From 178befdf9f02c1fcadcd1f3806dc98e9353f364b Mon Sep 17 00:00:00 2001 From: GitHub Date: Fri, 7 Jun 2024 01:05:58 +0000 Subject: [PATCH] [auto-verifier] docs commit f70d5fbd2c1406fa22bcfd5feccb4043abd9013c --- base.css | 148 --------- notebook.css | 26 -- notebook.html | 794 --------------------------------------------- notebook.pdf | Bin 462482 -> 0 bytes src/memo/Primes.md | 14 +- 5 files changed, 7 insertions(+), 975 deletions(-) delete mode 100644 base.css delete mode 100644 notebook.css delete mode 100644 notebook.html delete mode 100644 notebook.pdf diff --git a/base.css b/base.css deleted file mode 100644 index 64bcd8b..0000000 --- a/base.css +++ /dev/null @@ -1,148 +0,0 @@ -@import url('https://fonts.googleapis.com/css2?family=JetBrains+Mono:wght@100..800&family=M+PLUS+1p&family=Ubuntu:ital,wght@0,300;0,400;0,500;0,700;1,300;1,400;1,500;1,700&display=swap&family=Roboto:ital,wght@0,100;0,300;0,400;0,500;0,700;0,900;1,100;1,300;1,400;1,500;1,700;1,900&display=swap'); -/* @import url("https://cdn.jsdelivr.net/npm/katex@0.16.9/dist/katex.min.css"); */ -@import url("https://cdnjs.cloudflare.com/ajax/libs/prism-themes/1.9.0/prism-coldark-cold.min.css"); - - -html, -code { - font-family: 'JetBrains Mono', 'M PLUS 1p'; - font-variant-ligatures: none; -} - -pre { - white-space: pre-wrap; - margin: 0; -} - -div.content { - padding: 0.3em 0; - border-top: 1px solid; - border-bottom: 1px solid; -} - -h1, -h2, -h3, -h4, -h5, -h6 { - margin-block-start: 0.2em; - margin-block-end: 0.2em; - padding-block-start: 0.3em; - padding-block-end: 0.3em; - break-after: avoid; -} - -a { - color: currentColor; -} - -h1#title { - font-weight: 800; -} - -.section { - background-color: #005a8e99; - color: #ffffff; -} - -h2.section { - margin-left: -0.5mm; - margin-right: -0.5mm; - padding-left: 1.5mm; -} - -div.filename { - display: flex; - justify-content: space-between; - align-items: baseline; -} - -/* 印刷時の設定 */ -@media print { - - body { - column-count: 2; - column-rule: 1px solid; - column-gap: 6mm; - } - - @page { - size: A4 portrait; - margin: 8mm 2.5mm 2.5mm 2.5mm; - - /* ヘッダー */ - @top-left { - content: "tatyam/ICPC_notebook"; - } - - @top-right { - content: "Page " counter(page) " of " counter(pages); - } - } -} - -/* 目次にページ数を付加する */ -nav#toc ol { - list-style: none; -} - -nav#toc>ol { - padding-left: 0; -} - -nav#toc a { - display: inline-flex; - width: 100%; - text-decoration: none; - align-items: baseline; -} - -nav#toc a.section { - padding-left: 0.5em; -} - -nav#toc>ol>ol>li>a::before { - margin-left: 0.5em; - margin-right: 0.5em; - border-bottom: 1px dotted; - content: ''; - order: 1; - flex: auto; -} - -nav#toc>ol>ol>li>a::after { - text-align: right; - content: target-counter(attr(href), page); - align-self: flex-end; - flex: none; - order: 2; -} - -/* 表に罫線をつける */ -table { - border-spacing: 0; - border-top: 1px solid lightgray; - border-left: 1px solid lightgray; -} -td, th { - border-bottom: 1px solid lightgray; - border-right: 1px solid lightgray; - padding: 4px; -} - -/* シンタックスハイライトの色を調整 */ -.token.attr-name, -.token.boolean, -.token.boolean.important, -.token.number, -.token.constant, -.token.selector .token.attribute { - color: #001575; -} -.content { - break-before: avoid; -} -.content-md { - font-family: 'Roboto', 'M PLUS 1p'; -} diff --git a/notebook.css b/notebook.css deleted file mode 100644 index 0b7d11e..0000000 --- a/notebook.css +++ /dev/null @@ -1,26 +0,0 @@ -/* generated by build/build.js */ -@import url("base.css"); - -html, -code { - font-size: 7.4pt; -} - -nav#toc { - break-after: column; -} - -@media print { - body { - column-count: 2; - } - - @page { - size: A4 portrait; - - /* ヘッダー */ - @top-left { - content: "tatyam/ICPC_notebook"; - } - } -} \ No newline at end of file diff --git a/notebook.html b/notebook.html deleted file mode 100644 index f231054..0000000 --- a/notebook.html +++ /dev/null @@ -1,794 +0,0 @@ - - - - - - - ICPC Notebook - - - - - - - - -

