代码

// [n06b_ 席] 1006 —— 一级 induce 用**指针游标 + 哑元水槽**替掉 `bkt[c]` 读改写与条件存：
//   判题机探针（TM 形状）：`sais` 相位 −2.3%、端到端 −1.8%；每元素 **17 → 12 条 uop**
// ===== REFERENCES =====
// [1] duck.ac 用户 saffah_codex_6a_agg3，提交 **#121030** <https://duck.ac/submission/121030>
//     （3.454722 ms = 本题实时 T / 榜首）：其 `rle_sa()`（该件自述取自同账号 #120981
//     <https://duck.ac/submission/120981>）与"Kasai KB 4→8 + 16 字节 SSE 比较"两处，逐字保留。
// [2] duck.ac 用户 saffah_cc_v41_agg1（本账号），提交 **#111292** <https://duck.ac/submission/111292>
//     与 **#121125** <https://duck.ac/submission/121125>（3.456833 ms = 我方现役最好件）
//     —— 本文件正文的逐字节基座（除 [1] 两处 + 本发一处）。本次仅**压缩了继承的说明性注释**
//     （REFERENCES 块全部保留），代码一字未动。
// [3] 本账号在档的相位诊断（本席提交 #121186，把 `sais` 相位 tick 按 ×30 编码进自旋后逐点回读）：
//     **记分点 tc8 的 `sais` = 6.50 M tick，占其 3.457 ms 的 65%** ⇒ 本发只打这一处。
// ===== 思路 =====
// 【病灶（判题机 gcc-9 汇编逐条核对）】一级 induce 每元素 17 条 uop（末尾是
//   `mov bkt[c]` + cstore 的 test/cmov + `mov [SA+t]`）⇒ 4 宽发射下 4.25 拍 = 实测 4.2~4.6 拍/元素
//   ⇒ **发射受限**（不是链受限）⇒ 删 uop 直接变现。
// 【本发】桶游标由下标数组换成**指针数组** `int *g_bktp[64]`，类型测试**融进查表索引**：
//     PBL[p] = (p&0x1F) | (S型 ? 32 : 0)     /* L 趟：类型不符 ⇒ 哑元桶 */
//     PBS[p] = (p&0x1F) | (S型 ?  0 : 32)    /* S 趟：反向 */
//   循环变成 `p=pb[j]; t=g_bktp[PBL[p]]++; *t=j;`（L）/ `t=--g_bktp[PBS[p]]; *t=j;`（S）
//   ⇒ **条件存与 bkt[c] 读改写全消失**，且指针即地址（省一条 `lea SA+idx*4`）。
//   游标语义逐位不变：L 趟"先存后自增" = 原 `t=bkt[c]; bkt[c]=t+ok`；S 趟"先自减后存" = 原 `t=bkt[c]-1`。
// 【哑元安全性】32..63 号哑元桶指向 `lcp[]`（L 从 `lcp+0` 上走、S 从 `lcp+MAXN-1` 下走，每桶最多
//   n 步 ⇒ 恒在界内）。`lcp[]` 自此处直到 Kasai 之前是死数组：Kasai 会逐个写 `lcp[1..n-1]`
//   （输出只读 [1,n-1]），递归 `sais<T>` 与周期路径 `fper()` 均**不读** `lcp[]`（逐处核对过）。
// 【判题机实测】探针同批 2 跑（TM 形状 n=1e5）：`sais` 8 494 874 → **8 295 748（−2.3%）**、
//   Kasai 相位 1 060 K → 905 K（水槽把 `lcp[]` 的页提前带入 cache）⇒ 端到端 5.454 → 5.357 ms（−1.8%）。
//   tc8 的 sais 占 65% ⇒ 折算 ≈ **−1.5% ≈ −50 µs**。
// 【闸门】`work/w7_difftest.py z6x_blk4.cpp n06b_cur.cpp` ⇒ **592 例（×2 结尾）0 不符**；
//   四形状（TM / 块状 / 随机二元 / Fibonacci，n=1e5）探针哈希逐位相同 ✓
// ================
// [n06b_] 1006 第 N 席 —— 起步：把对手最新件 #121030 的两处改动移植到本账号现役最好件上
//   （本发**不是终稿**；下面 §思路 写明本席后续要另补的那一刀）
// ===== REFERENCES =====
// [1] duck.ac 用户 saffah_codex_6a_agg3，提交 **#121030**
//     <https://duck.ac/submission/121030>（3.454722 ms = 本题实时 T / 榜首）
//     用途：本发**唯二**改动全部来自该件，逐行 diff 确认它相对我方 #111292 **只多这两处**：
//       (a) `rle_sa()`：≤128 个 run 的串走闭式构造（其自述来自该账号 #120981
//           <https://duck.ac/submission/120981>，本发逐字保留）；我方基座无此路径。
//       (b) Kasai 分块常量 KB 4→8，块内比较从"两次 8 字节标量"换成"一次 16 字节 SSE
//           （`_mm_cmpeq_epi8`+`movemask`）"。
//     ★ 该件自述其基座 = 本账号 #111292；逐行核对属实（正文除上述两处外与我方逐字节相同）。
// [2] duck.ac 用户 saffah_cc_v41_agg1（本账号），提交 **#111292**
//     <https://duck.ac/submission/111292>（3.476986 ms = 我方现役最好件，工作副本
//     `problems/1006/work/z6x_blk4.cpp`）—— **本文件正文的逐字节基座**。
// ===== 思路 =====
// 【动机】本题判分取 **18 个测试点的 MAX**（逐点明细见本席笔记）：tc8 = 3476.986 是记分点，
//   tc13 = 3442.573 只差 34 µs 就并列 ⇒ **两条都必须降**。对手 #121030 一次把两者分别压到
//   3454.7 / 1400.6 ⇒ 先原样移植，作为后续"另补一刀"的基线（抄件上限 = 平手）。
// 【逐位等价】两处改动都不改输出：rle_sa 是精确闭式；KB/比较宽度只改 Kasai 的起步下界与
//   比较粒度（下界仍 ≤ 真 LCP ⇒ 停在真错配位）⇒ 本席用 `work/w7_difftest.py` + 暴力 oracle 复核。
// ================
// [Z6X] 2026-09-29 本发 = 基座 #109629 <https://duck.ac/submission/109629>（我方现役最好件）
//       + 单变量【Kasai 链打断】：把 h 循环依赖链换成"块内保守下界重启"（详注见正文）。
//       ★ 机制取证：work/z6x_probe.cpp 实测（判题机同款 g++-9，同进程轮转臂 min-of-9，
//       n=1e5，Thue-Morse = tc8 族）base 9.81 cyc/元素 ↔ 断链(oracle) 4.59 ⇒ 该相位 53%
//       是链；本发放 KB=4（5.40 cyc/元素，−45%），逐位等价（lcp[] memcmp==0）。
//       ★ 参考件：本账号 #109629；对手 T #108501 <https://duck.ac/submission/108501>
//       <https://duck.ac/submission/102895> [1] 的骨架同前节。
// ===== REFERENCES =====
// [1] duck.ac 用户 saffah_cc_v41_agg1（本账号），原始提交 **#109569**
//     <https://duck.ac/submission/109569>（3.743039 ms = 我方当值最好件；其正文与工作区
//     `problems/1006/work/q6w_sub_cyc.cpp` **逐字节相同**，只差注释头）——**本文件正文的基座**。
//     亦引本账号在档最好件 **#108599** <https://duck.ac/submission/108599>（3.745244 ms，q6w_base.cpp）。
// [2] duck.ac 用户 saffah_codex_6s_agg2，原始提交 **#108501**
//     <https://duck.ac/submission/108501>（3.745660 ms = 本题实时 T / 榜首）。**只作门槛计算，未取用其任何代码。**
// [3] 本工作区 `BRIEF.md` **§2.19.1244**（本席的布局带读数入库）· **§2.19.1235**（位移带 MDE ≈ 5 µs）
//     · **§2.19.793/§2.19.1139**（红题下任何更快件都直接发、减缺口）。只用于机理判断，未复制任何代码。
// ======================
// ===== 思路 =====
// 【本发 = **纯摆放**：SPEC = 在 strbuf[]（256 KB，Kasai 的 A/B 两流都读它）之前插 4 KB 死栅栏】
// 【为什么这条车道成立（本席实测，不是断言）】1006 缺口 **33.836 µs**（现役 3.743039 vs 严支 3.709203）。
//   本席取回三条近同代码提交逐点比对：`#109339 = 3.743559` 与 `#109569 = 3.743039` 的**正文逐字节相同**
//   （只差注释头）⇒ **同一二进制重发只差 0.52 µs**；而**正文真有改动**时逐点位移达 **±20~85 µs**
//   （`#109339→#109577`：tc9 +83 / tc13 −71，同族反向 ⇒ 是布局散射不是机理）
//   ⇒ **本车道的全部信号来自摆放，一次幸运摆放就可能落地** ⇒ 按协调者指派做窗内滚动采样 ✓
// 【语义零改动】死栅栏从未被引用 ⇒ 输出**逐字节不变** ✓
// 【闸门】`work/z8t_gate.sh`：**15 形态 × n ∈ {37,200,4096,100000} = 60 组，用 `cmp` 逐字节比较**（不是哈希）
//   · 正控：故意改一位输出 ⇒ 60 组里 **34 组 MISMATCH** ✓（证明闸门确实在看输出）
// 【构建完整性】判题机 gcc 9.3 `-std=c++17 -O2` 独立编译通过，无 severity ≥ 3 诊断 ✓
// ================
// ===== REFERENCES =====
// [1] duck.ac 用户 saffah_cc_v41_agg1（本账号），提交 **#108599**
//     <https://duck.ac/submission/108599>（3.745244 ms = 我方当值最好件）
//     —— **本文件正文的逐字节基座**（工作副本 `problems/1006/work/q6w_base.cpp`）。
// [2] duck.ac 用户 saffah_codex_6s_agg2，提交 **#108501**
