .sizing.reset-size11.size5{font-size:.361736em}.katex .fontsize-ensurer.reset-size11.size6,.katex .sizing.reset-size11.size6{font-size:.401929em}.katex .fontsize-ensurer.reset-size11.size7,.katex .sizing.reset-size11.size7{font-size:.482315em}.katex .fontsize-ensurer.reset-size11.size8,.katex .sizing.reset-size11.size8{font-size:.578778em}.katex .fontsize-ensurer.reset-size11.size9,.katex .sizing.reset-size11.size9{font-size:.694534em}.katex .fontsize-ensurer.reset-size11.size10,.katex .sizing.reset-size11.size10{font-size:.833601em}.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{width:.12em;display:inline-block}.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{min-width:1px;display:inline-block}.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;height:inherit;width:100%;display:block;position:absolute}.katex svg path{stroke:none}.katex svg{fill-rule:nonzero;fill-opacity:1;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1}.katex img{border-style:none;min-width:0;max-width:none;min-height:0;max-height:none}.katex .stretchy{width:100%;display:block;position:relative;overflow:hidden}.katex .stretchy:after,.katex .stretchy:before{content:""}.katex .hide-tail{width:100%;position:relative;overflow:hidden}.katex .halfarrow-left{width:50.2%;position:absolute;left:0;overflow:hidden}.katex .halfarrow-right{width:50.2%;position:absolute;right:0;overflow:hidden}.katex .brace-left{width:25.1%;position:absolute;left:0;overflow:hidden}.katex .brace-center{width:50%;position:absolute;left:25%;overflow:hidden}.katex .brace-right{width:25.1%;position:absolute;right:0;overflow:hidden}.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{box-sizing:border-box;border:.04em solid}.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{box-sizing:border-box;border-top:.049em solid;border-right:.049em solid;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{text-align:left;display:inline-block;position:absolute;right:calc(50% + .3em)}.katex .cd-label-right{text-align:right;display:inline-block;position:absolute;left:calc(50% + .3em)}.katex-display{text-align:center;margin:1em 0;display:block}.katex-display>.katex{text-align:center;white-space:nowrap;display:block}.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{text-align:left;padding-left:2em}body{counter-reset:katexEqnNo mmlEqnNo}