ICPC Notebook

- - - - -

template

- -
-

hash.sh

-
-
-
# 使い方: sh hash.sh -> コピペ -> Ctrl + D
-# コメント・空白・改行を削除して md5 でハッシュする
-g++ -dD -E -P -fpreprocessed - | tr -d '[:space:]' | md5sum | cut -c-6
-
-
- -
-

settings.sh

-
-
-
# CLion の設定
-Settings → Build → CMake → Reload CMake Project
-add_compile_options(-D_GLIBCXX_DEBUG)
-# Caps Lock を Ctrl に変更
-setxkbmap -option ctrl:nocaps
-
-
- -
-

template.hpp

- md5: 136d85 - -
-
-
#include <bits/stdc++.h>
-using namespace std;
-using ll = long long;
-const ll INF = LLONG_MAX / 4;
-#define rep(i, a, b) for(ll i = a; i < (b); i++)
-#define all(a) begin(a), end(a)
-#define sz(a) ssize(a)
-bool chmin(auto& a, auto b) { return a > b ? a = b, 1 : 0; }
-bool chmax(auto& a, auto b) { return a < b ? a = b, 1 : 0; }
-
-int main() {
-   cin.tie(0)->sync_with_stdio(0);
-   // your code here...
-}
-
-
- -

data-structure

- -
-

BIT.hpp

- md5: 8133c8 - -
-
-
struct BIT {
-   vector<ll> a;
-   BIT(ll n) : a(n + 1) {}
-   void add(ll i, ll x) {  // A[i] += x
-      i++;
-      while(i < sz(a)) {
-         a[i] += x;
-         i += i & -i;
-      }
-   }
-   ll sum(ll r) {
-      ll s = 0;
-      while(r) {
-         s += a[r];
-         r -= r & -r;
-      }
-      return s;
-   }
-   ll sum(ll l, ll r) {  // sum of A[l, r)
-      return sum(r) - sum(l);
-   }
-};
-
-
- -
-

FastSet.hpp

- md5: 2cb8c9 - -
-
-
// using u64 = uint64_t;
-const u64 B = 64;
-struct FastSet {
-   u64 n;
-   vector<vector<u64>> a;
-   FastSet(u64 n_) : n(n_) {
-      do a.emplace_back(n_ = (n_ + B - 1) / B);
-      while(n_ > 1);
-   }
-   // bool operator[](ll i) const { return a[0][i / B] >> (i % B) & 1; }
-   void set(ll i) {
-      for(auto& v : a) {
-         v[i / B] |= 1ULL << (i % B);
-         i /= B;
-      }
-   }
-   void reset(ll i) {
-      for(auto& v : a) {
-         v[i / B] &= ~(1ULL << (i % B));
-         if(v[i / B]) break;
-         i /= B;
-      }
-   }
-   ll next(ll i) {  // i を超える最⼩の要素
-      rep(h, 0, sz(a)) {
-         i++;
-         if(i / B >= sz(a[h])) break;
-         u64 d = a[h][i / B] >> (i % B);
-         if(d) {
-            i += countr_zero(d);
-            while(h--) i = i * B + countr_zero(a[h][i]);
-            return i;
-         }
-         i /= B;
-      }
-      return n;
-   }
-   ll prev(ll i) {  // i より小さい最⼤の要素
-      rep(h, 0, sz(a)) {
-         i--;
-         if(i < 0) break;
-         u64 d = a[h][i / B] << (~i % B);
-         if(d) {
-            i -= countl_zero(d);
-            while(h--) i = i * B + __lg(a[h][i]);
-            return i;
-         }
-         i /= B;
-      }
-      return -1;
-   }
-};
-
-
- -

math

- -
-

BinaryGCD.hpp

- md5: f3ab31 - -
-
-
u64 ctz(u64 x) { return countr_zero(x); }
-u64 binary_gcd(u64 x, u64 y) {
-   if(!x || !y) return x | y;
-   u64 n = ctz(x), m = ctz(y);
-   x >>= n, y >>= m;
-   while(x != y) {
-      if(x > y) x = (x - y) >> ctz(x - y);
-      else y = (y - x) >> ctz(y - x);
-   }
-   return x << min(n, m);
-}
-
-
- -
-