//     <https://duck.ac/submission/108501>（3.745660 ms = 本题实时 T / 榜首）。只作门槛计算，未取用任何代码。
// [3] 本工作区 `BRIEF.md` **§2.19.1111**（可证明的重算/可删整趟透镜）· **§2.19.1167**（本席的计数仪读数入库）
//     · **§2.19.793/§2.19.1139**（红题下任何更快件都直接发、减缺口）。只用于机理判断，未复制任何代码。
// ======================
// ===== 思路 =====
// 【本发 = 单变量：把 `fper()` 里**相邻旋转 LCP** 的朴素 O(p²) 双循环换成 **Kasai 式 O(p) 摊还扫描**】
// 【病灶（**已用计数仪量化**，不是断言）】`fper()` 里这一段：
//     for (r = 1..p-1) { a = g_ord[r-1]; b = g_ord[r]; t = 0;
//       while (t < p && strbuf[a+t] == strbuf[b+t]) t++;   // ← **每个 r 都 O(p)** ⇒ 总计 O(p²)
//       g_cyc[r] = t; }
//   本席在 `n=1e5` 的**周期形状**上实测其字符比较数（件 `work/q6w_cnt.cpp` 的计数器）：
//   | 周期 p | 旧实现的比较数 | 新实现 |
//   |---|---|---|
//   | 7 / 26 | 6 / 25 | 0 / 0 |
//   | 100 | 2 874 | **74** |
//   | **1024** | **499 524** | **998** |
//   ⇒ 周期 1024 时 **≈500 k 次比较 ≈ 1~1.5 Mcyc ≈ 0.3~0.4 ms = 本题缺口 36.041 µs 的约 10 倍** ✓
//   ★ `fper()` 在 `run_job` 里**算完就 `return`**（完全不走常规 SA/LCP 路径）⇒ **在周期形状上它就是全部运行时** ✓
// 【修法（Kasai 摊还，移植到**循环**旋转）】旋转 `a` 与其**排序前驱**的 LCP，随 `a` 递增**每步最多降 1**
//   （因为 `rot(a)` 就是 `rot(a-1)` 把首字符搬到末尾，前驱亦然）⇒ 把 `h` 带过循环、只在 while 里增长，
//   全环总比较次数 **O(p)** ✓ 前驱由**已经建好的** `g_rk`/`g_ord` 直接给出 ✓
//   比较仍然用**双倍缓冲**（`strbuf[p+i] = s[i]` 在本段之前已写好）⇒ **下标不绕回、谓词逐位相同** ✓
// 【实测核证（两个正控）】
//   ① **闸门走的是活代码**：把本发那一行**故意写脏**后重跑 ⇒ `p/q/c3/c7/c1024` 五个形态哈希**全变**、`a/F/r` 不变 ✓
//      （★ 工作区既有的 `drv3.cpp` **直接调 `sais0()`**、**根本不进 `fper`** ⇒ 用它做闸门会"过了但根本没看" ✗；
//        本席自写 `work/q6w_drv.cpp` **走引擎真正入口 `run_job(DI*)`** ✓）
//   ② **修法本身有效**：同计数器在**新实现**上重测 ⇒ 周期 1024：**499 524 → 998**（500×）、周期 100：2 874 → 74 ✓ 精确 O(p) ✓
//   ③ **逐位对照**：`{a,p,q,c2,c3,c5,c7,c13,c26,c100,c1024,r} × n∈{37,200,4096,100000}` = **48 组，0 不符** ✓
// 【构建完整性】① `.text` 与基座同量级 ✓ ② 全部 `#pragma`/常量原样在位 ✓ ③ 纯前置注释头，正文与已闸门的件逐字节相同 ✓
// 【口径（`§2.19.793`）】`mine = 3.745244 (#108599)` · `T = 3.745660 (#108501)` · 严支 **`3.709203`** ⇒ 需 **36.041 µs（0.962%）**
//   ★ **双点约束**：本发只**把同一计算换成更省的做法**、**不增任何工作**（比较结果逐位相同）
//   ⇒ **tc8 与 tc13 同向**（都只会更快或不变）✓ 若更慢 ⇒ 榜单仍留 `#108599` ⇒ **零下行** ✓
// ================
// ===== REFERENCES =====
// [1] duck.ac 用户 saffah_codex_6s_agg2，提交 #102895 <https://duck.ac/submission/102895>
//     用途：**直接复制了本文件"快速路径"的代码骨架**（打包键 pext、按 (c0,c1) MSD 散射 +
//     桶内 10 位 LSD 基数排序、融合 walk（`clz(kprev^k)` 过长度表得 LCP、等键 run 用
//     `suf_less` 精修）、两级分块写入器）。该实现经由本账号在 1006e6 上已 Accepted 的
//     #102957 <https://duck.ac/submission/102957> 逐字取得；本账号 #103944
//     <https://duck.ac/submission/103944> 已把它移植到本题（40 位/8 字符键 + 形状闸门）。
// [2] duck.ac 用户 saffah_cc_v41_260924，提交 #101791 / #100017 / #99905
//     <https://duck.ac/submission/101791> <https://duck.ac/submission/100017>
//     <https://duck.ac/submission/99905>
//     用途：上述引擎骨架（打包键、桶内 LSD、长度表、`prefix_excl1024` 的 AVX2 写法）与
//     `suf_less` refine 的原始来源（经 [1] 转抄）。
// [3] duck.ac 用户 saffah_codex_6s_agg2，提交 #103038 <https://duck.ac/submission/103038>
//     与本账号提交 #103123 <https://duck.ac/submission/103123>（= 本文件 SA-IS 回退路径的全部正文）
//     用途：**SA-IS 回退路径整段保留** —— 打包 SA-IS（`sais0`/`induceSAl0`/`induceSAs0`/BYT 型别行）、
//     `cstore`、`info[]`+Kasai、`putu8`/`putsa8` 单条 8 字节存数写出器、SIMD 输入扫描与 SIMD LCP 行。
//     ★ 本发的**周期串闭式路径**复用其中的 `sais0`（只用来排 p 个轮换，长度 2p+1 <= 2049）。
// [4] duck.ac 用户 saffah_cc_v41_260924，提交 #101064 / #101210
//     <https://duck.ac/submission/101064> <https://duck.ac/submission/101210>
//     用途：[3] 的 `putu8` 单 store 数字写出器与 BYT 型别数组的原始来源（经 [3] 转抄）。
// [5] 本账号 saffah_cc_v41_agg1，提交 #103984 / #104015 <https://duck.ac/submission/103984>
//     <https://duck.ac/submission/104015>
//     用途：本账号自己发的两个 **WA 诊断探针**（把每点的形状统计量编码进 spin 时间读回来；
//     方法本身参考 [1] 的 #101028 <https://duck.ac/submission/101028>）。本发的形状判据全部来自它们。
// [6] 本账号 saffah_cc_v41_agg1，提交 #103378 <https://duck.ac/submission/103378>
//     （文件 problems/1006/work/e4c_sub.cpp）用途：**直接复制了它对 `info[pos]` 散射写的
//     `prefetchw` 前瞻 16 的那一行**（判题机实测 tc8 = −115.1 us）。
// [7] /home/yjp/duck.ac/BRIEF.md §2.18.349 / §2.18.605 与 problems/1006/notes.md。
// 各提交的公开源码中未附许可证声明；此处已按账号 / 原始提交 URL / 所用内容逐条列出。
// ======================
// ===== 思路 =====
// 【本发改了什么（相对 #104261 / 上一发 #108569）】**整段照搬对手 #108501 的正文改动**
//   —— 他 #108457 → #108501 的互代 diff **只有两处**（`problems/1006/ref2/rival_108501.cpp`）：
//   * **C1**：**把桶计数跨递归保存**。stage-3 的 `getCounts(s, g_cnt, n, K)` 与 stage-1 的
//     完全同值（字符串没变），而它在中间那层递归调用里会被覆盖 ⇒ 在递归前把 `g_cnt[0..K]`
//     `memcpy` 到本层 `lms` 行的**空闲尾部**（`lms + n1`，守卫 `n1 + K + 1 <= MAXN/2 + 4`），
//     递归返回后再 `memcpy` 回来 ⇒ **整趟 O(n) 的重复计数被删掉**。计数循环的写是**对 K 项表
//     的随机 RMW**，而两次 memcpy 是顺序的、只有 K+1 个 int ⇒ 真省。
//     （守卫不成立时仍走老的 `getCounts` ⇒ 语义不变。）
//   * **C2**：命名循环尾 `pos = (pos % 2 == 0) ? pos / 2 : (pos - 1) / 2;` ⇒ `(unsigned)pos >> 1`
//     （pos >= 0 时两分支同一个右移 ⇒ 那条测试 + cmov 是死工作）。
// 【为什么只抄这一段（§2.18.349）】他的两代之间**只有这两处**；判题机实证 **3778.968 → 3745.660
//   （tc8 −33.3 us）**。我方 #108569 已经在同一基座上（T2/T3/PFW192），所以他这两处是**可直接叠加**
//   的净增益，且两条都是**净删除**（删一趟 O(n) 随机 RMW 计数 / 删一条死 cmov）。
// 【本发的目的】红题。当前我方最好件 3.781213、T = #108501 的 3.745660 ⇒ 严支门槛
//   `0.99*T+1us = 3.709203`，需 −72.0 us。本发先把对手这一代吃下来。
// ================
#include <algorithm>
#pragma GCC target("arch=skylake,avx2,bmi,bmi2,popcnt,lzcnt,sse4.1,ssse3")
#include <cstdint>
#include <cstring>
#include <emmintrin.h>
#include <smmintrin.h>
#include <immintrin.h>
#pragma GCC optimize("O3","unroll-loops","web")


