代码

// ===== REFERENCES =====
// [1] duck.ac 用户 saffah_codex_6s_agg2，提交 #106431 <https://duck.ac/submission/106431>
//     （348.431031 ms，本题当前榜首）—— **本提交的直接基座：代码正文逐字节取自该提交的公开源码**
//     （抓取件 `problems/noi18e/ref2/rival_106431.cpp`，本工作区 `tools/fetch_rival.py` 抓取；
//     结构 diff：与本账号 #104110 相比只有 5 处）。该件自述其父链为 #106428 / #106421 / #106420 /
//     #106414，并自述其基底是**本账号提交 #104110**（"Direct copy of its accepted tree-centre engine"）
//     ⇒ 本提交是对"对手从我们件起跳的那 5 处改动"的**反向移植**（`§2.19.136` 的标准流程）。
//     该 5 处（其自述 + 我逐行核对）：
//       (a) 欧拉序 RMQ：把 `st_[LG][2*MAXN]`（u16，3.4 MB）换成 **8 元素块的前/后缀最小 + 块间稀疏表**
//           （`rmq_pref/rmq_suf` u32 + `rmq_st[14][RMQNB]`，值打包成 `(dep<<16)|node` ⇒ 比较只要 1 个 u32）;
//       (b) `calc` 删掉 `if (g_c0)` 分支（统一走通用 LCA 式；c=0 时 lcadis 恰为 0，语义不变）；
//       (c) `leafval` 单例快路径：叶子的两端点相同时直接 `2*(w - dis[v])`，省一次 RMQ；
//       (d) `ins` 里 `v2 = (x==y) ? v1 : calc(pt,y)` 去重；
//       (e) RMQ 的建表改写。
// [2] 本账号 `saffah_cc_v41_agg1` 提交 #104110 <https://duck.ac/submission/104110>（353.567967 ms）——
//     经 [1] 继承（其自身的 REFERENCES 亦在 [1] 的文件内保留）。
// [3] 本工作区 `e18_` 代理在本題留下、**已建好且过了全部逐位闸门但从未提交**的两把刀
//     （`work/e18_gen.py`，本地归档 `.cache/noi18e/e18_v3.cpp`；本提交逐字复用其替换文本与论证）：
//       (A) `--nopre`：删 `pre_[]`/`ord_[]`（题面硬保证 `a_i < b_i` 且 `b_i` 互不相同 ⇒ `par_[v]=a_v<v`
//           ⇒ 结点编号本身就是合法拓扑序 ⇒ 主循环按编号降序迭代即可）。该刀在 #104056 那一代上
//           判题机单价 **−4.81 ms**（`#104056 = 368.133696` vs `#103923 = 372.946573`，同批同基底）。
//       (B) `--deferedge`：把三件「链组完全用不到」的活（`deg[]` 清零、每条边两次 `deg[a]++;deg[b]++;`、
//           c=0 侦察）挪到 `if (g_chain) … return;` 之后（**本件里 `g_c0` 已不再被 `calc` 使用，
//           但 `deg` 的 2(n−1) 次随机 RMW 仍然照旧浪费掉**）。判题机单价 −2.34 ms
//           （`#104078 = 365.797389` vs `#104056 = 368.133696`）。
// [4] 其余（32 B `Pool` 节点、迭代式 `ins`、`Item` 内联 `first_[v]` 的 `lcadis`、链特化 `solve_chain`
//     的两棵区间最大值线段树、六数组 u16 化）经 [1]/[2] 继承。上述公开提交均未附许可证声明，
//     本件按本工作区惯例注明账号、原始提交地址与所用内容；未取用其它他人代码。
// ======================
// ===== 思路 =====
// 现状：`mine = 353.567967`（#104110）· `T = 348.431031`（#106431）⇒ **严支线 = 0.99·T + 1µs =
//       344.947721 ⇒ 还需 8.620 ms（2.438%）**（我方一交件即翻严支）。
//
// ★ 靶心更正（本席本轮最重要的一步取证，**推翻本文件旧的"计分点 = tc6 = 纯链组"**）：
//   `tools/pertest.py 104110` 给出我方**当前**最好件的逐测试点表 ⇒
//   **MAX = tc15 = 353.568 ms，mem 23532 KB** —— 即计分点是**通用路径**的测试点，
//   不是链组（tc6 现在只有 267.171 ms / mem 4952 KB）。旧结论来自 #104078 那一代，早已过期。
//   ⇒ 一切只有链路径受益的刀（`--fastio` 的解析、链特化微调）都**不进分**；而对手这 5 处
//     改动全部落在**通用路径**（`calc`/`leafval`/`ins`/欧拉序 RMQ）上 —— 与"他们的 MAX 也在通用点"
//     完全一致 ⇒ **靶心 = 通用路径的 RMQ/LCA 热链**。
//
// ★ 本发 = **(A) 反向移植 [1] 的 5 处** + **(B) 叠加 [3] 的两把已计价、与本发正交的刀**。
//   (A) 的动机是纯"足迹与常数"：RMQ 从 3.4 MB 的 u16 稀疏表 + 4 次取数（st/ st/ dep/ dep）压到
//       ~1.5 MB + 每比较 1 个 u32（打包 dep 与结点）⇒ 判题机实测 353.568 → 348.431 = **−5.14 ms**。
//   (B) 的 `--nopre` 把通用主循环的**随机取数**（`ord_[oi]`）换成**顺序计数器**（t = n−oi），
//       并删掉 200 KB 的两个数组与一趟 O(n)；`--deferedge` 把链组的 n+2(n−1) 次无条件操作挪到早退之后。
//
// ★ 预测：`mine_new ≈ 353.568 − 5.14 (A) − 4.81 (B1) − 2.34 (B2) ≈ 341.3 ms ≤ 344.948` ✓（均为判题机单价，
//   见 [3] 的两条读数；两把刀与本发作用在不同代码段 ⇒ 可加性假设成立）。
//
// ★ 正确性：本发对 [1] 的改动只有 (A) 的**反向移植**（[1] 自身已判题机 AC，其 5 处均为等价改写）
//   与 (B) 的两处**等价搬移/等价迭代序**（(B1) 依据题面硬保证 `par_[v] < v`；(B2) 纯位置搬移；
//   两者都不改任何数值路径）⇒ 输出应与 [1] **逐字节相同**。交前闸门：
//   四套随机对拍（rt/chainrt/czerort/mixc0rt）+ 三份大用例（tc6chain 68.9 MB / tc9rand 63.6 MB /
//   tc9z 55.8 MB）与 [1] 的二进制**逐字节比对**。
// ================
#ifdef LOCAL_TEST
#include <cstdio>
#endif
#ifdef DBG
#include <cstdio>
#endif
#if defined(LOCAL_TEST) || defined(DBG)
#include <cstdio>
#include <cstdlib>
#include <cstring>
typedef unsigned long long u64;
static char g_in[48 << 20];
static char g_out[8 << 20];
#else
typedef unsigned long long u64;
#endif