ExtGCD.hpp

- md5: c3fa9b - -
-
-
// returns gcd(a, b) and assign x, y to integers
-// s.t. ax + by = gcd(a, b) and |x| + |y| is minimized
-ll extgcd(ll a, ll b, ll& x, ll& y) {
-   // assert(a >= 0 && b >= 0);
-   if(!b) return x = 1, y = 0, a;
-   ll d = extgcd(b, a % b, y, x);
-   y -= a / b * x;
-   return d;
-}
-
-
- -

modint

- -
-

BarrettReduction.hpp

- md5: 2ca7f3 - -
-
-
// using u64 = uint64_t;
-struct Barrett {  // mod < 2^32
-   u64 m, im;
-   Barrett(u64 mod) : m(mod), im(-1ULL / m + 1) {}
-   // input: a * b < 2^64, output: a * b % mod
-   u64 mul(u64 a, u64 b) const {
-      a *= b;
-      u64 x = ((__uint128_t)a * im) >> 64;
-      a -= x * m;
-      if((ll)a < 0) a += m;
-      return a;
-   }
-};
-
-
- -
-

modint.hpp

- md5: 81b530 - -
-
-
const ll mod = 998244353;
-struct mm {
-   ll x;
-   mm(ll x_ = 0) : x(x_ % mod) {
-      if(x < 0) x += mod;
-   }
-   friend mm operator+(mm a, mm b) { return a.x + b.x; }
-   friend mm operator-(mm a, mm b) { return a.x - b.x; }
-   friend mm operator*(mm a, mm b) { return a.x * b.x; }
-   friend mm operator/(mm a, mm b) { return a * b.inv(); }
-   // 4 行コピペ  Alt + Shift + クリックで複数カーソル
-   friend mm& operator+=(mm& a, mm b) { return a = a.x + b.x; }
-   friend mm& operator-=(mm& a, mm b) { return a = a.x - b.x; }
-   friend mm& operator*=(mm& a, mm b) { return a = a.x * b.x; }
-   friend mm& operator/=(mm& a, mm b) { return a = a * b.inv(); }
-   mm inv() const { return pow(mod - 2); }
-   mm pow(ll b) const {
-      mm a = *this, c = 1;
-      while(b) {
-         if(b & 1) c *= a;
-         a *= a;
-         b >>= 1;
-      }
-      return c;
-   }
-};
-
-
- -

FPS

- -
-

FFT.hpp

- md5: 3138c7 - -
-
-
// {998244353, 3}, {1811939329, 13}, {2013265921, 31}
-mm g = 3;  // 原始根
-void fft(vector<mm>& a) {
-   ll n = sz(a), lg = __lg(n);
-   assert((1 << lg) == n);
-   vector<mm> b(n);
-   rep(l, 1, lg + 1) {
-      ll w = n >> l;
-      mm s = 1, r = g.pow(mod >> l);
-      for(ll u = 0; u < n / 2; u += w) {
-         rep(d, 0, w) {
-            mm x = a[u << 1 | d], y = a[u << 1 | w | d] * s;
-            b[u | d] = x + y;
-            b[n >> 1 | u | d] = x - y;
-         }
-         s *= r;
-      }
-      swap(a, b);
-   }
-}
-vector<mm> conv(vector<mm> a, vector<mm> b) {
-   if(a.empty() || b.empty()) return {};
-   size_t s = sz(a) + sz(b) - 1, n = bit_ceil(s);
-   // if(min(sz(a), sz(b)) <= 60) 愚直に掛け算
-   a.resize(n);
-   b.resize(n);
-   fft(a);
-   fft(b);
-   mm inv = mm(n).inv();
-   rep(i, 0, n) a[i] *= b[i] * inv;
-   reverse(1 + all(a));
-   fft(a);
-   a.resize(s);
-   return a;
-}
-
-
- -
-