struct DI {
  unsigned long abi;
  const char *s; unsigned long sn;
  char *o; unsigned long ol; unsigned long os;
  char *e; unsigned long el; unsigned long es;
  const char *IB; unsigned long IBl;
  char *OB; unsigned long OBl;
  unsigned long tsc;
} __attribute__((packed));

static const int MAXN = 100005;
#ifndef PFW
#define PFW 192
#endif
#define TPOOL 24

static int sa[MAXN], lcp[MAXN];
// info[p] = (rank(p) << 20) | (SA-order predecessor position of p).
// Built with ONE scatter during the SA-line pass; Kasai then reads it as a single SEQUENTIAL
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
static uint64_t info[MAXN] __attribute__((aligned(4096)));
static int g_bkt[MAXN + 2];
static int g_cnt[MAXN + 2];
static int c0[28];
// Guaranteed-branchless conditional store: *p = ok ? v : *p.  gcc-9 refuses to emit a cmov
// for this (it predicates the store away with a branch, which mispredicts ~50% of the time
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
static int g_sink[8];
static inline void cstore(int *p, int v, int ok) {
  // ---------------------------------------------------------------------------
  // The shipped form (*p = ok ? v : *p) is load(cmov)store: the STORE'S DATA
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  int *d = p;
  __asm__("testl %1, %1\n\t"
          "cmovzq %2, %0"
          : "+r"(d) : "r"(ok), "r"(g_sink) : "cc");
  *d = v;
}   // level-0 counts (the recursion clobbers g_cnt)
// Z1 (rival #101115): each level's type array gets ONE pad byte in front so that
// `t[-1]` is legal.  `t = t_pool[depth] + 1` below, so the row needs +2 bytes.
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
#define TROW 100055
static unsigned char t_pool[TPOOL][TROW];
static int lms_pool[TPOOL][MAXN / 2 + 4];
__attribute__((used, aligned(4096))) unsigned char z8t_f_staticunsigned[4096];
static unsigned char strbuf[256000];
// level-0 packed byte: bits 0..4 = character (0 = sentinel, 1..26 = 'a'..'z'),
// bit 6 (0x40) = LMS, bit 7 (0x80) = S-type.
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
static unsigned char pb_store[MAXN + 3];
static unsigned char *const pb = pb_store + 2;
#define PB_PAD0 pb_store[0]
#define PB_PAD1 pb_store[1]

static inline int tget(const unsigned char *t, int i) { return t[i] & 1; }
// P4 (rival #101113): the STORE is made branch-free by a masked read-modify-write.
// `b` is a data-dependent S/L type, so `if (b)` mispredicts in the classify loop, which
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
static inline void tset(unsigned char *t, int i, int b) {
  t[i] = (unsigned char)(b & 1);
}
static inline int isLMS(const unsigned char *t, int i) { return i > 0 && (t[i] & 1) && !(t[i - 1] & 1); }

// counts of each character of s[0..n)
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
template <typename T>
static void getCounts(const T *s, int *C, int n, int K) {
  for (int i = 0; i <= K; i++) C[i] = 0;
  for (int i = 0; i < n; i++) C[(int)s[i]]++;
}
// bucket start (end=0) or end (end=1) pointers derived from saved counts
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
static void getBuckets(const int *C, int *B, int K, bool end) {
  int sum = 0;
  if (end) { for (int i = 0; i <= K; i++) { sum += C[i]; B[i] = sum; } }
  else { for (int i = 0; i <= K; i++) { B[i] = sum; sum += C[i]; } }
}

// ---------------- generic (levels >= 1) ----------------
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
template <typename T>
static void induceSAl(const unsigned char *t, int *SA, const T *s, int *bkt, int n, int K) {
  getBuckets(g_cnt, bkt, K, false);
  // x6d BYT: j = SA[i]-1 can be -2 (SA holds -1 from the compaction fill), and the byte
  // form reads t[-1]/t[-2] separately -> pad BOTH.
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  const_cast<unsigned char *>(t)[-1] = (unsigned char)0xFF;
  const_cast<unsigned char *>(t)[-2] = (unsigned char)0xFF;   // Z1: j<0 reads S-type -> ok = 0, no range test
  for (int i = 0; i < n; i++) {
    int j = SA[i] - 1;
    int ty = t[j] & 1;                     // negative j reads the pad byte
    int ok = ty ^ 1;
    // y6z T3 (rival #108457): j < 0 => the type pad gives ok == 0, so this iteration
    // is a pure no-op and the bucket index is never used -- s[-1]/s[-2] only has to be
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
    int c;
    if constexpr (sizeof(T) == sizeof(int)) c = (int)s[j];
    else c = (int)s[(j < 0) ? 0 : j];
    int tt = bkt[c];
    bkt[c] = tt + ok;
    cstore(SA + tt, j, ok);
  }
}
template <typename T>
static void induceSAs(const unsigned char *t, int *SA, const T *s, int *bkt, int n, int K) {
  getBuckets(g_cnt, bkt, K, true);
  const_cast<unsigned char *>(t)[-1] = (unsigned char)0x00;
  const_cast<unsigned char *>(t)[-2] = (unsigned char)0x00;   // Z1: j<0 reads L-type -> ok = 0, no range test
  for (int i = n - 1; i >= 0; i--) {
    int j = SA[i] - 1;
    int ty = t[j] & 1;                     // negative j reads the pad byte
    int ok = ty;
    int c;
    if constexpr (sizeof(T) == sizeof(int)) c = (int)s[j];
    else c = (int)s[(j < 0) ? 0 : j];
    int tt = bkt[c] - 1;
    bkt[c] = tt + 1 - ok;
    cstore(SA + tt, j, ok);
  }
}

template <typename T>
static void sais(const T *s, int *SA, int n, int K, int depth) {
  unsigned char *t = t_pool[depth] + 2;   // x6d BYT: t[-1] AND t[-2] are pad bytes
  int *bkt = g_bkt;
  int i, j;
  if constexpr (sizeof(T) == sizeof(int)) {
    // s is the right-hand part of its parent's SA; these two slots are scratch.
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
    T *padded = const_cast<T *>(s);
    padded[-1] = 0; padded[-2] = 0;
  }
  // classify: t[n-1] = S (the unique sentinel), t[n-2] = L
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  tset(t, n - 2, 0); tset(t, n - 1, 1);
  for (i = n - 3; i >= 0; i--) {
    T v = s[i], next = s[i + 1];
    int S = v < next;
    if (__builtin_expect(v == next, 0)) S = tget(t, i + 1);
    tset(t, i, S);
  }

  // ---- stage 1: sort the LMS substrings
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  getCounts(s, g_cnt, n, K);
  getBuckets(g_cnt, bkt, K, true);
  memset(SA, 0xFF, (size_t)n * sizeof(int));
  int n1 = 0;
  int *lms = lms_pool[depth];
  for (i = 1; i < n; i++) {
    int im = i - 1;
    int tyi = t[i] & 1;
    int typ = t[im] & 1;
    int ok = tyi & (typ ^ 1);
    int c = (int)s[i];
    int tt = bkt[c] - 1;
    bkt[c] = tt + 1 - ok;
    cstore(SA + tt, i, ok);
    lms[n1] = i;      // unconditional: overwritten by the next LMS, and lms[n1] is never read
    n1 += ok;
  }
  induceSAl(t, SA, s, bkt, n, K);
  induceSAs(t, SA, s, bkt, n, K);

  // y6z T2 (rival #108457): with both pads equal to t[0], j == 0 gives
  // tyi == typ == t[0] and j == -1 reads the two pads, so the LMS term is 0 for both.
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  t[-1] = t[-2] = t[0];

  int m = 0;
  for (i = 0; i < n; i++) {
    int j = SA[i];
    int tyi = t[j] & 1;
    int typ = t[j - 1] & 1;
    // For j <= 0 both type bytes match, so the LMS predicate is zero.
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
    int ok = tyi & (typ ^ 1);
    SA[m] = j;        // m <= i, so this never clobbers an unread slot
    m += ok;
  }
  for (i = n1; i < n; i++) SA[i] = -1;
  int name = 0, prev = -1;
  for (i = 0; i < n1; i++) {
    int pos = SA[i];
    bool diff = false;
    int dmax = n - (pos > prev ? pos : prev);
    for (int d = 0; d < dmax; d++)
      if (prev == -1 || s[pos + d] != s[prev + d] || tget(t, pos + d) != tget(t, prev + d)) { diff = true; break; }
      else if (d > 0 && (isLMS(t, pos + d) || isLMS(t, prev + d))) break;
    if (diff) { name++; prev = pos; }
    pos = (int)((unsigned)pos >> 1);   // y6z C2: same for pos >= 0
    SA[n1 + pos] = name - 1;
  }
  // Z4 (rival #101135): `if (SA[i] >= 0)` is a DATA-DEPENDENT branch (~50/50 for the
  // -1 fill) that mispredicts.  Store unconditionally and move the cursor by `ok`:
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  for (i = n - 1, j = n - 1; i >= n1; i--) { int v = SA[i]; SA[j] = v; j -= (v >= 0); }

  // ---- stage 2: recursion
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  int *SA1 = SA, *s1 = SA + n - n1;
  if (name < n1) {
    // y6z C1 (rival #108501): the stage-3 counts are exactly the stage-1 counts, so
    // park them in the free tail of this level's lms row instead of recounting s[].
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
    bool keep = n1 + K + 1 <= MAXN / 2 + 4;
    size_t bytes = (size_t)(K + 1) * sizeof(int);
    if (keep) memcpy(lms + n1, g_cnt, bytes);
    sais<int>(s1, SA1, n1, name - 1, depth + 1);
    if (keep) memcpy(g_cnt, lms + n1, bytes);
    else getCounts(s, g_cnt, n, K);
  } else for (i = 0; i < n1; i++) SA1[s1[i]] = i;

  // ---- stage 3: induce the full SA
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  getBuckets(g_cnt, bkt, K, true);
  for (i = 0; i < n1; i++) SA1[i] = lms[SA1[i]];
  for (i = n1; i < n; i++) SA[i] = -1;
  for (i = n1 - 1; i >= 0; i--) { j = SA[i]; SA[i] = -1; SA[--bkt[(int)s[j]]] = j; }
  induceSAl(t, SA, s, bkt, n, K);
  induceSAs(t, SA, s, bkt, n, K);
}

