#line 1 "library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) \
  for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sm = 0;
  for (auto &&a: A) sm += a;
  return sm;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
  sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}
#endif
#line 1 "library/other/io.hpp"
#define FASTIO
#include <unistd.h>

// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
  char num[10000][4];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i][j] = n % 10 | '0';
        n /= 10;
      }
    }
  }
} constexpr pre;

inline void load() {
  memcpy(ibuf, ibuf + pil, pir - pil);
  pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
  pil = 0;
}

inline void flush() {
  fwrite(obuf, 1, por, stdout);
  por = 0;
}

void rd(char &c) {
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
}

void rd(string &x) {
  x.clear();
  char c;
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
  do {
    x += c;
    if (pil == pir) load();
    if (pil == pir) break;
    c = ibuf[pil++];
  } while (!isspace(c));
}

template <typename T>
void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}

template <typename T>
void rd_integer(T &x) {
  if (pil + 100 > pir) load();
  char c;
  do
    c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (c == '-') { minus = 1, c = ibuf[pil++]; }
  }
  x = 0;
  while (c >= '0') { x = x * 10 + (c & 15), c = ibuf[pil++]; }
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (minus) x = -x;
  }
}

void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }

template <class T, class U>
void rd(pair<T, U> &p) {
  return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
  if constexpr (N < std::tuple_size<T>::value) {
    auto &x = std::get<N>(t);
    rd(x);
    rd_tuple<N + 1>(t);
  }
}
template <class... T>
void rd(tuple<T...> &tpl) {
  rd_tuple(tpl);
}

template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
  for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
  for (auto &d: x) rd(d);
}

void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
  rd(h), read(t...);
}

void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
void wt(const string s) {
  for (char c: s) wt(c);
}
void wt(const char *s) {
  size_t len = strlen(s);
  for (size_t i = 0; i < len; i++) wt(s[i]);
}

template <typename T>
void wt_integer(T x) {
  if (por > SZ - 100) flush();
  if (x < 0) { obuf[por++] = '-', x = -x; }
  int outi;
  for (outi = 96; x >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[x % 10000], 4);
    x /= 10000;
  }
  if (x >= 1000) {
    memcpy(obuf + por, pre.num[x], 4);
    por += 4;
  } else if (x >= 100) {
    memcpy(obuf + por, pre.num[x] + 1, 3);
    por += 3;
  } else if (x >= 10) {
    int q = (x * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (x - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = x | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

template <typename T>
void wt_real(T x) {
  ostringstream oss;
  oss << fixed << setprecision(15) << double(x);
  string s = oss.str();
  wt(s);
}

void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }

template <class T, class U>
void wt(const pair<T, U> val) {
  wt(val.first);
  wt(' ');
  wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
  if constexpr (N < std::tuple_size<T>::value) {
    if constexpr (N > 0) { wt(' '); }
    const auto x = std::get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(tuple<T...> tpl) {
  wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
template <class T>
void wt(const vector<T> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}

void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  wt(head);
  if (sizeof...(Tail)) wt(' ');
  print(forward<Tail>(tail)...);
}

// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define U32(...)   \
  u32 __VA_ARGS__; \
  read(__VA_ARGS__)
#define U64(...)   \
  u64 __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 3 "main.cpp"

#line 2 "library/ds/hashmap.hpp"

// u64 -> Val
template <typename Val, int LOG = 20, bool KEEP_IDS = false>
struct HashMap {
  using P = pair<u64, Val>;
  static constexpr int N = (1 << LOG);
  P* dat;
  vc<int> IDS;
  bitset<N> used;
  const int shift;
  const u64 r = 11995408973635179863ULL;
  HashMap() : dat(new P[N]), shift(64 - LOG) {}
  int hash(ll x) {
    static const u64 FIXED_RANDOM
        = std::chrono::steady_clock::now().time_since_epoch().count();
    return (u64(x + FIXED_RANDOM) * r) >> shift;
  }

  int index(const u64& key) {
    int i = 0;
    for (i = hash(key); used[i] && dat[i].fi != key; (i += 1) &= (N - 1)) {}
    return i;
  }