typedef long long i64;
typedef unsigned int u32;

#define MAXN 50005
#define MAXM 100005
#define MAXE 100005
#define MAXIT 200010
#define MAXPOOL 3600005
#define LG 18

static const i64 NINF = -(i64)1 << 60;

// ---------------- tree ----------------
static u32 head_[MAXN + 2];
static unsigned short eto[MAXE]; static u32 ew[MAXE];
static unsigned short par_[MAXN], dep_[MAXN];
static i64 dis_[MAXN];
static unsigned short euler[2 * MAXN];
static u32 first_[MAXN];   // Euler POSITION (<=2n-1=100009) needs 17 bits: stays u32
// Sixteen-entry Euler blocks: packed depth+node prefix/suffix minima and
// a sparse table over the block minima, about 1.2 MB in total.
#define RMQB 8
#define RMQNB ((2 * MAXN + RMQB - 1) / RMQB)
static u32 rmq_pref[2 * MAXN], rmq_suf[2 * MAXN];
static u32 rmq_st[14][RMQNB];
static inline u32 rmq_pack(u32 v) { return ((u32)dep_[v] << 16) | v; }
static inline u32 rmq_pick(u32 a, u32 b) { return (a >> 16) < (b >> 16) ? a : b; }
static inline u32 rmq_query(u32 l, u32 r) {
  if (l > r) { u32 z=l; l=r; r=z; }
  u32 bl=l>>3, br=r>>3;
  if (bl==br) {
    u32 z=rmq_pack(euler[l]);
    for (u32 j=l+1;j<=r;j++) z=rmq_pick(z,rmq_pack(euler[j]));
    return z;
  }
  u32 z=rmq_pick(rmq_suf[l],rmq_pref[r]);
  if (bl+1<br) {
    u32 L=bl+1, R=br-1, len=R-L+1;
    u32 k=31u-(u32)__builtin_clz(len);
    z=rmq_pick(z,rmq_pick(rmq_st[k][L],rmq_st[k][R-(1u<<k)+1]));
  }
  return z;
}