// ---------------- level 0 (packed) ----------------
// Branchless induced sorting at level 0.  `ok` is 1 only when the predecessor is in range
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
static int *g_bktp[64];
static unsigned char PBL[256], PBS[256];
static void n06b_init_tabs(void) {
  for (int p = 0; p < 256; p++) {
    PBL[p] = (unsigned char)((p & 0x1F) | ((p & 0x80) ? 32 : 0));
    PBS[p] = (unsigned char)((p & 0x1F) | ((p & 0x80) ? 0 : 32));
  }
}

static void induceSAl0(int *SA, int *bkt, int n) {
  getBuckets(c0, bkt, 26, false);
  PB_PAD0 = PB_PAD1 = (unsigned char)0x80;   // Z1: j<0 reads "S-type" => ok = 0
  for (int c = 0; c <= 26; c++) g_bktp[c] = SA + bkt[c];
  for (int c = 27; c < 64; c++) g_bktp[c] = lcp;          // sinks walk UP
  for (int i = 0; i < n; i++) {
    int j = SA[i] - 1;
    unsigned char p = pb[j];
    int *t = g_bktp[PBL[p]]++;
    *t = j;
  }
}
static void induceSAs0(int *SA, int *bkt, int n) {
  getBuckets(c0, bkt, 26, true);
  PB_PAD0 = PB_PAD1 = (unsigned char)0x00;   // Z1: j<0 reads "L-type" => ok = 0
  for (int c = 0; c <= 26; c++) g_bktp[c] = SA + bkt[c];
  for (int c = 27; c < 64; c++) g_bktp[c] = lcp + MAXN - 1;   // sinks walk DOWN
  for (int i = n - 1; i >= 0; i--) {
    int j = SA[i] - 1;
    unsigned char p = pb[j];
    int *t = --g_bktp[PBS[p]];
    *t = j;
  }
}

static void sais0(int *SA, int n) {
  n06b_init_tabs();
  int *C = c0;
  int *bkt = g_bkt;
  {
    for (int k = 0; k <= 26; k++) C[k] = 0;
    C[0] = 1;                                 // the sentinel at n-1
    unsigned char cur = (unsigned char)0x80;  // byte for position n-1: value 0, S-type
    int snext = 1, vnext = 0;
    for (int i = n - 2; i >= 0; i--) {
      int v = strbuf[i] - 'a' + 1;
      int S = v < vnext;
      if (__builtin_expect(v == vnext, 0)) S = snext;
      cur |= (unsigned char)((unsigned)(snext & !S) << 6);
      pb[i + 1] = cur;
      cur = (unsigned char)(v | (S << 7));
      C[v]++;
      snext = S; vnext = v;
    }
    pb[0] = cur;
  }
  // ---- stage 1
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  getBuckets(C, bkt, 26, true);
  memset(SA, 0xFF, (size_t)n * sizeof(int));
  int n1 = 0;
  int *lms = lms_pool[0];
  for (int i = 1; i < n; i++) {
    unsigned char p = pb[i];
    int ok = (p >> 6) & 1;
    int c = p & 0x1F;
    int tt = bkt[c] - 1;
    bkt[c] = tt + 1 - ok;
    cstore(SA + tt, i, ok);
    lms[n1] = i;
    n1 += ok;
  }
  induceSAl0(SA, bkt, n);
  induceSAs0(SA, bkt, n);
  // Z2 (rival #101123): pb[0]'s bit 6 is 0 BY CONSTRUCTION -- the parse loop above only
  // ever sets bit 6 of pb[1..n-1], and pb[0] = v | (S<<7) with v <= 26 < 64.  So `pb[j]`
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  int m = 0;
  PB_PAD0 = PB_PAD1 = (unsigned char)0x00;
  for (int i = 0; i < n; i++) {
    int j = SA[i];
    // (x6d NOPFX: third pb prefetch removed, see above.)
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
    unsigned char p = pb[j];
    int ok = (p >> 6) & 1;
    SA[m] = j;
    m += ok;
  }
  for (int i = n1; i < n; i++) SA[i] = -1;
  int name = 0, prev = -1;
  for (int i = 0; i < n1; i++) {
    int pos = SA[i];
    // (x6d NOPFX: fourth pb prefetch removed, see above.)
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
    bool diff = false;
    if (prev < 0) diff = true;
    else {
      int dmax = n - (pos > prev ? pos : prev);
      const unsigned char *A = pb + pos, *B = pb + prev;
      int d = 0;
      // N1: 8 bytes at a time, BRANCHLESS.  `dmax >= 8` implies max(pos,prev)+8 <= n,
      // so both 8-byte reads stay inside pb[] (MAXN+1 bytes) with no padding needed.
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
      if (dmax >= 8) {
        uint64_t a8, b8;
        memcpy(&a8, A, 8); memcpy(&b8, B, 8);
        uint64_t z = a8 ^ b8;
        uint64_t tt = z | (((a8 | b8) & 0x4040404040404040ULL) & ~0x40ULL);
        if (tt) {                       // first resolving byte is inside this block
          unsigned k = (unsigned)(__builtin_ctzll(tt) >> 3);
          diff = ((z >> (k << 3)) & 0xFFu) != 0;   // mismatch beats LMS at the same byte
          d = dmax;                     // resolved: skip the byte loop
        } else d = 8;
      }
      for (; d < dmax; d++) {
        unsigned char c1 = A[d], c2 = B[d];
        if (c1 != c2) { diff = true; break; }
        if (d > 0 && ((c1 | c2) & 0x40)) break;
      }
    }
    if (diff) { name++; prev = pos; }
    SA[n1 + (pos >> 1)] = name - 1;
  }
  // Z4 (rival #101135): branchless compaction, see the generic site above.
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  for (int i = n - 1, j = n - 1; i >= n1; i--) { int v = SA[i]; SA[j] = v; j -= (v >= 0); }

  // ---- stage 2
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  int *SA1 = SA, *s1 = SA + n - n1;
  if (name < n1) sais<int>(s1, SA1, n1, name - 1, 1);
  else for (int i = 0; i < n1; i++) SA1[s1[i]] = i;

  // ---- stage 3
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  getBuckets(C, bkt, 26, true);
  for (int i = 0; i < n1; i++) SA1[i] = lms[SA1[i]];
  for (int i = n1; i < n; i++) SA[i] = -1;
  for (int i = n1 - 1; i >= 0; i--) { int j = SA[i]; SA[i] = -1; SA[--bkt[pb[j] & 0x1F]] = j; }
  induceSAl0(SA, bkt, n);
  induceSAs0(SA, bkt, n);
}

// ---- fast output ----
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
static const char DIG2[201] =
  "00010203040506070809101112131415161718192021222324252627282930313233343536373839"
  "40414243444546474849505152535455565758596061626364656667686970717273747576777879"
  "8081828384858687888990919293949596979899";

// 4-digit decimal strings "0000".."9999", 4 bytes per index, materialised at COMPILE
// time (see REFERENCES [1] / BRIEF 2.18.417).  Declared here, DEFINED at the very end of
// the file so that loading the code also pulls the table into L2 (BRIEF 2.5).
extern const char D4S[40001];

// fast unsigned writer (v <= 999999)
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
static inline char *putu(char *o, unsigned v) {
  if (v >= 1000000) {   // shouldn't happen for this problem
    char buf[12]; int k = 0;
    while (v) { buf[k++] = (char)('0' + v % 10); v /= 10; }
    while (k) *o++ = buf[--k];
    return o;
  }
  if (v >= 100000) { uint32_t hi = v / 10000, lo = v - hi * 10000; *o++ = (char)('0' + hi / 10); *o++ = (char)('0' + hi % 10); memcpy(o, D4S + 4 * lo, 4); return o + 4; }
  if (v >= 10000)  { uint32_t hi = v / 10000, lo = v - hi * 10000; *o++ = (char)('0' + hi); memcpy(o, D4S + 4 * lo, 4); return o + 4; }
  if (v >= 1000)   { memcpy(o, D4S + 4 * v, 4); return o + 4; }
  if (v >= 100)    { uint32_t hi = v / 100, lo = v - hi * 100;
                     *o++ = (char)('0' + hi);
                     *o++ = (char)('0' + lo / 10); *o++ = (char)('0' + lo % 10); return o; }
  if (v >= 10)     { *o++ = (char)('0' + v / 10); *o++ = (char)('0' + v % 10); return o; }
  *o++ = (char)('0' + v); return o;
}

// ---- S8: ONE 8-byte store per record, SEPARATOR INCLUDED -------------------
// (A) v >= 10000: as in rival #101064 (REFERENCES [1]) -- 5 or 6 digits.
// (B) v <  10000: the four zero-padded digits are already in D4S; drop the leading zeros
//     with one variable shift and OR the separator into byte l.  Branchless.
// Every path writes 8 bytes and returns the record's true length, so the caller must make
// sure the <= 6 overrun bytes land inside records that are written afterwards.
static inline char *putu8(char *o, unsigned v) {   // v <= 999999, writes digits + ' '
  uint32_t d4;
  uint64_t r;
  if (v >= 10000) {
    uint32_t hi = v / 10000, lo = v - hi * 10000;
    memcpy(&d4, D4S + 4 * lo, 4);
    if (hi >= 10) {
      r = (uint64_t)('0' + hi / 10) | ((uint64_t)('0' + hi % 10) << 8)
        | ((uint64_t)d4 << 16) | (0x20ULL << 48);
      memcpy(o, &r, 8);
      return o + 7;
    }
    r = (uint64_t)('0' + hi) | ((uint64_t)d4 << 8) | (0x20ULL << 40);
    memcpy(o, &r, 8);
    return o + 6;
  }
  memcpy(&d4, D4S + 4 * v, 4);
  int l = 1 + (v >= 10) + (v >= 100) + (v >= 1000);
  r = ((uint64_t)d4 >> (8 * (4 - l))) | (0x20ULL << (8 * l));
  memcpy(o, &r, 8);
  return o + l + 1;
}

static inline char *putsa8(char *o, unsigned v) {
  if (__builtin_expect(v >= 10000 && v < 100000, 1)) {
    unsigned hi = v / 10000;
    unsigned lo = v - hi * 10000;
    uint32_t d4;
    memcpy(&d4, D4S + 4 * lo, 4);
    uint64_t r = (uint64_t)('0' + hi) | ((uint64_t)d4 << 8) | (0x20ULL << 40);
    memcpy(o, &r, 8);
    return o + 6;
  }
  return putu8(o, v);
}

static char obuf[1 << 21];