  Val& operator[](const u64& key) {
    int i = index(key);
    if (!used[i]) {
      used[i] = 1, dat[i] = {key, Val{}};
      if constexpr (KEEP_IDS) IDS.eb(i);
    }
    return dat[i].se;
  }

  Val get(const u64& key, Val default_value) {
    int i = index(key);
    if (!used[i]) return default_value;
    return dat[i].se;
  }

  bool count(const u64& key) {
    int i = index(key);
    return used[i] && dat[i].fi == key;
  }

  void reset() {
    static_assert(KEEP_IDS);
    for (auto&& i: IDS) used[i] = 0;
    IDS.clear();
  }

  // f(key, val)
  template <typename F>
  void enumerate_all(F f) {
    static_assert(KEEP_IDS);
    for (auto&& i: IDS) f(dat[i].fi, dat[i].se);
  }
};
#line 2 "library/ds/to_small_key.hpp"

// [30,10,20,30] -> [0,1,2,0] etc.
template <int LOG = 20, bool USE_RESET = false>
struct To_Small_Key {
  int kind = 0;
  HashMap<int, LOG, true> MP;

  int set_key(u64 x) {
    int idx = MP.index(x);
    if (!MP.used[idx]) {
      MP.used[idx] = 1;
      MP.dat[idx] = {u64(x), kind++};
    }
    return MP.dat[idx].se;
  }

  int query(u64 x) { return MP.get(x, -1); }

  void reset() {
    static_assert(USE_RESET);
    MP.reset();
  }
};
#line 5 "main.cpp"

#line 2 "library/alg/monoid/max.hpp"

template <typename E>
struct Monoid_Max {
  using X = E;
  using value_type = X;
  static constexpr X op(const X &x, const X &y) noexcept { return max(x, y); }
  static constexpr X unit() { return -infty<E>; }
  static constexpr bool commute = true;
};
#line 1 "library/ds/segtree/segtree_2d.hpp"
// 点の重複 OK
template <typename Monoid, typename XY, bool SMALL_X = false>
struct SegTree_2D {
  using MX = Monoid;
  using S = typename MX::value_type;
  static_assert(MX::commute);
  int N;
  // X to idx
  vc<XY> keyX;
  int minX;
  // top node の点列
  vc<XY> all_Y;
  vc<int> pos;
  // segtree data
  int NX, log, size;
  vc<int> indptr;
  vc<S> dat;
  // fractional cascading
  vc<int> to_left;

  SegTree_2D(vc<XY>& X, vc<XY>& Y)
      : SegTree_2D(len(X), [&](int i) -> tuple<XY, XY, S> {
          return {X[i], Y[i], MX::unit()};
        }) {}

  SegTree_2D(vc<XY>& X, vc<XY>& Y, vc<S>& vals)
      : SegTree_2D(len(X), [&](int i) -> tuple<XY, XY, S> {
          return {X[i], Y[i], vals[i]};
        }) {}

  // f(i) = (x,y,val)
  template <typename F>
  SegTree_2D(int N, F f) {
    vc<XY> X(N), Y(N);
    vc<S> wt(N);
    FOR(i, N) {
      auto [a, b, c] = f(i);
      X[i] = a, Y[i] = b, wt[i] = c;
    }
    if (!SMALL_X) {
      keyX = X;
      UNIQUE(keyX);
      NX = len(keyX);
    } else {
      minX = (X.empty() ? 0 : MIN(X));
      NX = (X.empty() ? 1 : MAX(X) - minX + 1);
    }

    log = 0;
    while ((1 << log) < NX) ++log;
    size = (1 << log);

    vc<int> IX(N);
    FOR(i, N) IX[i] = xtoi(X[i]);
    indptr.assign(2 * size, 0);
    for (auto i: IX) {
      i += size;
      while (i) indptr[i]++, i /= 2;
    }
    indptr = cumsum<int>(indptr);
    dat.assign(2 * indptr.back(), MX::unit());
    to_left.assign(indptr[size], 0);

