#line 1 "main.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/919"
#line 1 "library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")

#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;
  if (pir < SZ) ibuf[pir++] = '\n';
}

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();
    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 ('0' <= c) { 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;

#if defined(LOCAL)
#define SHOW(...) \
  SHOW_IMPL(__VA_ARGS__, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) \
  print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#else
#define SHOW(...)
#endif

#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 1 "library/ds/bit_vector.hpp"
struct Bit_Vector {
  int n;
  vc<pair<u64, u32>> dat;
  Bit_Vector(int n) : n(n) { dat.assign((n + 127) >> 6, {0, 0}); }
  void set(int i) { dat[i >> 6].fi |= u64(1) << (i & 63); }
  void reset() { fill(all(dat), pair<u64, u32>{0, 0}); }
  void build() {
    FOR(i, len(dat) - 1) dat[i + 1].se = dat[i].se + popcnt(dat[i].fi);
  }
  // [0, k) 内の 1 の個数
  int count(int k, bool f) {
    auto [a, b] = dat[k >> 6];
    int ret = b + popcnt(a & ((u64(1) << (k & 63)) - 1));
    return (f ? ret : k - ret);
  }
  int count(int L, int R, bool f) { return count(R, f) - count(L, f); }
  string to_string() {
    string ans;
    FOR(i, n) ans += '0' + (dat[i / 64].fi >> (i % 64) & 1);
    return ans;
  }
};
#line 1 "library/ds/index_compression.hpp"
template <typename T>
struct Index_Compression_DISTINCT_SMALL {
  static_assert(is_same_v<T, int>);
  int mi, ma;
  vc<int> dat;
  vc<int> build(vc<int> X) {
    mi = 0, ma = -1;
    if (!X.empty()) mi = MIN(X), ma = MAX(X);
    dat.assign(ma - mi + 2, 0);
    for (auto& x: X) dat[x - mi + 1]++;
    FOR(i, len(dat) - 1) dat[i + 1] += dat[i];
    for (auto& x: X) { x = dat[x - mi]++; }
    FOR_R(i, 1, len(dat)) dat[i] = dat[i - 1];
    dat[0] = 0;
    return X;
  }
  int operator()(ll x) { return dat[clamp<ll>(x - mi, 0, ma - mi + 1)]; }
};

template <typename T>
struct Index_Compression_SAME_SMALL {
  static_assert(is_same_v<T, int>);
  int mi, ma;
  vc<int> dat;
  vc<int> build(vc<int> X) {
    mi = 0, ma = -1;
    if (!X.empty()) mi = MIN(X), ma = MAX(X);
    dat.assign(ma - mi + 2, 0);
    for (auto& x: X) dat[x - mi + 1] = 1;
    FOR(i, len(dat) - 1) dat[i + 1] += dat[i];
    for (auto& x: X) { x = dat[x - mi]; }
    return X;
  }
  int operator()(ll x) { return dat[clamp<ll>(x - mi, 0, ma - mi + 1)]; }
};

template <typename T>
struct Index_Compression_SAME_LARGE {
  vc<T> dat;
  vc<int> build(vc<T> X) {
    vc<int> I = argsort(X);
    vc<int> res(len(X));
    for (auto& i: I) {
      if (!dat.empty() && dat.back() == X[i]) {
        res[i] = len(dat) - 1;
      } else {
        res[i] = len(dat);
        dat.eb(X[i]);
      }
    }
    dat.shrink_to_fit();
    return res;
  }
  int operator()(T x) { return LB(dat, x); }
};

template <typename T>
struct Index_Compression_DISTINCT_LARGE {
  vc<T> dat;
  vc<int> build(vc<T> X) {
    vc<int> I = argsort(X);
    vc<int> res(len(X));
    for (auto& i: I) { res[i] = len(dat), dat.eb(X[i]); }
    dat.shrink_to_fit();
    return res;
  }
  int operator()(T x) { return LB(dat, x); }
};

template <typename T, bool SMALL>
using Index_Compression_DISTINCT =
    typename std::conditional<SMALL, Index_Compression_DISTINCT_SMALL<T>,
                              Index_Compression_DISTINCT_LARGE<T>>::type;
template <typename T, bool SMALL>
using Index_Compression_SAME =
    typename std::conditional<SMALL, Index_Compression_SAME_SMALL<T>,
                              Index_Compression_SAME_LARGE<T>>::type;