static int g_c0;             // 1 <=> every c_i of this group is 0
static int g_chain;          // 1 <=> the tree is the literal chain 1-2-...-n

static inline int lca_of(int u, int v) {   // node identity, used once per path
  return (int)(rmq_query(first_[u],first_[v]) & 0xffffu);
}
// hot path: the callers only need dis[lca], never which node it is.  Takes the two
// Euler first-occurrence positions straight out of the item (no first_[] load).
static inline i64 lcadis(u32 fu, u32 fv) {
  return dis_[rmq_query(fu,fv) & 0xffffu];
}

// ---------------- items (32B, self-contained for cache) ----------------
struct Item { u32 v; u32 fv; i64 w, f2, g2; };   // fv = first_[v]; w = dis[v] + w
static Item itm[MAXIT];
static u32 phead[MAXN], pnxt[MAXIT];
static u32 pkey[MAXIT], ppt[MAXIT];

// ---------------- segment tree ----------------
// own (mf,mg) = max f2/g2 over the key range; e,f = children (leaf: item ids).
// 32B aligned => one node is always inside one cache line.
struct TNode { i64 mf, mg; u32 e, f; } __attribute__((aligned(32)));
static TNode pool[MAXPOOL];
static u32 pool_n;
static i64 ans;

static inline i64 calc(int x, int y) {   // itm[].w already carries dis[v]
  return itm[x].w + itm[y].w - 2 * lcadis(itm[x].fv, itm[y].fv);
}

static void pushup(u32 o) {
  u32 l = pool[o].e, r = pool[o].f;
  i64 f = NINF, g = NINF;
  if (l) { i64 x = pool[l].mf; if (x > f) f = x; x = pool[l].mg; if (x > g) g = x; }
  if (r) { i64 x = pool[r].mf; if (x > f) f = x; x = pool[r].mg; if (x > g) g = x; }
  pool[o].mf = f; pool[o].mg = g;
}

static inline i64 leafval(u32 o) {
  u32 x = pool[o].e, y = pool[o].f;
  if (x == y) return 2 * (itm[x].w - dis_[itm[x].v]);   // LCA(v,v)=v
  return calc((int)x, (int)y);
}

static void leaf_combine(u32 a, u32 b, i64 deep2) {
  int ax = (int)pool[a].e, ay = (int)pool[a].f;
  int bx = (int)pool[b].e, by = (int)pool[b].f;
  i64 best = NINF, cross = NINF;
  int rx = 0, ry = 0;
  { i64 v = leafval(a); best = v; rx = ax; ry = ay; }
  { i64 v = leafval(b); if (v > best) { best = v; rx = bx; ry = by; } }
  if (ax) {
    if (bx) { i64 v = calc(ax, bx); if (v > best) { best = v; rx = ax; ry = bx; } if (v > cross) cross = v; }
    if (by) { i64 v = calc(ax, by); if (v > best) { best = v; rx = ax; ry = by; } if (v > cross) cross = v; }
  }
  if (ay) {
    if (bx) { i64 v = calc(ay, bx); if (v > best) { best = v; rx = ay; ry = bx; } if (v > cross) cross = v; }
    if (by) { i64 v = calc(ay, by); if (v > best) { best = v; rx = ay; ry = by; } if (v > cross) cross = v; }
  }
  if (pool[b].mf > pool[a].mf) pool[a].mf = pool[b].mf;
  if (pool[b].mg > pool[a].mg) pool[a].mg = pool[b].mg;
  pool[a].e = (u32)rx; pool[a].f = (u32)ry;
  if (cross != NINF) { i64 t = cross - deep2; if (t > ans) ans = t; }
}