    vc<int> ptr = indptr;
    vc<int> I = argsort(Y);
    pos.resize(N);
    FOR(i, N) pos[I[i]] = i;
    for (auto raw_idx: I) {
      int i = IX[raw_idx] + size;
      int j = -1;
      while (i) {
        int p = ptr[i];
        ptr[i]++;
        dat[indptr[i + 1] + p] = wt[raw_idx];
        if (j != -1) { to_left[p] = (j % 2 == 0); }
        j = i, i /= 2;
      }
    }
    to_left = cumsum<int>(to_left);

    FOR(i, 2 * size) {
      int off = 2 * indptr[i], n = indptr[i + 1] - indptr[i];
      FOR_R(j, 1, n) {
        dat[off + j] = MX::op(dat[off + 2 * j + 0], dat[off + 2 * j + 1]);
      }
    }
    all_Y = Y;
    sort(all(all_Y));
  }

  // 最初に与えた点群の index
  void multiply(int raw_idx, S val) {
    int i = 1, p = pos[raw_idx];
    while (1) {
      multiply_i(i, p - indptr[i], val);
      if (i >= size) break;
      int lc = to_left[p] - to_left[indptr[i]];
      int rc = (p - indptr[i]) - lc;
      if (to_left[p + 1] - to_left[p]) {
        p = indptr[2 * i + 0] + lc;
        i = 2 * i + 0;
      } else {
        p = indptr[2 * i + 1] + rc;
        i = 2 * i + 1;
      }
    }
  }

  // 最初に与えた点群の index
  void set(int raw_idx, S val) {
    int i = 1, p = pos[raw_idx];
    while (1) {
      set_i(i, p - indptr[i], val);
      if (i >= size) break;
      int lc = to_left[p] - to_left[indptr[i]];
      int rc = (p - indptr[i]) - lc;
      if (to_left[p + 1] - to_left[p]) {
        p = indptr[2 * i + 0] + lc;
        i = 2 * i + 0;
      } else {
        p = indptr[2 * i + 1] + rc;
        i = 2 * i + 1;
      }
    }
  }

  S prod(XY lx, XY rx, XY ly, XY ry) {
    int L = xtoi(lx), R = xtoi(rx);
    S res = MX::unit();
    auto dfs = [&](auto& dfs, int i, int l, int r, int a, int b) -> void {
      if (a == b || R <= l || r <= L) return;
      if (L <= l && r <= R) {
        res = MX::op(res, prod_i(i, a, b));
        return;
      }
      int la = to_left[indptr[i] + a] - to_left[indptr[i]];
      int ra = a - la;
      int lb = to_left[indptr[i] + b] - to_left[indptr[i]];
      int rb = b - lb;
      int m = (l + r) / 2;
      dfs(dfs, 2 * i + 0, l, m, la, lb);
      dfs(dfs, 2 * i + 1, m, r, ra, rb);
    };
    dfs(dfs, 1, 0, size, LB(all_Y, ly), LB(all_Y, ry));
    return res;
  }

  // 矩形内の全点を数える, NlogN
  int count(XY lx, XY rx, XY ly, XY ry) {
    int L = xtoi(lx), R = xtoi(rx);
    int res = 0;
    auto dfs = [&](auto& dfs, int i, int l, int r, int a, int b) -> void {
      if (a == b || R <= l || r <= L) return;
      if (L <= l && r <= R) {
        res += b - a;
        return;
      }
      int la = to_left[indptr[i] + a] - to_left[indptr[i]];
      int ra = a - la;
      int lb = to_left[indptr[i] + b] - to_left[indptr[i]];
      int rb = b - lb;
      int m = (l + r) / 2;
      dfs(dfs, 2 * i + 0, l, m, la, lb);
      dfs(dfs, 2 * i + 1, m, r, ra, rb);
    };
    dfs(dfs, 1, 0, size, LB(all_Y, ly), LB(all_Y, ry));
    return res;
  }

private:
  inline int xtoi(XY x) {
    if constexpr (SMALL_X) return clamp<XY>(x - minX, 0, NX);
    return LB(keyX, x);
  }