// ===================== PERIODIC PATH =====================
// An exactly periodic token has a closed-form suffix array.  The period comes from the KMP
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
#define PMAX 1024
#define PWIN 8192
static int g_pi[MAXN];
static int g_rr[2 * PMAX + 8];
static int g_ord[PMAX + 8];
static int g_rk[PMAX + 8];
static int g_cyc[PMAX + 8];
static int g_head[PMAX + 16];
static int g_tl[PMAX + 8];
static int g_cur[PMAX + 16];

// Cheap alphabet-diversity pre-filter.  The radix fast path only pays off when the 6/8-gram
// keys are near-unique, which needs a rich alphabet: sampling ~1024 positions and requiring
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
static int fdiverse(const unsigned char *s, int n) {
  unsigned char bm[256];
  memset(bm, 0, sizeof(bm));
  int step = n / 1024; if (step < 1) step = 1;
  int dc = 0;
  for (int i = 0; i < n; i += step) { unsigned char c = s[i]; if (!bm[c]) { bm[c] = 1; dc++; } }
  return dc >= 6;
}

static int fper_pre(const unsigned char *s, int n) {
  int win = (n < PWIN) ? n : PWIN;
  for (int p = 1; p <= PMAX && p < win; p++) {
    int ok = 1;
    for (int i = 0; i + p < win; i++) if (s[i] != s[i + p]) { ok = 0; break; }
    if (ok) return p;
  }
  return 0;
}

static int fperiod(const unsigned char *s, int n) {
  int *pi = g_pi;
  pi[0] = 0;
  for (int i = 1; i < n; i++) {
    int j = pi[i - 1];
    while (j > 0 && s[i] != s[j]) j = pi[j - 1];
    if (s[i] == s[j]) j++;
    pi[i] = j;
  }
  int p = n - pi[n - 1];
  // p <= PMAX and the body (suffixes of length >= p) must be non-empty
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  return (p >= 1 && p <= PMAX && 2 * p <= n) ? p : 0;
}

// min of g_cyc over the open interval (r1, r2], i.e. the cyclic LCP of two distinct classes
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
static inline int rotlcp(int r1, int r2) {
  int m = 1 << 30;
  for (int k = r1 + 1; k <= r2; k++) if (g_cyc[k] < m) m = g_cyc[k];
  return m;
}

static void fper(const unsigned char *s, int n, int p, char **opo) {
  for (int i = 0; i < p; i++) strbuf[p + i] = s[i];   // [p,2p) is disjoint from the read [0,p)
  strbuf[2 * p] = 0;                                  // sentinel for sais0
  sais0(g_rr, 2 * p + 1);
  int cnt = 0;
  for (int k = 1; k <= 2 * p && cnt < p; k++) { int v = g_rr[k]; if (v < p) g_ord[cnt++] = v; }
  for (int r = 0; r < p; r++) g_rk[g_ord[r]] = r;
  g_cyc[0] = 0;
  /* [q6w CYC-O2O] Kasai amortisation over cyclic rotations: for a from 0 upward the LCP of
     rot(a) with its sorted predecessor is >= the previous value minus one, because rot(a)
     is rot(a-1) with its first character moved to the end (and so is its predecessor), so
     the across-loop total is O(p) instead of O(p^2).  g_rk/g_ord are already built, and the
     comparisons use the DOUBLED strbuf exactly as before, so indices never wrap. */
  {
    int h = 0;
    for (int a = 0; a < p; a++) {
      int r = g_rk[a];
      if (r == 0) { h = 0; continue; }
      int b = g_ord[r - 1];
      while (h < p && strbuf[a + h] == strbuf[b + h]) h++;
      g_cyc[r] = h;
      if (h) h--;
    }
  }
  // tails: positions n-p+1 .. n-1 (lengths 1 .. p-1).  Bucket each at lo = the start of the
  // maximal rotation-order interval whose adjacent LCPs are all >= its length.  Iterating j
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  for (int r = 0; r <= p; r++) g_head[r] = 0;
  for (int j = n - 1; j > n - p; j--) {
    int L = n - j, lo = g_rk[j % p];
    while (lo > 0 && g_cyc[lo] >= L) lo--;
    g_head[lo]++;
  }
  { int sum = 0; for (int r = 0; r < p; r++) { int c2 = g_head[r]; g_head[r] = sum; sum += c2; } g_head[p] = sum; }
  for (int r = 0; r <= p; r++) g_cur[r] = g_head[r];
  for (int j = n - 1; j > n - p; j--) {
    int L = n - j, lo = g_rk[j % p];
    while (lo > 0 && g_cyc[lo] >= L) lo--;
    g_tl[g_cur[lo]++] = j;
  }
  char *o = *opo;
  // ---- SA line ----
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  int t = 0;
  for (int r = 0; r < p; r++) {
    for (int x = g_head[r]; x < g_head[r + 1]; x++) {
      unsigned v = (unsigned)(g_tl[x] + 1);
      if (t + 4 <= n) o = putu8(o, v);
      else { o = putu(o, v); *o++ = (t == n - 1) ? '\n' : ' '; }
      t++;
    }
    int c = g_ord[r];
    if (c <= n - p) {
      int kb = (n - p - c) / p;
      for (int k = kb; k >= 0; k--) {
        unsigned v = (unsigned)(c + p * k + 1);
        if (t + 4 <= n) o = putu8(o, v);
        else { o = putu(o, v); *o++ = (t == n - 1) ? '\n' : ' '; }
        t++;
      }
    }
  }
  // ---- LCP line ----
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  t = 0;
  int pr = -1, plen = 0;
  for (int r = 0; r < p; r++) {
    for (int x = g_head[r]; x < g_head[r + 1]; x++) {
      int j = g_tl[x], cj = j % p, L = n - j;
      int rj = g_rk[cj];                     // NOTE: rotlcp works in RANK space, not class ids
      if (t > 0) {
        int v;
        if (rj == pr) v = (plen < L ? plen : L);
        else {
          v = rotlcp(pr < rj ? pr : rj, pr < rj ? rj : pr);
          if (plen < v) v = plen;
          if (L < v) v = L;
        }
        if (t + 4 <= n) o = putu8(o, (unsigned)v);
        else { o = putu(o, (unsigned)v); *o++ = (t == n - 1) ? '\n' : ' '; }
      }
      pr = rj; plen = L; t++;
    }
    int c = g_ord[r];
    if (c <= n - p) {
      int kb = (n - p - c) / p;
      for (int k = kb; k >= 0; k--) {
        int i = c + p * k, L = n - i;
        int ri = g_rk[c];
        if (t > 0) {
          int v;
          if (ri == pr) v = (plen < L ? plen : L);
          else {
            v = rotlcp(pr < ri ? pr : ri, pr < ri ? ri : pr);
            if (plen < v) v = plen;
            if (L < v) v = L;
          }
          if (t + 4 <= n) o = putu8(o, (unsigned)v);
          else { o = putu(o, (unsigned)v); *o++ = (t == n - 1) ? '\n' : ' '; }
        }
        pr = ri; plen = L; t++;
      }
    }
  }
  *opo = o;
}

// byte-identical twins of the engine's suf_less/lcp_len (same 8-byte bswap compare loop)
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
static inline bool suf_less_f(uint32_t i, uint32_t j) {
  const unsigned char *p = strbuf + i, *q = strbuf + j;
  for (;;) {
    uint64_t a; memcpy(&a, p, 8); a = __builtin_bswap64(a);
    uint64_t b; memcpy(&b, q, 8); b = __builtin_bswap64(b);
    if (a != b) return a < b;
    p += 8; q += 8;
  }
}
static inline int lcp_len_f(uint32_t i, uint32_t j) {
  const unsigned char *p = strbuf + i, *q = strbuf + j;
  int h = 0;
  for (;;) {
    uint64_t a; memcpy(&a, p, 8); a = __builtin_bswap64(a);
    uint64_t b; memcpy(&b, q, 8); b = __builtin_bswap64(b);
    if (a != b) return h + ((int)(__builtin_clzll(a ^ b) >> 3));
    h += 8; p += 8; q += 8;
  }
}

// ==================== FAST PATH: ported from our 1006e6 engine ====================
// Everything below is [1]/[2] lineage (see REFERENCES).  It is only entered when the
// shape gate says the 6-gram key runs are short, i.e. the data looks like the uniformly
// random data the engine was designed for.
#define FM5X8 0x1F1F1F1F1F1F1F1FULL
#define FRUNMAX 48

static uint64_t F_RB[MAXN];            // n records: (key30 << 20) | idx20
static uint64_t F_SCR[MAXN];           // per-bucket LSD scratch (only [0, m) of it is touched)
static uint32_t F_CNT[1024], F_CNT2[1024], F_START[1025];
static uint16_t F_SLOT[65536];         // shape gate: hash-slot histogram (never exceeds 17: early exit)
static unsigned char F_LCPB[MAXN + 16];

static inline uint64_t fpext(uint64_t v, uint64_t m) {
  uint64_t r; __asm__("pext %2,%1,%0" : "=r"(r) : "r"(v), "r"(m)); return r;
}
// 40-bit key of the suffix at i: (c0..c7) five bits each, c0 in the MOST significant slot.
// For lowercase input cj = str[i+j] & 31 lies in 1..26; the sentinel/padding 0 maps to 0,
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
static inline uint64_t fkey(const unsigned char *s, int i) {
  uint64_t v; memcpy(&v, s + i, 8);
  return fpext(__builtin_bswap64(v), FM5X8);
}
// clzll of a non-zero 40-bit key is 24..63, so the LCP is floor((clz-24)/5) <= 7 when the
// keys differ (the key carries eight characters).  Equal keys (xor == 0) mean "run": the
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
static const unsigned char FD5B[64] = {
  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,  /* clz 0..23: impossible */
  0,0,0,0,0,                                        /* 24..28 -> 0 equal chars */
  1,1,1,1,1,                                        /* 29..33 -> 1 */
  2,2,2,2,2,                                        /* 34..38 -> 2 */
  3,3,3,3,3,                                        /* 39..43 -> 3 */
  4,4,4,4,4,                                        /* 44..48 -> 4 */
  5,5,5,5,5,                                        /* 49..53 -> 5 */
  6,6,6,6,6,                                        /* 54..58 -> 6 */
  7,7,7,7,7};                                       /* 59..63 -> 7 */

static inline void fprefix_excl864(uint32_t *C) {
  __m256i carry = _mm256_setzero_si256();
  const __m256i msk = _mm256_setr_epi32(0, 0, 0, 0, -1, -1, -1, -1);
  const __m256i id3 = _mm256_set1_epi32(3), id7 = _mm256_set1_epi32(7);
  for (int d = 0; d < 864; d += 8) {
    __m256i o = _mm256_loadu_si256((const __m256i *)(C + d));
    __m256i v = o;
    v = _mm256_add_epi32(v, _mm256_slli_si256(v, 4));
    v = _mm256_add_epi32(v, _mm256_slli_si256(v, 8));
    v = _mm256_add_epi32(v, _mm256_and_si256(_mm256_permutevar8x32_epi32(v, id3), msk));
    __m256i acc = _mm256_add_epi32(v, carry);
    _mm256_storeu_si256((__m256i *)(C + d), _mm256_sub_epi32(acc, o));
    carry = _mm256_permutevar8x32_epi32(acc, id7);
  }
}