// Iterative insert.  With a node now storing its OWN range maxes, inserting one item
// changes every node on the root-to-leaf path by exactly max(old, f2) / max(old, g2) --
// so the recursion AND all 1.2M pushup calls in this path disappear.
static u32 ins(u32 o, int l, int r, int pos, int pt, i64 deep2) {
  i64 f2 = itm[pt].f2, g2 = itm[pt].g2;
  u32 root = o, *link = &root;
  int lo = l, hi = r;
  while (lo < hi) {
    if (!o) {
      o = ++pool_n;
      pool[o].e = 0; pool[o].f = 0;
      pool[o].mf = f2; pool[o].mg = g2;
      *link = o;
    } else {
      { i64 nf = pool[o].mf; nf = f2 > nf ? f2 : nf;
        i64 ng = pool[o].mg; ng = g2 > ng ? g2 : ng;
        pool[o].mf = nf; pool[o].mg = ng; }
    }
    int mid = (lo + hi) >> 1;
    if (pos <= mid) {
      u32 rc = pool[o].f;                    // sibling's right half is deeper
      if (rc) { i64 v = f2 + pool[rc].mg - deep2; if (v > ans) ans = v; }
      link = &pool[o].e; o = pool[o].e; hi = mid;
    } else {
      u32 lc = pool[o].e;                    // this item is the deeper one
      if (lc) { i64 v = pool[lc].mf + g2 - deep2; if (v > ans) ans = v; }
      link = &pool[o].f; o = pool[o].f; lo = mid + 1;
    }
  }
  if (!o) {                                  // leaf at lo == hi == pos, first item in it
    o = ++pool_n;
    pool[o].e = (u32)pt; pool[o].f = (u32)pt;
    pool[o].mf = f2; pool[o].mg = g2;
    *link = o;
    return root;
  }
  if (f2 > pool[o].mf) pool[o].mf = f2;
  if (g2 > pool[o].mg) pool[o].mg = g2;
  u32 x = pool[o].e, y = pool[o].f;
  if (!x) { pool[o].e = pool[o].f = (u32)pt; return root; }
  i64 v1 = calc(pt, (int)x), v2 = (x == y) ? v1 : calc(pt, (int)y);
  i64 v = v1 > v2 ? v1 : v2;
  { i64 t = v - deep2; if (t > ans) ans = t; }
  i64 v0 = leafval(o);
  if (v0 >= v1 && v0 >= v2) return root;
  if (v1 >= v2) pool[o].f = (u32)pt; else pool[o].e = (u32)pt;
  return root;
}

static u32 merge_tr(u32 a, u32 b, int l, int r, i64 deep2) {
  if (!a) return b;
  if (!b) return a;
  if (l == r) { leaf_combine(a, b, deep2); return a; }
  int mid = (l + r) >> 1;
  u32 al = pool[a].e, ar = pool[a].f, bl = pool[b].e, br = pool[b].f;
  i64 amf0 = pool[a].mf, amg0 = pool[a].mg, bmf0 = pool[b].mf, bmg0 = pool[b].mg;
  { i64 am = al ? pool[al].mf : NINF;
    if (am != NINF) { i64 v = am + (br ? pool[br].mg : NINF) - deep2; if (v > ans) ans = v; }
    i64 bm = bl ? pool[bl].mf : NINF;
    if (bm != NINF) { i64 v = bm + (ar ? pool[ar].mg : NINF) - deep2; if (v > ans) ans = v; } }
  if (al) __builtin_prefetch(&pool[al], 1, 3);
  if (ar) __builtin_prefetch(&pool[ar], 1, 3);
  if (bl) __builtin_prefetch(&pool[bl], 1, 3);
  if (br) __builtin_prefetch(&pool[br], 1, 3);
  pool[a].e = merge_tr(al, bl, l, mid, deep2);
  pool[a].f = merge_tr(ar, br, mid + 1, r, deep2);
  pool[a].mf = amf0 > bmf0 ? amf0 : bmf0;
  pool[a].mg = amg0 > bmg0 ? amg0 : bmg0;
  return a;
}

// keys > K never occur (presence rule), so clearing key K is enough; but the range
// version below is equivalent and simpler to keep exact.
static u32 wipe(u32 o, int l, int r, int K) {
  if (!o || r < K) return o;
  if (l >= K) return 0;
  int mid = (l + r) >> 1;
  if (K <= mid) {
    u32 c0 = wipe(pool[o].e, l, mid, K);
    if (!c0) return 0;
    pool[o].e = c0; pool[o].f = 0;
    pool[o].mf = pool[c0].mf; pool[o].mg = pool[c0].mg;
    return o;
  }
  u32 c0 = pool[o].e;
  u32 c1 = wipe(pool[o].f, mid + 1, r, K);
  pool[o].f = c1;
  if (!c1) {
    if (!c0) return 0;
    pool[o].mf = pool[c0].mf; pool[o].mg = pool[c0].mg;
    return o;
  }
  i64 f = pool[c1].mf, g = pool[c1].mg;
  if (c0) { i64 x = pool[c0].mf; if (x > f) f = x; x = pool[c0].mg; if (x > g) g = x; }
  pool[o].mf = f; pool[o].mg = g;
  return o;
}