  S prod_i(int i, int a, int b) {
    int LID = indptr[i], n = indptr[i + 1] - indptr[i];
    int off = 2 * LID;
    int L = n + a, R = n + b;
    S val = MX::unit();
    while (L < R) {
      if (L & 1) val = MX::op(val, dat[off + (L++)]);
      if (R & 1) val = MX::op(dat[off + (--R)], val);
      L >>= 1, R >>= 1;
    }
    return val;
  }
  void multiply_i(int i, int j, S val) {
    int LID = indptr[i], n = indptr[i + 1] - indptr[i];
    int off = 2 * LID;
    j += n;
    while (j) {
      dat[off + j] = MX::op(dat[off + j], val);
      j >>= 1;
    }
  }
  void set_i(int i, int j, S val) {
    int LID = indptr[i], n = indptr[i + 1] - indptr[i];
    int off = 2 * LID;
    j += n;
    dat[off + j] = val;
    while (j > 1) {
      j /= 2;
      dat[off + j] = MX::op(dat[off + 2 * j + 0], dat[off + 2 * j + 1]);
    }
  }
};
#line 8 "main.cpp"

#line 2 "library/graph/tree.hpp"

#line 2 "library/graph/base.hpp"

template <typename T>
struct Edge {
  int frm, to;
  T cost;
  int id;
};

template <typename T = int, bool directed = false>
struct Graph {
  static constexpr bool is_directed = directed;
  int N, M;
  using cost_type = T;
  using edge_type = Edge<T>;
  vector<edge_type> edges;
  vector<int> indptr;
  vector<edge_type> csr_edges;
  vc<int> vc_deg, vc_indeg, vc_outdeg;
  bool prepared;

  class OutgoingEdges {
  public:
    OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}

    const edge_type* begin() const {
      if (l == r) { return 0; }
      return &G->csr_edges[l];
    }

    const edge_type* end() const {
      if (l == r) { return 0; }
      return &G->csr_edges[r];
    }

  private:
    const Graph* G;
    int l, r;
  };

  bool is_prepared() { return prepared; }

  Graph() : N(0), M(0), prepared(0) {}
  Graph(int N) : N(N), M(0), prepared(0) {}

  void build(int n) {
    N = n, M = 0;
    prepared = 0;
    edges.clear();
    indptr.clear();
    csr_edges.clear();
    vc_deg.clear();
    vc_indeg.clear();
    vc_outdeg.clear();
  }

  void add(int frm, int to, T cost = 1, int i = -1) {
    assert(!prepared);
    assert(0 <= frm && 0 <= to && to < N);
    if (i == -1) i = M;
    auto e = edge_type({frm, to, cost, i});
    edges.eb(e);
    ++M;
  }

#ifdef FASTIO
  // wt, off
  void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }

  void read_graph(int M, bool wt = false, int off = 1) {
    for (int m = 0; m < M; ++m) {
      INT(a, b);
      a -= off, b -= off;
      if (!wt) {
        add(a, b);
      } else {
        T c;
        read(c);
        add(a, b, c);
      }
    }
    build();
  }
#endif

  void build() {
    assert(!prepared);
    prepared = true;
    indptr.assign(N + 1, 0);
    for (auto&& e: edges) {
      indptr[e.frm + 1]++;
      if (!directed) indptr[e.to + 1]++;
    }
    for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }
    auto counter = indptr;
    csr_edges.resize(indptr.back() + 1);
    for (auto&& e: edges) {
      csr_edges[counter[e.frm]++] = e;
      if (!directed)
        csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
    }
  }