FFT_fast.hpp

- md5: c8c567 - -
-
-
// modint を u32 にして加減算を真面目にやると速い
-mm g = 3;  // 原始根
-void fft(vector<mm>& a) {
-   ll n = sz(a), lg = __lg(n);
-   static auto z = [] {
-      vector<mm> z(30);
-      mm s = 1;
-      rep(i, 2, 32) {
-         z[i - 2] = s * g.pow(mod >> i);
-         s *= g.inv().pow(mod >> i);
-      }
-      return z;
-   }();
-   rep(l, 0, lg) {
-      ll w = 1 << (lg - l - 1);
-      mm s = 1;
-      rep(k, 0, 1 << l) {
-         ll o = k << (lg - l);
-         rep(i, o, o + w) {
-            mm x = a[i], y = a[i + w] * s;
-            a[i] = x + y;
-            a[i + w] = x - y;
-         }
-         s *= z[countr_zero<uint64_t>(~k)];
-      }
-   }
-}
-// コピペ
-void ifft(vector<mm>& a) {
-   ll n = sz(a), lg = __lg(n);
-   static auto z = [] {
-      vector<mm> z(30);
-      mm s = 1;
-      rep(i, 2, 32) {  // g を逆数に
-         z[i - 2] = s * g.inv().pow(mod >> i);
-         s *= g.pow(mod >> i);
-      }
-      return z;
-   }();
-   for(ll l = lg; l--;) {  // 逆順に
-      ll w = 1 << (lg - l - 1);
-      mm s = 1;
-      rep(k, 0, 1 << l) {
-         ll o = k << (lg - l);
-         rep(i, o, o + w) {
-            mm x = a[i], y = a[i + w];  // *s を下に移動
-            a[i] = x + y;
-            a[i + w] = (x - y) * s;
-         }
-         s *= z[countr_zero<uint64_t>(~k)];
-      }
-   }
-}
-vector<mm> conv(vector<mm> a, vector<mm> b) {
-   if(a.empty() || b.empty()) return {};
-   size_t s = sz(a) + sz(b) - 1, n = bit_ceil(s);
-   // if(min(sz(a), sz(b)) <= 60) 愚直に掛け算
-   a.resize(n);
-   b.resize(n);
-   fft(a);
-   fft(b);
-   mm inv = mm(n).inv();
-   rep(i, 0, n) a[i] *= b[i] * inv;
-   ifft(a);
-   a.resize(s);
-   return a;
-}
-
-
- -

graph

- -

graph/tree

- -

flow

- -
-

燃やす埋める.md

-
-
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
変形前の制約変形後の制約
$x$ が $0$ のとき $z$ 失う$(x, T, z)$
$x$ が $0$ のとき $z$ 得る無条件で $z$ 得る; $(S, x, z)$
$x$ が $1$ のとき $z$ 失う$(S, x, z)$
$x$ が $1$ のとき $z$ 得る無条件で $z$ 得る; $(x, T, z)$
$x, y, \dots$ がすべて $0$ のとき $z$ 得る無条件で $z$ 得る; $(S, w, z), (w, x, \infty), (w, y, \infty)$
$x, y, \dots$ がすべて $1$ のとき $z$ 得る無条件で $z$ 得る; $(w, T, z), (x, w, \infty), (y, w, \infty)$
-
- -

string

- -
-

KMP.hpp

- md5: 886c63 - -
-
-
// kmp[i] := max{ l ≤ i | s[:l] == s[(i+1)-l:i+1] }
-// abacaba -> 0010123
-auto KMP(string s) {
-   vector<ll> p(sz(s));
-   rep(i, 1, sz(s)) {
-      ll g = p[i - 1];
-      while(g && s[i] != s[g]) g = p[g - 1];
-      p[i] = g + (s[i] == s[g]);
-   }
-   return p;
-}
-
-
- -
-

Manacher.hpp

- md5: 5882fb - -
-
-
// 各位置での回文半径を求める
-// aaabaaa -> 1214121
-// 偶数長の回文を含めて直径を知るには,N+1 個の $ を挿入して 1 を引く
-// $a$a$a$b$a$a$a$ -> 123432181234321
-auto manacher(string s) {
-   ll n = sz(s), i = 0, j = 0;
-   vector<ll> r(n);
-   while(i < n) {
-      while(i >= j && i + j < n && s[i - j] == s[i + j]) j++;
-      r[i] = j;
-      ll k = 1;
-      while(i >= k && i + k < n && k + r[i - k] < j) {
-         r[i + k] = r[i - k];
-         k++;
-      }
-      i += k, j -= k;
-   }
-   return r;
-}
-
-
- -
-