// ---------------- io ----------------
#ifdef LOCAL_TEST
static const unsigned char *ip_, *ie_;
static char *op_;
#else
struct DI {
  u64 abi;
  const char *s; u64 sn;
  char *o; u64 ol; u64 os;
  char *e; u64 el; u64 es;
  const char *IB; u64 IBl;
  char *OB; u64 OBl;
  u64 tsc;
} __attribute__((packed));
static DI *D;
static const unsigned char *ip_, *ie_;
static char *op_;
#endif

static inline i64 nll() {
  const unsigned char *p = ip_;
  while (*p <= ' ') p++;
  i64 v = 0;
  while (*p > ' ') { v = v * 10 + (i64)(*p - '0'); p++; }
  ip_ = p;
  return v;
}
static inline int ni() { return (int)nll(); }
static inline void pc(char c) { *op_++ = c; }
static inline void pll(i64 v) {
  char t[24]; int q = 0;
  if (v < 0) { pc('-'); v = -v; }
  if (!v) t[q++] = '0';
  while (v) { t[q++] = (char)('0' + (int)(v % 10)); v /= 10; }
  while (q) pc(t[--q]);
}


// ---------------- chain specialist (a_i = b_i - 1) ----------------
#define MAXS 131072
static u32 cw_[MAXN + 2];
static i64 dis2_[MAXN + 2];
static u32 ox[MAXM], oy[MAXM], ord2[MAXM + 1], cstart[MAXN + 3];
static i64 ow[MAXM];
static i64 trC[2 * MAXS];
// trN has exactly two operations: "increase the value at p" and "max over [p, n]".  Reversing
// the index turns the suffix query into a prefix max, so a Fenwick max tree gives both in
// ~log/2 probes instead of the segment tree's ~2*log (query) / ~log (update); the per-group
// clear also drops from 2*base to bnN = n+1.
static i64 bitN[MAXS + 2];
static int bnN;
static inline i64 asuf_qry(int p) {
  i64 res = NINF;
  for (int i = bnN - p; i > 0; i -= i & -i) { i64 t = bitN[i]; if (t > res) res = t; }
  return res;
}
static inline void asuf_upd(int p, i64 v) {
  for (int i = bnN - p; i <= bnN; i += i & -i) { if (bitN[i] >= v) break; bitN[i] = v; }
}

static i64 range_max(const i64 *tr, int l, int r, int base) {
  i64 res = NINF;
  if (l > r) return res;
  int lo = base + l, hi = base + r + 1;
  while (lo < hi) {
    if (lo & 1) { if (tr[lo] > res) res = tr[lo]; lo++; }
    if (hi & 1) { hi--; if (tr[hi] > res) res = tr[hi]; }
    lo >>= 1; hi >>= 1;
  }
  return res;
}
static void point_max(i64 *tr, int p, i64 v, int base) {
  int i = base + p;
  if (tr[i] >= v) return;
  tr[i] = v;
  i >>= 1;
  while (i) {
    i64 a = tr[2 * i], b = tr[2 * i + 1];
    i64 mx = a > b ? a : b;
    if (tr[i] == mx) break;
    tr[i] = mx;
    i >>= 1;
  }
}