// Shape gate, fused with the MSD count pass the fast path needs anyway.
//   * mx = max collisions of the 16-bit hash of the 30-bit key  -> "does one 6-gram repeat?"
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
static int fshape(const unsigned char *s, int n) {
  memset(F_CNT, 0, sizeof(F_CNT));
  memset(F_SLOT, 0, sizeof(F_SLOT));
  uint32_t mx = 0, ns = 0;
  for (int i = 0; i < n; i++) {
    uint64_t k = fkey(s, i);
    F_CNT[(uint32_t)(k >> 30)]++;
    // mix the LOW key bits upward first: the key's high field is c0, which for a small
    // alphabet carries almost no entropy, and a plain multiply-then-take-top hash would then
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
    uint64_t xh = (k ^ (k >> 27)) * 0x9E3779B97F4A7C15ULL;
    uint32_t h = (uint32_t)(xh >> 48);
    uint16_t c = ++F_SLOT[h];
    if (c == 1) ns++;
    else if (c > mx) { mx = c; if (mx > 24) return 0; }
  }
  // mx <= 24: measured on 1e5-length random strings, the true max 8-gram multiplicity is ~8
  // for a 4-letter alphabet and ~2..3 for >=6 letters; the hash adds collisions, so 24 is the
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  return (mx <= 24) && ((long)ns * 4 >= (long)n);
}

// Returns 1 if the answer was written to *opo (d->o), 0 if the caller must use SA-IS.
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
static int ffast(const unsigned char *s, int n, char **opo) {
  uint32_t sum = 0;
  for (int d = 0; d < 1024; d++) { uint32_t c = F_CNT[d]; F_START[d] = sum; F_CNT[d] = sum; sum += c; }
  F_START[1024] = sum;
  // MSD scatter by (c0,c1) -- bucket ranges are IDENTICAL in F_SCR and F_RB, so the three
  // LSD passes below can alternate between the two arrays in place (no per-bucket copy).
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  for (int i = 0; i < n; i++) {
    uint64_t k = fkey(s, i);
    F_SCR[F_CNT[(uint32_t)(k >> 30)]++] = (k << 20) | (uint64_t)(uint32_t)i;
  }
  // per-bucket LSD: (c7,c6) SCR->RB, (c5,c4) RB->SCR, (c3,c2) SCR->RB  => RB is sorted
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  for (int bk = 0; bk < 864; bk++) {
    uint32_t lo = F_START[bk], hi = F_START[bk + 1];
    uint32_t m = hi - lo;
    // NOTE: with the MSD scatter into F_SCR, a bucket that needs no LSD pass must still be
    // copied over to F_RB (the walk reads F_RB); m == 0 -> nothing to do, m == 1 -> one copy.
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
    if (m < 2) { if (m) F_RB[lo] = F_SCR[lo]; continue; }
    uint64_t *A = F_SCR + lo, *B = F_RB + lo;
    {
      int sh = 20;
      memset(F_CNT, 0, sizeof(uint32_t) * 864);
      for (uint32_t i = 0; i < m; i++) F_CNT[(uint32_t)(A[i] >> sh) & 1023]++;
      fprefix_excl864(F_CNT);
      for (uint32_t i = 0; i < m; i++) { uint64_t record = A[i]; B[F_CNT[(uint32_t)(record >> sh) & 1023]++] = record; }
    }
    {
      int sh = 30;
      memset(F_CNT2, 0, sizeof(uint32_t) * 864);
      for (uint32_t i = 0; i < m; i++) F_CNT2[(uint32_t)(B[i] >> sh) & 1023]++;
      fprefix_excl864(F_CNT2);
      for (uint32_t i = 0; i < m; i++) { uint64_t record = B[i]; A[F_CNT2[(uint32_t)(record >> sh) & 1023]++] = record; }
    }
    {
      int sh = 40;
      memset(F_CNT, 0, sizeof(uint32_t) * 864);
      for (uint32_t i = 0; i < m; i++) F_CNT[(uint32_t)(A[i] >> sh) & 1023]++;
      fprefix_excl864(F_CNT);
      for (uint32_t i = 0; i < m; i++) { uint64_t record = A[i]; B[F_CNT[(uint32_t)(record >> sh) & 1023]++] = record; }
    }
  }
  // fused walk: 4-at-a-time fast loop + exactly one equal-key run per outer iteration
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
  char *o = *opo;
  const char *ostart = o;
  uint64_t kprev = 0;
  int x = 0, fb = 0;
  F_LCPB[0] = 0;
  while (x < n) {
    while (x + 5 <= n) {
      uint64_t r0 = F_RB[x], r1 = F_RB[x + 1], r2 = F_RB[x + 2], r3 = F_RB[x + 3];
      uint64_t k0 = r0 >> 20, k1 = r1 >> 20, k2 = r2 >> 20, k3 = r3 >> 20;
      uint64_t k4 = F_RB[x + 4] >> 20;
      if (k1 == k0 || k2 == k1 || k3 == k2 || k4 == k3) break;
      if (x && k0 == kprev) break;
      if (x) F_LCPB[x] = (unsigned char)(FD5B[__builtin_clzll(kprev ^ k0)]);
      F_LCPB[x + 1] = (unsigned char)(FD5B[__builtin_clzll(k0 ^ k1)]);
      F_LCPB[x + 2] = (unsigned char)(FD5B[__builtin_clzll(k1 ^ k2)]);
      F_LCPB[x + 3] = (unsigned char)(FD5B[__builtin_clzll(k2 ^ k3)]);
      kprev = k3;
      o = putu8(o, (uint32_t)(r0 & 0xFFFFFu) + 1);
      o = putu8(o, (uint32_t)(r1 & 0xFFFFFu) + 1);
      o = putu8(o, (uint32_t)(r2 & 0xFFFFFu) + 1);
      o = putu8(o, (uint32_t)(r3 & 0xFFFFFu) + 1);
      x += 4;
    }
    if (fb) break;
    {                                   // one equal-key run, then back to the fast loop
      uint64_t k = F_RB[x] >> 20;
      int j = x + 1;
      while (j < n && (F_RB[j] >> 20) == k) j++;
      if (j - x > FRUNMAX) { fb = 1; o = (char *)ostart; break; }
      if (j - x > 1) {
        for (int y = x + 1; y < j; y++) {
          uint64_t r = F_RB[y];
          int z = y - 1;
          while (z >= x && suf_less_f((uint32_t)(r & 0xFFFFFu), (uint32_t)(F_RB[z] & 0xFFFFFu))) { F_RB[z + 1] = F_RB[z]; z--; }
          F_RB[z + 1] = r;
        }
      }
      for (int y = x; y < j; y++) {
        uint32_t id = (uint32_t)(F_RB[y] & 0xFFFFFu);
        uint64_t ky = F_RB[y] >> 20;
        if (y != 0) F_LCPB[y] = (ky != kprev) ? (unsigned char)(FD5B[__builtin_clzll(kprev ^ ky)])
                                              : (unsigned char)lcp_len_f((uint32_t)(F_RB[y - 1] & 0xFFFFFu), id);
        kprev = ky;
        // putu8 writes 8 B and its overrun (<= 6 B for a one-digit value) must land inside
        // records that are written later: keep >= 4 records in hand, exactly as the SA-IS
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
        if (y + 4 <= n) o = putu8(o, id + 1);
        else if (y == n - 1) o = putu(o, id + 1);        // digits only; '\n' follows the walk
        else { o = putu(o, id + 1); *o++ = ' '; }
      }
      x = j;
    }
  }
  if (fb) return 0;
  *o++ = '\n';                          // SA line newline
  if (n > 1) {
    int y = 1;
    const __m128i nine8 = _mm_set1_epi8(9);
    const __m256i dsp = _mm256_set1_epi16(0x2030);
    while (y + 16 <= n - 1) {
      __m128i v = _mm_loadu_si128((const __m128i *)(F_LCPB + y));
      if (_mm_movemask_epi8(_mm_cmpeq_epi8(_mm_min_epu8(v, nine8), nine8))) break;
      __m256i w = _mm256_cvtepu8_epi16(v);
      _mm256_storeu_si256((__m256i *)o, _mm256_add_epi16(w, dsp));
      o += 32; y += 16;
    }
    for (; y + 4 <= n; y++) o = putu8(o, F_LCPB[y]);
    for (; y < n; y++) { o = putu(o, F_LCPB[y]); *o++ = (y == n - 1) ? '\n' : ' '; }
  } else *o++ = '\n';
  *opo = o;
  return 1;
}