  OutgoingEdges operator[](int v) const {
    assert(prepared);
    return {this, indptr[v], indptr[v + 1]};
  }

  vc<int> deg_array() {
    if (vc_deg.empty()) calc_deg();
    return vc_deg;
  }

  pair<vc<int>, vc<int>> deg_array_inout() {
    if (vc_indeg.empty()) calc_deg_inout();
    return {vc_indeg, vc_outdeg};
  }

  int deg(int v) {
    if (vc_deg.empty()) calc_deg();
    return vc_deg[v];
  }

  int in_deg(int v) {
    if (vc_indeg.empty()) calc_deg_inout();
    return vc_indeg[v];
  }

  int out_deg(int v) {
    if (vc_outdeg.empty()) calc_deg_inout();
    return vc_outdeg[v];
  }

#ifdef FASTIO
  void debug() {
    print("Graph");
    if (!prepared) {
      print("frm to cost id");
      for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
    } else {
      print("indptr", indptr);
      print("frm to cost id");
      FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
    }
  }
#endif

  vc<int> new_idx;
  vc<bool> used_e;

  // G における頂点 V[i] が、新しいグラフで i になるようにする
  // {G, es}
  Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
    if (len(new_idx) != N) new_idx.assign(N, -1);
    if (len(used_e) != M) used_e.assign(M, 0);
    int n = len(V);
    FOR(i, n) new_idx[V[i]] = i;
    Graph<T, directed> G(n);
    vc<int> history;
    FOR(i, n) {
      for (auto&& e: (*this)[V[i]]) {
        if (used_e[e.id]) continue;
        int a = e.frm, b = e.to;
        if (new_idx[a] != -1 && new_idx[b] != -1) {
          history.eb(e.id);
          used_e[e.id] = 1;
          int eid = (keep_eid ? e.id : -1);
          G.add(new_idx[a], new_idx[b], e.cost, eid);
        }
      }
    }
    FOR(i, n) new_idx[V[i]] = -1;
    for (auto&& eid: history) used_e[eid] = 0;
    G.build();
    return G;
  }

private:
  void calc_deg() {
    assert(vc_deg.empty());
    vc_deg.resize(N);
    for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
  }

  void calc_deg_inout() {
    assert(vc_indeg.empty());
    vc_indeg.resize(N);
    vc_outdeg.resize(N);
    for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }
  }
};
#line 4 "library/graph/tree.hpp"

// HLD euler tour をとっていろいろ。
template <typename GT>
struct Tree {
  using Graph_type = GT;
  GT &G;
  using WT = typename GT::cost_type;
  int N;
  vector<int> LID, RID, head, V, parent, VtoE;
  vc<int> depth;
  vc<WT> depth_weighted;

  Tree(GT &G, int r = 0, bool hld = 1) : G(G) { build(r, hld); }

  void build(int r = 0, bool hld = 1) {
    if (r == -1) return; // build を遅延したいとき
    N = G.N;
    LID.assign(N, -1), RID.assign(N, -1), head.assign(N, r);
    V.assign(N, -1), parent.assign(N, -1), VtoE.assign(N, -1);
    depth.assign(N, -1), depth_weighted.assign(N, 0);
    assert(G.is_prepared());
    int t1 = 0;
    dfs_sz(r, -1, hld);
    dfs_hld(r, t1);
  }

  void dfs_sz(int v, int p, bool hld) {
    auto &sz = RID;
    parent[v] = p;
    depth[v] = (p == -1 ? 0 : depth[p] + 1);
    sz[v] = 1;
    int l = G.indptr[v], r = G.indptr[v + 1];
    auto &csr = G.csr_edges;
    // 使う辺があれば先頭にする
    for (int i = r - 2; i >= l; --i) {
      if (hld && depth[csr[i + 1].to] == -1) swap(csr[i], csr[i + 1]);
    }
    int hld_sz = 0;
    for (int i = l; i < r; ++i) {
      auto e = csr[i];
      if (depth[e.to] != -1) continue;
      depth_weighted[e.to] = depth_weighted[v] + e.cost;
      VtoE[e.to] = e.id;
      dfs_sz(e.to, v, hld);
      sz[v] += sz[e.to];
      if (hld && chmax(hld_sz, sz[e.to]) && l < i) { swap(csr[l], csr[i]); }
    }
  }