static void solve_chain(int n, const u32 *ea, const u32 *ec) {
  for (int i = 0; i < n - 1; i++) cw_[ea[i]] = ec[i];
  dis2_[1] = 0;
  for (int v = 2; v <= n; v++) dis2_[v] = dis2_[v - 1] + (i64)cw_[v - 1];
  int m = ni();
  int cnt = 0;
  for (int i = 0; i < m; i++) {
    int x = ni(), y = ni();
    i64 v = nll();
    if (x == y) continue;                 // covers no edge -> can never share one
    if (x > y) { int t = x; x = y; y = t; }
    ox[cnt] = (u32)x; oy[cnt] = (u32)y;
    ow[cnt] = (dis2_[y] - dis2_[x]) - v;
    cnt++;
  }
  if (cnt < 2) { pc('F'); pc('\n'); return; }
  int base = 1;
  while (base <= n) base <<= 1;
  for (int i = 0; i < 2 * base; i++) trC[i] = NINF;
  bnN = n + 1;
  for (int i = 1; i <= bnN; i++) bitN[i] = NINF;
  for (int i = 0; i <= n + 1; i++) cstart[i] = 0;
  for (int i = 0; i < cnt; i++) cstart[ox[i]]++;
  { u32 s = 0;
    for (int i = 0; i <= n + 1; i++) { u32 c = cstart[i]; cstart[i] = s; s += c; } }
  for (int i = 0; i < cnt; i++) ord2[cstart[ox[i]]++] = (u32)i;
  i64 best = NINF;
  for (int k = 0; k < cnt; k++) {
    int qi = (int)ord2[k];
    int xq = (int)ox[qi], yq = (int)oy[qi];
    i64 wq = ow[qi];
    { i64 a = range_max(trC, xq + 1, yq, base);
      if (a > NINF / 2) { i64 t = a + wq + dis2_[xq]; if (t > best) best = t; } }
    { i64 b = asuf_qry(yq);
      if (b > NINF / 2) { i64 t = b - (dis2_[yq] - dis2_[xq] - wq); if (t > best) best = t; } }
    point_max(trC, yq, wq - dis2_[yq], base);
    asuf_upd(yq, wq);
  }
  if (best <= NINF / 2) { pc('F'); } else pll(best);
  pc('\n');
}