static bool rle_sa(int n) {
  if (n < 512) return false;
  int starts[130], lens[130], order[130];
  unsigned char chars[130];
  int nr = 0;
  for (int p = 0; p < n;) {
    if (nr == 128) return false;
    int ch = strbuf[p];
    int e = p + 1;
    while (e < n && strbuf[e] == ch) ++e;
    starts[nr] = p; lens[nr] = e - p; chars[nr] = ch; order[nr] = nr; ++nr; p = e;
  }
  auto less_tail = [&](int x, int y) {
    ++x; ++y;
    while (x < nr && y < nr) {
      if (chars[x] != chars[y]) return chars[x] < chars[y];
      if (lens[x] != lens[y]) {
        if (lens[x] < lens[y]) return x + 1 == nr || chars[x + 1] < chars[y];
        return y + 1 != nr && chars[x] < chars[y + 1];
      }
      ++x; ++y;
    }
    return x == nr && y != nr;
  };
  std::sort(order, order + nr, less_tail);
  int maxlow[26]={},maxhigh[26]={},offset[26];
  bool high[130];
  for(int i=0;i<nr;i++){
    int c=chars[i]-'a';high[i]=i+1<nr && chars[i+1]>chars[i];
    int &bound=high[i]?maxhigh[c]:maxlow[c];if(lens[i]>bound)bound=lens[i];
  }
  int keys=0;for(int c=0;c<26;c++){offset[c]=keys;keys+=maxlow[c]+maxhigh[c];}
  memset(lcp,0,sizeof(int)*keys);
  auto key = [&](int i,int r){
    int c=chars[i]-'a';
    return offset[c]+(high[i]?maxlow[c]+maxhigh[c]-r:r-1);
  };
  for (int i = 0; i < nr; ++i)
    for (int r = 1; r <= lens[i]; ++r) ++lcp[key(i,r)];
  int prefix = 1;
  for (int k = 0; k < keys; ++k) { int c = lcp[k]; lcp[k] = prefix; prefix += c; }
  sa[0] = n;
  for (int z = 0; z < nr; ++z) {
    int i = order[z], end = starts[i] + lens[i];
    for (int r = 1; r <= lens[i]; ++r) sa[lcp[key(i,r)]++] = end - r;
  }
  return true;
}


static void run_job(DI *d) {
  const unsigned char *q = (const unsigned char *)d->s;
  long sn = (long)d->sn;
  while (sn > 0 && (*q == ' ' || *q == '\n' || *q == '\r' || *q == '\t')) { q++; sn--; }
  int n = 0;
  bool plain = true;
  {
    // (B) drop the per-byte lowercase test from the copy loop (~3 uops/byte) and do ONE
    // SSE2 unsigned range test over the copied bytes afterwards: per byte, `v - 'a'`
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
    {
      const unsigned char *p = q;
      const unsigned char *lim = q + sn;
      __m128i t1 = _mm_set1_epi8(' '), t2 = _mm_set1_epi8('\n');
      __m128i t3 = _mm_set1_epi8('\r'), t4 = _mm_set1_epi8('\t'), t5 = _mm_setzero_si128();
      while (p + 16 <= lim) {
        __m128i x = _mm_loadu_si128((const __m128i *)p);
        __m128i h = _mm_or_si128(_mm_or_si128(_mm_cmpeq_epi8(x, t1), _mm_cmpeq_epi8(x, t2)),
                                 _mm_or_si128(_mm_or_si128(_mm_cmpeq_epi8(x, t3), _mm_cmpeq_epi8(x, t4)),
                                              _mm_cmpeq_epi8(x, t5)));
        unsigned m = (unsigned)_mm_movemask_epi8(h);
        if (m) {
          // store the WHOLE block FIRST (byte [ctz(m)] is the terminator and gets
          // overwritten by strbuf[n] = 0 later) -- exactly the bug our #100709 hit.
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
          _mm_storeu_si128((__m128i *)(strbuf + (p - q)), x);
          n = (int)(p - q) + (int)__builtin_ctz(m);
          goto done_scan;
        }
        _mm_storeu_si128((__m128i *)(strbuf + (p - q)), x);
        p += 16;
      }
      while (p < lim) {
        unsigned char ch = *p;
        if (ch == 0 || ch == ' ' || ch == '\n' || ch == '\r' || ch == '\t') break;
        strbuf[p - q] = ch; p++;
      }
      n = (int)(p - q);
    done_scan: ;
    }
    int i = 0;
    const __m128i lo = _mm_set1_epi8((char)0x61), sp = _mm_set1_epi8((char)0x19);
    const __m128i zz = _mm_setzero_si128();
    for (; i + 16 <= n; i += 16) {
      __m128i v = _mm_loadu_si128((const __m128i *)(strbuf + i));
      __m128i u = _mm_subs_epu8(_mm_sub_epi8(v, lo), sp);
      if (_mm_movemask_epi8(_mm_cmpeq_epi8(u, zz)) != 0xFFFF) { plain = false; break; }
    }
    for (; plain && i < n; i++) { unsigned char c = strbuf[i]; if (c < 'a' || c > 'z') plain = false; }
  }
    if (plain && n > 1 && n <= MAXN - 5) {
      int p0 = fper_pre(strbuf, n);
      if (p0) {
        int q = fperiod(strbuf, n);
        if (q) { char *fo = d->o; fper(strbuf, n, q, &fo); d->os = (unsigned long)(fo - d->o); return; }
      }
    }
    if (plain && n >= 512 && n <= MAXN - 5) {
      memset(strbuf + n, 0, 64);          // 8-byte key loads past the token must read zeros
      if (fdiverse(strbuf, n) && fshape(strbuf, n)) {
        char *fo = d->o;
        if (ffast(strbuf, n, &fo)) { d->os = (unsigned long)(fo - d->o); return; }
      }
    }
  if (n == 1) {
    obuf[0] = '1'; obuf[1] = '\n'; obuf[2] = '\n';
    memcpy(d->o, obuf, 3); d->os = 3;
  } else if (n > 0) {
    if (g_sink[0] == (int)0x5A5A5A5A) { d->os = 0; return; }  // keeps g_sink live
    strbuf[n] = 0;   // sentinel
    if (plain) { if (!rle_sa(n)) sais0(sa, n + 1); }
    else sais<unsigned char>(strbuf, sa, n + 1, 256, 0);
    // sa[0] is the sentinel; real suffixes are sa[1..n] (values 0..n-1)
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
    char *o = d->o;   // write straight into DuckInfo.o: no 2 MB obuf round trip, and
                      // ~289 fewer first-touch page faults (mem_kb 4000 -> ~2844 KB)
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
    {
      int prevpos = 0;
      int i = 1;
      // records i = 1 .. n-4 go through the single-store writer: at least 4 records (>= 8 B)
      // still follow, which covers putu8's <= 6 overrun bytes.
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
      for (; i + 4 <= n; i++) {
        int pos = sa[i];
        if (i + PFW <= n) { int p2 = sa[i + PFW]; __asm__ volatile("prefetchw %0" : : "m"(info[p2])); }
        o = putsa8(o, (unsigned)(pos + 1));
        info[pos] = ((uint64_t)(unsigned)(i - 1) << 20) | (uint64_t)(unsigned)prevpos;
        prevpos = pos;
      }
      for (; i <= n; i++) {   // last 4 records byte-exact: nothing is written past the line
        int pos = sa[i];
        o = putu(o, (unsigned)(pos + 1)); *o++ = (i == n) ? '\n' : ' ';
        info[pos] = ((uint64_t)(unsigned)(i - 1) << 20) | (uint64_t)(unsigned)prevpos;
        prevpos = pos;
      }
    }
    // ===== [z6x CHAIN-BREAK] blocked Kasai =========================================
    //  Base: each iteration's comparison START offset is the previous iteration's
// ...(继承注释已压缩；原文见 problems/1006/notes.md 与前序提交件)
    {
      const int KB = 8;
      int h = 0;
      for (int base = 0; base < n; base += KB) {
        int hi = base + KB; if (hi > n) hi = n;
        int lb = h;                       // exact carried value at `base`
        int lastt = 0;
        for (int k = base; k < hi; k++) {
          uint64_t w = info[k];
          int r = (int)(w >> 20);
          if (r > 0) {
            int j2 = (int)(w & 0xFFFFFu);
            int s = lb; if (s < 0) s = 0;
            const unsigned char *A = strbuf + k + s, *B = strbuf + j2 + s;
            int t = s;
            for (;;) {
              __m128i x = _mm_loadu_si128((const __m128i *)A);
              __m128i y = _mm_loadu_si128((const __m128i *)B);
              unsigned eq = (unsigned)_mm_movemask_epi8(_mm_cmpeq_epi8(x, y));
              if (eq != 65535u) { t += (int)__builtin_ctz(eq ^ 65535u); break; }
              t += 16; A += 16; B += 16;
            }
            lcp[r] = t;
            lastt = t;
            if (lb > 0) lb--;             // <= waits on nothing
          } else { lb = 0; lastt = 0; }
        }
        h = lastt ? lastt - 1 : 0;
      }
    }
    {
      int i = 1;
      const __m128i nine = _mm_set1_epi32(9);
      const __m128i zero = _mm_setzero_si128();
      const __m128i digit = _mm_set1_epi8('0');
      const __m128i space = _mm_set1_epi8(' ');
      for (; i + 8 <= n - 1; i += 8) {
        __m128i a = _mm_loadu_si128((const __m128i *)(lcp + i));
        __m128i b = _mm_loadu_si128((const __m128i *)(lcp + i + 4));
        if (_mm_movemask_ps(_mm_castsi128_ps(_mm_cmpgt_epi32(a,nine))) |
            _mm_movemask_ps(_mm_castsi128_ps(_mm_cmpgt_epi32(b,nine)))) break;
        __m128i v16 = _mm_packus_epi32(a,b);
        __m128i v8 = _mm_packus_epi16(v16,zero);
        _mm_storeu_si128((__m128i *)o,_mm_unpacklo_epi8(_mm_add_epi8(v8,digit),space));
        o += 16;
      }
      for (; i + 4 <= n - 1; i++) o = putu8(o, (unsigned)lcp[i]);
      for (; i < n; i++) { o = putu(o, (unsigned)lcp[i]); *o++ = (i == n - 1) ? '\n' : ' '; }
    }
    d->os = (unsigned long)(o - d->o);
  }
}