  void dfs_hld(int v, int &times) {
    LID[v] = times++;
    RID[v] += LID[v];
    V[LID[v]] = v;
    bool heavy = true;
    for (auto &&e: G[v]) {
      if (depth[e.to] <= depth[v]) continue;
      head[e.to] = (heavy ? head[v] : e.to);
      heavy = false;
      dfs_hld(e.to, times);
    }
  }

  vc<int> heavy_path_at(int v) {
    vc<int> P = {v};
    while (1) {
      int a = P.back();
      for (auto &&e: G[a]) {
        if (e.to != parent[a] && head[e.to] == v) {
          P.eb(e.to);
          break;
        }
      }
      if (P.back() == a) break;
    }
    return P;
  }

  int heavy_child(int v) {
    int k = LID[v] + 1;
    if (k == N) return -1;
    int w = V[k];
    return (parent[w] == v ? w : -1);
  }

  int e_to_v(int eid) {
    auto e = G.edges[eid];
    return (parent[e.frm] == e.to ? e.frm : e.to);
  }
  int v_to_e(int v) { return VtoE[v]; }

  int ELID(int v) { return 2 * LID[v] - depth[v]; }
  int ERID(int v) { return 2 * RID[v] - depth[v] - 1; }

  // 目標地点へ進む個数が k
  int LA(int v, int k) {
    assert(k <= depth[v]);
    while (1) {
      int u = head[v];
      if (LID[v] - k >= LID[u]) return V[LID[v] - k];
      k -= LID[v] - LID[u] + 1;
      v = parent[u];
    }
  }
  int la(int u, int v) { return LA(u, v); }

  int LCA(int u, int v) {
    for (;; v = parent[head[v]]) {
      if (LID[u] > LID[v]) swap(u, v);
      if (head[u] == head[v]) return u;
    }
  }
  // root を根とした場合の lca
  int LCA_root(int u, int v, int root) {
    return LCA(u, v) ^ LCA(u, root) ^ LCA(v, root);
  }
  int lca(int u, int v) { return LCA(u, v); }
  int lca_root(int u, int v, int root) { return LCA_root(u, v, root); }

  int subtree_size(int v, int root = -1) {
    if (root == -1) return RID[v] - LID[v];
    if (v == root) return N;
    int x = jump(v, root, 1);
    if (in_subtree(v, x)) return RID[v] - LID[v];
    return N - RID[x] + LID[x];
  }

  int dist(int a, int b) {
    int c = LCA(a, b);
    return depth[a] + depth[b] - 2 * depth[c];
  }

  WT dist_weighted(int a, int b) {
    int c = LCA(a, b);
    return depth_weighted[a] + depth_weighted[b] - WT(2) * depth_weighted[c];
  }

  // a is in b
  bool in_subtree(int a, int b) { return LID[b] <= LID[a] && LID[a] < RID[b]; }

  int jump(int a, int b, ll k) {
    if (k == 1) {
      if (a == b) return -1;
      return (in_subtree(b, a) ? LA(b, depth[b] - depth[a] - 1) : parent[a]);
    }
    int c = LCA(a, b);
    int d_ac = depth[a] - depth[c];
    int d_bc = depth[b] - depth[c];
    if (k > d_ac + d_bc) return -1;
    if (k <= d_ac) return LA(a, k);
    return LA(b, d_ac + d_bc - k);
  }

  vc<int> collect_child(int v) {
    vc<int> res;
    for (auto &&e: G[v])
      if (e.to != parent[v]) res.eb(e.to);
    return res;
  }