RollingHash.hpp

- md5: adb8d3 - -
-
-
// using u64 = uint64_t;
-const u64 mod = INF;
-u64 add(u64 a, u64 b) {
-   a += b;
-   if(a >= mod) a -= mod;
-   return a;
-}
-u64 mul(u64 a, u64 b) {
-   auto c = (__uint128_t)a * b;
-   return add(c >> 61, c & mod);
-}
-random_device rnd;
-const u64 r = ((u64)rnd() << 32 | rnd()) % mod;
-struct RH {
-   ll n;
-   vector<u64> hs, pw;
-   RH(string s) : n(sz(s)), hs(n + 1), pw(n + 1, 1) {
-      rep(i, 0, n) {
-         pw[i + 1] = mul(pw[i], r);
-         hs[i + 1] = add(mul(hs[i], r), s[i]);
-      }
-   }
-   u64 get(ll l, ll r) const { return add(hs[r], mod - mul(hs[l], pw[r - l])); }
-};
-
-
- -
-

SuffixArray.hpp

- md5: 1d70ce - -
-
-
// returns pair{sa, lcp}
-// sa 長さ n : s[sa[0]:] < s[sa[1]:] < … < s[sa[n-1]:]
-// lcp 長さ n-1 : lcp[i] = LCP(s[sa[i]:], s[sa[i+1]:])
-auto SA(string s) {
-   ll n = sz(s) + 1, lim = 256;
-   // assert(lim > ranges::max(s));
-   vector<ll> sa(n), lcp(n), x(all(s) + 1), y(n), ws(max(n, lim)), rk(n);
-   iota(all(sa), 0);
-   for(ll j = 0, p = 0; p < n; j = max(1LL, j * 2), lim = p) {
-      p = j;
-      iota(all(y), n - j);
-      rep(i, 0, n) if(sa[i] >= j) y[p++] = sa[i] - j;
-      fill(all(ws), 0);
-      rep(i, 0, n) ws[x[i]]++;
-      rep(i, 1, lim) ws[i] += ws[i - 1];
-      for(ll i = n; i--;) sa[--ws[x[y[i]]]] = y[i];
-      swap(x, y);
-      p = 1;
-      x[sa[0]] = 0;
-      rep(i, 1, n) {
-         ll a = sa[i - 1], b = sa[i];
-         x[b] = (y[a] == y[b] && y[a + j] == y[b + j]) ? p - 1 : p++;
-      }
-   }
-   rep(i, 1, n) rk[sa[i]] = i;
-   for(ll i = 0, k = 0; i < n - 1; lcp[rk[i++]] = k) {
-      if(k) k--;
-      while(s[i + k] == s[sa[rk[i] - 1] + k]) k++;
-   }
-   sa.erase(begin(sa));
-   lcp.erase(begin(lcp));
-   return pair{sa, lcp};
-}
-
-
- -
-

Zalgorithm.hpp

- md5: b20b04 - -
-
-
// Z[i] := LCP(s, s[i:])
-// abacaba -> 7010301
-auto Z(string s) {
-   ll n = sz(s), l = -1, r = -1;
-   vector<ll> z(n, n);
-   rep(i, 1, n) {
-      ll& x = z[i] = i < r ? min(r - i, z[i - l]) : 0;
-      while(i + x < n && s[i + x] == s[x]) x++;
-      if(i + x > r) l = i, r = i + x;
-   }
-   return z;
-}
-
-
- -

algorithm

- -

geometry

- -

memo

- -
-

Primes.md

-
-

素数の個数

- - - - - - - - - - - - - - - - - - - - - - - - - -
$n$$10^2$$10^3$$10^4$$10^5$$10^6$$10^7$$10^8$$10^9$
$\pi(n)$$25$$168$$1229$$9592$$78498$$6.6 \times 10^5$$5.8 \times 10^6$$5.1 \times 10^7$
-