static void solve_group() {
  int n = ni();
  static u32 deg[MAXN + 2];
  static u32 ea[MAXN], eb[MAXN], ec[MAXN];
  g_chain = 1;
  for (int i = 0; i < n - 1; i++) {
    int a = ni(), b = ni(), c = ni();
    if (b != a + 1) g_chain = 0;
    ea[i] = a; eb[i] = b; ec[i] = c;
  }
  if (g_chain) { solve_chain(n, ea, ec); return; }   // chain groups never need deg/g_c0/CSR
  for (int i = 1; i <= n; i++) deg[i] = 0;
  for (int i = 0; i < n - 1; i++) { deg[ea[i]]++; deg[eb[i]]++; }
  g_c0 = 1;
  for (int i = 0; i < n - 1; i++) if (ec[i]) { g_c0 = 0; break; }
  {
    u32 s = 0;
    for (int i = 1; i <= n; i++) { head_[i] = s; s += deg[i]; }
    head_[n + 1] = s;
  }
  {
    static u32 pos[MAXN + 2];
    for (int i = 1; i <= n; i++) pos[i] = head_[i];
    for (int i = 0; i < n - 1; i++) {
      u32 a = ea[i], b = eb[i], c = ec[i];
      eto[pos[a]] = b; ew[pos[a]++] = c;
      eto[pos[b]] = a; ew[pos[b]++] = c;
    }
  }
  {
    int top = 0;
    static u32 stk[MAXN], ptr[MAXN];
    par_[1] = 0; dep_[1] = 0; dis_[1] = 0;
    stk[0] = 1; ptr[1] = head_[1];
    int ec_ = 0;
    euler[ec_] = 1; first_[1] = ec_; ec_++;
    while (top >= 0) {
      u32 u = stk[top];
      if (ptr[u] < head_[u + 1]) {
        u32 idx = ptr[u]++;
        u32 v = eto[idx];
        if (v == par_[u]) continue;
        par_[v] = u; dep_[v] = dep_[u] + 1; dis_[v] = dis_[u] + ew[idx];
        first_[v] = ec_; euler[ec_] = v; ec_++;
        stk[++top] = v; ptr[v] = head_[v];
      } else {
        top--;
        if (top >= 0) { euler[ec_] = stk[top]; ec_++; }
      }
    }
  }
  {
    int m_ = 2 * n - 1;
    if (!g_chain) {
      int nb=(m_+RMQB-1)/RMQB;
      for (int b=0;b<nb;b++) {
        int l=b*RMQB, r=l+RMQB; if(r>m_)r=m_;
        u32 z=0;
        for (int i=l;i<r;i++) { u32 p=rmq_pack(euler[i]); z=(i==l)?p:rmq_pick(z,p); rmq_pref[i]=z; }
        for (int i=r-1;i>=l;i--) { u32 p=rmq_pack(euler[i]); z=(i==r-1)?p:rmq_pick(p,z); rmq_suf[i]=z; }
        rmq_st[0][b]=rmq_pref[r-1];
      }
      for (int k=1;(1<<k)<=nb;k++)
        for (int b=0;b+(1<<k)<=nb;b++)
          rmq_st[k][b]=rmq_pick(rmq_st[k-1][b],rmq_st[k-1][b+(1<<(k-1))]);
    }
  }
  int m = ni();
  u32 maxdep = 0;
  for (int v = 1; v <= n; v++) if (dep_[v] > maxdep) maxdep = dep_[v];
  static u32 tat[MAXIT];   /* pkey/ppt are written directly at the source: the
                              previous tkey/tpt arrays existed only to be copied
                              into pkey/ppt by the reverse linked-list pass. */
  int nit = 0;
  for (int i = 0; i < m; i++) {
    int x = ni(), y = ni();
    i64 cost = nll();
    int anc = lca_of(x, y);
    i64 len = dis_[x] + dis_[y] - 2 * dis_[anc];
    i64 f2 = 2 * (len - cost);
    i64 g2 = f2 + 2 * dis_[anc];
    i64 base = len - 2 * cost;
    if (x != anc) {
      int id = 2 * i + 1;
      itm[id].v = (u32)y; itm[id].fv = first_[y];
      itm[id].w = base + dis_[x] + dis_[y];
      itm[id].f2 = f2; itm[id].g2 = g2;
      pkey[nit] = dep_[anc] + 1; tat[nit] = x; ppt[nit] = id;
      nit++;
    }
    if (y != anc) {
      int id = 2 * i + 2;
      itm[id].v = (u32)x; itm[id].fv = first_[x];
      itm[id].w = base + dis_[x] + dis_[y];
      itm[id].f2 = f2; itm[id].g2 = g2;
      pkey[nit] = dep_[anc] + 1; tat[nit] = y; ppt[nit] = id;
      nit++;
    }
  }
  for (int v = 1; v <= n; v++) phead[v] = 0;
  for (int e = nit - 1; e >= 0; e--) {
    u32 v = tat[e];
    pnxt[e] = phead[v]; phead[v] = (u32)(e + 1);
  }
  static u32 rt[MAXN];
  for (int v = 1; v <= n; v++) rt[v] = 0;
  pool_n = 0;
  int S = (int)maxdep + 1; if (S < 1) S = 1;
  ans = NINF;
  for (int oi = 0; oi < n; oi++) {
    u32 t = (u32)n - (u32)oi;   // par_[v] = a_v < v => descending labels = valid order
    i64 deep2 = 2 * dis_[t];
    for (u32 c = head_[t]; c < head_[t + 1]; c++) {
      u32 v = eto[c];
      if (v == par_[t]) continue;
      if (!rt[v]) continue;
      if (!rt[t]) rt[t] = rt[v];
      else rt[t] = merge_tr(rt[t], rt[v], 1, S, deep2);
    }
    for (u32 e = phead[t]; e; e = pnxt[e - 1])
      rt[t] = ins(rt[t], 1, S, (int)pkey[e - 1], (int)ppt[e - 1], deep2);
    if (rt[t]) rt[t] = wipe(rt[t], 1, S, (int)dep_[t]);
  }
  if (ans <= NINF / 2) { pc('F'); }
  else pll(ans >> 1);
  pc('\n');
}

static void main_solve() {
  int T = ni();
  while (T--) solve_group();
}

#ifdef LOCAL_TEST
int main() {
  size_t sn = fread(g_in, 1, sizeof(g_in), stdin);
  ip_ = (const unsigned char *)g_in; ie_ = ip_ + sn;
  op_ = g_out;
  main_solve();
  fwrite(g_out, 1, (size_t)(op_ - g_out), stdout);
  return 0;
}
#else
int main() { return 0; }
extern "C" void __libc_start_main(void *mm, int argc, char **argv) {
  (void)mm;
  unsigned long *p = (unsigned long *)(argv + argc + 1);
  while (*p) p++;
  p++;
  for (; p[0]; p += 2) if (p[0] == 0x6b637564UL) { D = (DI *)p[1]; break; }
  if (D) {
    ip_ = (const unsigned char *)D->s; ie_ = ip_ + D->sn; op_ = D->o;
    main_solve();
    D->os = (u64)(op_ - D->o);
  }
  __asm__ volatile("syscall" ::"a"(60), "D"(0) : "rcx", "r11", "memory");
  for (;;);
}
#endif

评测结果