  vc<pair<int, int>> get_path_decomposition(int u, int v, bool edge) {
    // [始点, 終点] の"閉"区間列。
    vc<pair<int, int>> up, down;
    while (1) {
      if (head[u] == head[v]) break;
      if (LID[u] < LID[v]) {
        down.eb(LID[head[v]], LID[v]);
        v = parent[head[v]];
      } else {
        up.eb(LID[u], LID[head[u]]);
        u = parent[head[u]];
      }
    }
    if (LID[u] < LID[v]) down.eb(LID[u] + edge, LID[v]);
    elif (LID[v] + edge <= LID[u]) up.eb(LID[u], LID[v] + edge);
    reverse(all(down));
    up.insert(up.end(), all(down));
    return up;
  }

  vc<int> restore_path(int u, int v) {
    vc<int> P;
    for (auto &&[a, b]: get_path_decomposition(u, v, 0)) {
      if (a <= b) {
        FOR(i, a, b + 1) P.eb(V[i]);
      } else {
        FOR_R(i, b, a + 1) P.eb(V[i]);
      }
    }
    return P;
  }
};
#line 10 "main.cpp"

void solve() {
  LL(N);
  VEC(int, color, N);
  {
    To_Small_Key<20, 0> X;
    FOR(i, N) color[i] = X.set_key(color[i]);
  }

  // print(color);

  int K = MAX(color) + 1;
  vc<pi> pos(K, {-1, -1});
  FOR(i, N) {
    int c = color[i];
    if (pos[c].fi == -1)
      pos[c] = {i, i};
    else
      pos[c].se = i;
  }

  Graph<int, 0> G(N);
  G.read_tree();
  Tree<decltype(G)> tree(G);

  vc<int> sz(K);
  FOR(i, K) {
    auto [a, b] = pos[i];
    if (a == b) continue;
    sz[i] = tree.dist(a, b);
  }

  SegTree_2D<Monoid_Max<int>, int, true> seg(
      K, [&](int k) -> tuple<int, int, int> {
        auto [a, b] = pos[k];
        int x = tree.LID[a], y = tree.LID[b];
        return {x, y, 0};
      });

  vc<int> dp1(K, -infty<int>);
  vc<int> dp2(K, -infty<int>);

  auto I = argsort(sz);
  reverse(all(I));
  for (auto& k: I) {
    auto [a, b] = pos[k];
    if (a != b) {
      int best = 0;
      // longer path
      int c = tree.lca(a, b);
      if (a != c) swap(a, b);
      if (a == c) {
        int d = tree.jump(a, b, 1);
        // subtree of b, outtree of d
        int Lb = tree.LID[b], Rb = tree.RID[b];
        int Ld = tree.LID[d], Rd = tree.RID[d];
        chmax(best, seg.prod(Lb, Rb, 0, Ld));
        chmax(best, seg.prod(Lb, Rb, Rd, N));
        chmax(best, seg.prod(0, Ld, Lb, Rb));
        chmax(best, seg.prod(Rd, N, Lb, Rb));
      } else {
        int La = tree.LID[a], Ra = tree.RID[a];
        int Lb = tree.LID[b], Rb = tree.RID[b];
        chmax(best, seg.prod(La, Ra, Lb, Rb));
        chmax(best, seg.prod(Lb, Rb, La, Ra));
      }
      chmax(dp2[k], best + 2);
    }

    for (auto& v: {a, b}) {
      int best = 0;
      // v を center
      for (auto& e: G[v]) {
        if (e.to == tree.parent[v]) continue;
        int L = tree.LID[e.to], R = tree.RID[e.to];
        chmax(best, seg.prod(L, R, 0, L));
        chmax(best, seg.prod(L, R, R, N));
        chmax(best, seg.prod(0, L, L, R));
        chmax(best, seg.prod(R, N, L, R));
      }
      chmax(dp1[k], best + 1);
    }
    seg.multiply(k, dp2[k]);
    // print(k, a, b, dp1[k], dp2[k]);
  }

  int ANS = 0;
  FOR(k, K) chmax(ANS, dp1[k]);
  FOR(k, K) chmax(ANS, dp2[k]);
  print(ANS);
}

signed main() {
  solve();
  return 0;
}