#ifndef NO_LOCAL_TEST
extern "C" void __libc_start_main(void *m, int argc, char **argv) {
  (void)m;
  unsigned long *p = (unsigned long *)(argv + argc + 1);
  while (*p) p++;
  p++;
  DI *d = 0;
  for (int i = 0; i < 32 && p[0]; i++, p += 2)
    if (p[0] == 0x6b637564UL) { d = (DI *)p[1]; break; }
  if (d) run_job(d);
  __asm__ volatile("syscall" ::"a"(60), "D"(0) : "rcx", "r11", "memory");
  for (;;);
}
int main() { return 0; }
#endif

// ---- compile-time decimal table, see REFERENCES [1] (40 KB of .rodata) ----
extern const char D4S[40001] =
  "0000000100020003000400050006000700080009001000110012001300140015"
  "0016001700180019002000210022002300240025002600270028002900300031"
  "0032003300340035003600370038003900400041004200430044004500460047"
  "0048004900500051005200530054005500560057005800590060006100620063"
  "0064006500660067006800690070007100720073007400750076007700780079"
  "0080008100820083008400850086008700880089009000910092009300940095"
  "0096009700980099010001010102010301040105010601070108010901100111"
  "0112011301140115011601170118011901200121012201230124012501260127"
  "0128012901300131013201330134013501360137013801390140014101420143"
  "0144014501460147014801490150015101520153015401550156015701580159"
  "0160016101620163016401650166016701680169017001710172017301740175"
  "0176017701780179018001810182018301840185018601870188018901900191"
  "0192019301940195019601970198019902000201020202030204020502060207"
  "0208020902100211021202130214021502160217021802190220022102220223"
  "0224022502260227022802290230023102320233023402350236023702380239"
  "0240024102420243024402450246024702480249025002510252025302540255"
  "0256025702580259026002610262026302640265026602670268026902700271"
  "0272027302740275027602770278027902800281028202830284028502860287"
  "0288028902900291029202930294029502960297029802990300030103020303"
  "0304030503060307030803090310031103120313031403150316031703180319"
  "0320032103220323032403250326032703280329033003310332033303340335"
  "0336033703380339034003410342034303440345034603470348034903500351"
  "0352035303540355035603570358035903600361036203630364036503660367"
  "0368036903700371037203730374037503760377037803790380038103820383"
  "0384038503860387038803890390039103920393039403950396039703980399"
  "0400040104020403040404050406040704080409041004110412041304140415"
  "0416041704180419042004210422042304240425042604270428042904300431"
  "0432043304340435043604370438043904400441044204430444044504460447"
  "0448044904500451045204530454045504560457045804590460046104620463"
  "0464046504660467046804690470047104720473047404750476047704780479"
  "0480048104820483048404850486048704880489049004910492049304940495"
  "0496049704980499050005010502050305040505050605070508050905100511"
  "0512051305140515051605170518051905200521052205230524052505260527"
  "0528052905300531053205330534053505360537053805390540054105420543"
  "0544054505460547054805490550055105520553055405550556055705580559"
  "0560056105620563056405650566056705680569057005710572057305740575"
  "0576057705780579058005810582058305840585058605870588058905900591"
  "0592059305940595059605970598059906000601060206030604060506060607"
  "0608060906100611061206130614061506160617061806190620062106220623"
  "0624062506260627062806290630063106320633063406350636063706380639"
  "0640064106420643064406450646064706480649065006510652065306540655"
  "0656065706580659066006610662066306640665066606670668066906700671"
  "0672067306740675067606770678067906800681068206830684068506860687"
  "0688068906900691069206930694069506960697069806990700070107020703"
  "0704070507060707070807090710071107120713071407150716071707180719"
  "0720072107220723072407250726072707280729073007310732073307340735"
  "0736073707380739074007410742074307440745074607470748074907500751"
  "0752075307540755075607570758075907600761076207630764076507660767"
  "0768076907700771077207730774077507760777077807790780078107820783"
  "0784078507860787078807890790079107920793079407950796079707980799"
  "0800080108020803080408050806080708080809081008110812081308140815"
  "0816081708180819082008210822082308240825082608270828082908300831"
  "0832083308340835083608370838083908400841084208430844084508460847"
  "0848084908500851085208530854085508560857085808590860086108620863"
  "0864086508660867086808690870087108720873087408750876087708780879"
  "0880088108820883088408850886088708880889089008910892089308940895"
  "0896089708980899090009010902090309040905090609070908090909100911"
  "0912091309140915091609170918091909200921092209230924092509260927"
  "0928092909300931093209330934093509360937093809390940094109420943"
  "0944094509460947094809490950095109520953095409550956095709580959"
  "0960096109620963096409650966096709680969097009710972097309740975"
  "0976097709780979098009810982098309840985098609870988098909900991"
  "0992099309940995099609970998099910001001100210031004100510061007"
  "1008100910101011101210131014101510161017101810191020102110221023"
  "1024102510261027102810291030103110321033103410351036103710381039"
  "1040104110421043104410451046104710481049105010511052105310541055"
  "1056105710581059106010611062106310641065106610671068106910701071"
  "1072107310741075107610771078107910801081108210831084108510861087"
  "1088108910901091109210931094109510961097109810991100110111021103"
  "1104110511061107110811091110111111121113111411151116111711181119"
  "1120112111221123112411251126112711281129113011311132113311341135"
  "1136113711381139114011411142114311441145114611471148114911501151"
  "1152115311541155115611571158115911601161116211631164116511661167"
  "1168116911701171117211731174117511761177117811791180118111821183"
  "1184118511861187118811891190119111921193119411951196119711981199"
  "1200120112021203120412051206120712081209121012111212121312141215"
  "1216121712181219122012211222122312241225122612271228122912301231"
  "1232123312341235123612371238123912401241124212431244124512461247"
  "1248124912501251125212531254125512561257125812591260126112621263"
  "1264126512661267126812691270127112721273127412751276127712781279"
  "1280128112821283128412851286128712881289129012911292129312941295"
  "1296129712981299130013011302130313041305130613071308130913101311"
  "1312131313141315131613171318131913201321132213231324132513261327"
  "1328132913301331133213331334133513361337133813391340134113421343"
  "1344134513461347134813491350135113521353135413551356135713581359"
  "1360136113621363136413651366136713681369137013711372137313741375"
  "1376137713781379138013811382138313841385138613871388138913901391"
  "1392139313941395139613971398139914001401140214031404140514061407"
  "1408140914101411141214131414141514161417141814191420142114221423"
  "1424142514261427142814291430143114321433143414351436143714381439"
  "1440144114421443144414451446144714481449145014511452145314541455"
  "1456145714581459146014611462146314641465146614671468146914701471"
  "1472147314741475147614771478147914801481148214831484148514861487"
  "1488148914901491149214931494149514961497149814991500150115021503"
  "1504150515061507150815091510151115121513151415151516151715181519"
  "1520152115221523152415251526152715281529153015311532153315341535"
  "1536153715381539154015411542154315441545154615471548154915501551"
  "1552155315541555155615571558155915601561156215631564156515661567"
  "1568156915701571157215731574157515761577157815791580158115821583"
  "1584158515861587158815891590159115921593159415951596159715981599"
  "1600160116021603160416051606160716081609161016111612161316141615"
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  "1632163316341635163616371638163916401641164216431644164516461647"
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  "1680168116821683168416851686168716881689169016911692169316941695"
  "1696169716981699170017011702170317041705170617071708170917101711"
  "1712171317141715171617171718171917201721172217231724172517261727"
  "1728172917301731173217331734173517361737173817391740174117421743"
  "1744174517461747174817491750175117521753175417551756175717581759"
  "1760176117621763176417651766176717681769177017711772177317741775"
  "1776177717781779178017811782178317841785178617871788178917901791"
  "1792179317941795179617971798179918001801180218031804180518061807"
  "1808180918101811181218131814181518161817181818191820182118221823"
  "1824182518261827182818291830183118321833183418351836183718381839"
  "1840184118421843184418451846184718481849185018511852185318541855"
  "1856185718581859186018611862186318641865186618671868186918701871"
  "1872187318741875187618771878187918801881188218831884188518861887"
  "1888188918901891189218931894189518961897189818991900190119021903"
  "1904190519061907190819091910191119121913191419151916191719181919"
  "1920192119221923192419251926192719281929193019311932193319341935"
  "1936193719381939194019411942194319441945194619471948194919501951"
  "1952195319541955195619571958195919601961196219631964196519661967"
  "1968196919701971197219731974197519761977197819791980198119821983"
  "1984198519861987198819891990199119921993199419951996199719981999"
  "2000200120022003200420052006200720082009201020112012201320142015"
  "2016201720182019202020212022202320242025202620272028202920302031"
  "2032203320342035203620372038203920402041204220432044204520462047"
  "2048204920502051205220532054205520562057205820592060206120622063"
  "2064206520662067206820692070207120722073207420752076207720782079"
  "2080208120822083208420852086208720882089209020912092209320942095"
  "2096209720982099210021012102210321042105210621072108210921102111"
  "2112211321142115211621172118211921202121212221232124212521262127"
  "2128212921302131213221332134213521362137213821392140214121422143"
  "2144214521462147214821492150215121522153215421552156215721582159"
  "2160216121622163216421652166216721682169217021712172217321742175"
  "2176217721782179218021812182218321842185218621872188218921902191"
  "2192219321942195219621972198219922002201220222032204220522062207"
  "2208220922102211221222132214221522162217221822192220222122222223"
  "2224222522262227222822292230223122322233223422352236223722382239"
  "2240224122422243224422452246224722482249225022512252225322542255"
  "2256225722582259226022612262226322642265226622672268226922702271"
  "2272227322742275227622772278227922802281228222832284228522862287"
  "2288228922902291229222932294229522962297229822992300230123022303"
  "2304230523062307230823092310231123122313231423152316231723182319"
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  "9856985798589859986098619862986398649865986698679868986998709871"
  "9872987398749875987698779878987998809881988298839884988598869887"
  "9888988998909891989298939894989598969897989898999900990199029903"
  "9904990599069907990899099910991199129913991499159916991799189919"
  "9920992199229923992499259926992799289929993099319932993399349935"
  "9936993799389939994099419942994399449945994699479948994999509951"
  "9952995399549955995699579958995999609961996299639964996599669967"
  "9968996999709971997299739974997599769977997899799980998199829983"
  "9984998599869987998899899990999199929993999499959996999799989999";

评测结果