高度合成数

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
$≤n$$10^3$$10^4$$10^5$$10^6$$10^7$$10^8$$10^9$
$x$840756083160720720864864073513440735134400
$d^0(x)$32641282404487681344
- - - - - - - - - - - - - - - - - - - - - - - - - - - -
$≤n$$10^{10}$$10^{11}$$10^{12}$$10^{13}$$10^{14}$$10^{15}$$10^{16}$$10^{17}$$10^{18}$
$d^0(x)$2304403267201075217280268804147264512103680
-

素数階乗

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
$n$$2$$3$$5$$7$$11$$13$$17$$19$$23$$29$
$n\#$26302102310300305105109699690$2.2 \times 10^8$$6.5 \times 10^9$
-

階乗

- - - - - - - - - - - - - - - - - - - - - - - -
$5!$$6!$$7!$$8!$$9!$$10!$$11!$$12!$
1207205040403203628803628800$4.0 \times 10^7$$4.8 \times 10^8$
-
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z*4PoW8T(T6RHM1@fgqUl2%mOWLO-*dZa{fHiv2j~wl&zA{^~X^)V2k6|0L;hRI+>d z@#6x+wf(HVTW9zQ)!cpYK?#+t$&R@q(w=~|PHgfW0@NRo@8B7a;{8E#F$t-KVZi$+f%)*E7!=o;l!>odXw72 zi8|!@zLIDq(j@UMXcDDFc%+bOcvBaFe>f;@`r!J?Y^f7qBe*!SaC14!)0~Iz6ICbV zqIS#`pWtLAR9l96KKaA*XSesE{*%AFx2E(*FoauEyu9~7=2346@%ox7LVVw8ZWUKw z6Q};(p^RHO3jPol8O43yFwygeT)I@J<;)^|YI*(xRm9P1@eOKf=^pVxmr8{r#~tO9 zImGq*7`J@hk(5tHNjz+-WStrNL{7_`v^Q(?vpFB!RCe6SN%g{dC{jg|c(!$w{wqYR h(wC#Z*)%#j={q>NIee}@tn5t8EL_lJWTNt7{|9g}CW8O~ diff --git a/src/memo/Primes.md b/src/memo/Primes.md index 5fcc8eb..dcbbae5 100644 --- a/src/memo/Primes.md +++ b/src/memo/Primes.md @@ -1,8 +1,8 @@ #### 素数の個数 -| $n$ | $10^2$ | $10^3$ | $10^4$ | $10^5$ | $10^6$ | $10^7$ | $10^8$ | $10^9$ | -| --- | --- | --- | --- | --- | --- | --- | --- | --- | -| $\pi(n)$ | $25$ | $168$ | $1229$ | $9592$ | $78498$ | $6.6 \times 10^5$ | $5.8 \times 10^6$ | $5.1 \times 10^7$ | +| $n$ | $10^2$ | $10^3$ | $10^4$ | $10^5$ | $10^6$ | $10^7$ | $10^8$ | $10^9$ | $10^{10}$ | +| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | +| $\pi(n)$ | 25 | 168 | 1229 | 9592 | 78498 | 664579 | 5.76e+6 | 5.08e+7 | 4.55e+8 | #### 高度合成数 @@ -19,10 +19,10 @@ | $n$ | $2$ | $3$ | $5$ | $7$ | $11$ | $13$ | $17$ | $19$ | $23$ | $29$ | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | -| $n\\#$ | 2 | 6 | 30 | 210 | 2310 | 30030 | 510510 | 9699690 | $2.2 \times 10^8$ | $6.5 \times 10^9$ | +| $n\\#$ | 2 | 6 | 30 | 210 | 2310 | 30030 | 510510 | 9.70e+6 | 2.23e+8 | 6.47e+9 | #### 階乗 -| $5!$ | $6!$ | $7!$ | $8!$ | $9!$ | $10!$ | $11!$ | $12!$ | -| --- | --- | --- | --- | --- | --- | --- | --- | -| 120 | 720 | 5040 | 40320 | 362880 | 3628800 | $4.0 \times 10^7$ | $4.8 \times 10^8$ | +| $4!$ | $5!$ | $6!$ | $7!$ | $8!$ | $9!$ | $10!$ | $11!$ | $12!$ | $13!$ | +| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | +| 24 | 120 | 720 | 5040 | 40320 | 362880 | 3.63e+6 | 3.99e+7 | 4.79e+8 | 6.23e+9 |