// SAME: [2,3,2] -> [0,1,0]
// DISTINCT: [2,2,3] -> [0,2,1]
// (x): lower_bound(X,x) をかえす
template <typename T, bool SAME, bool SMALL>
using Index_Compression =
    typename std::conditional<SAME, Index_Compression_SAME<T, SMALL>,
                              Index_Compression_DISTINCT<T, SMALL>>::type;
#line 2 "library/alg/monoid/add.hpp"

template <typename E>
struct Monoid_Add {
  using X = E;
  using value_type = X;
  static constexpr X op(const X &x, const X &y) noexcept { return x + y; }
  static constexpr X inverse(const X &x) noexcept { return -x; }
  static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; }
  static constexpr X unit() { return X(0); }
  static constexpr bool commute = true;
};
#line 4 "library/ds/wavelet_matrix/wavelet_matrix.hpp"

// 静的メソッドinverseの存在をチェックするテンプレート
template <typename, typename = std::void_t<>>
struct has_inverse : std::false_type {};

template <typename T>
struct has_inverse<T, std::void_t<decltype(
                          T::inverse(std::declval<typename T::value_type>()))>>
    : std::true_type {};

struct Dummy_Data_Structure {
  using MX = Monoid_Add<bool>;
  void build(const vc<bool>& A) {}
};

template <typename Y, bool SMALL_Y, typename SEGTREE = Dummy_Data_Structure>
struct Wavelet_Matrix {
  using Mono = typename SEGTREE::MX;
  using T = typename Mono::value_type;
  static_assert(Mono::commute);

  int n, log, K;
  Index_Compression<Y, true, SMALL_Y> IDX;
  vc<Y> ItoY;
  vc<int> mid;
  vc<Bit_Vector> bv;
  vc<SEGTREE> seg;

  Wavelet_Matrix() {}
  Wavelet_Matrix(const vc<Y>& A) { build(A); }
  Wavelet_Matrix(const vc<Y>& A, vc<T>& SUM_Data) { build(A, SUM_Data); }
  template <typename F>
  Wavelet_Matrix(int n, F f) {
    build(n, f);
  }

  template <typename F>
  void build(int m, F f) {
    vc<Y> A(m);
    vc<T> S(m);
    for (int i = 0; i < m; ++i) tie(A[i], S[i]) = f(i);
    build(A, S);
  }

  void build(const vc<Y>& A) { build(A, vc<T>(len(A), Mono::unit())); }
  void build(const vc<Y>& A, vc<T> S) {
    n = len(A);
    vc<int> B = IDX.build(A);
    K = 0;
    for (auto& x: B) chmax(K, x + 1);
    ItoY.resize(K);
    FOR(i, n) ItoY[B[i]] = A[i];
    log = 0;
    while ((1 << log) < K) ++log;
    mid.resize(log), bv.assign(log, Bit_Vector(n));
    vc<int> B0(n), B1(n);
    vc<T> S0(n), S1(n);
    seg.resize(log + 1);
    seg[log].build(S);
    for (int d = log - 1; d >= 0; --d) {
      int p0 = 0, p1 = 0;
      for (int i = 0; i < n; ++i) {
        bool f = (B[i] >> d & 1);
        if (!f) { B0[p0] = B[i], S0[p0] = S[i], p0++; }
        if (f) { bv[d].set(i), B1[p1] = B[i], S1[p1] = S[i], p1++; }
      }
      swap(B, B0), swap(S, S0);
      move(B1.begin(), B1.begin() + p1, B.begin() + p0);
      move(S1.begin(), S1.begin() + p1, S.begin() + p0);
      mid[d] = p0, bv[d].build(), seg[d].build(S);
    }
  }

  // [L,R) x [0,y)
  int prefix_count(int L, int R, Y y) {
    int p = IDX(y);
    if (p == 0) return 0;
    if (p == K) return R - L;
    int cnt = 0;
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (p >> d & 1) cnt += r0 - l0, L = l1, R = r1;
      if (!(p >> d & 1)) L = l0, R = r0;
    }
    return cnt;
  }

  // [L,R) x [y1,y2)
  int count(int L, int R, Y y1, Y y2) {
    return prefix_count(L, R, y2) - prefix_count(L, R, y1);
  }

  // [L,R) x [0,y)
  pair<int, T> prefix_count_and_prod(int L, int R, Y y) {
    int p = IDX(y);
    if (p == 0) return {0, Mono::unit()};
    if (p == K) return {R - L, seg[log].prod(L, R)};
    int cnt = 0;
    T t = Mono::unit();
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (p >> d & 1) {
        cnt += r0 - l0, t = Mono::op(t, seg[d].prod(l0, r0)), L = l1, R = r1;
      }
      if (!(p >> d & 1)) L = l0, R = r0;
    }
    return {cnt, t};
  }

  // [L,R) x [y1,y2)
  pair<int, T> count_and_prod(int L, int R, Y y1, Y y2) {
    if constexpr (has_inverse<Mono>::value) {
      auto [c1, t1] = prefix_count_and_prod(L, R, y1);
      auto [c2, t2] = prefix_count_and_prod(L, R, y2);
      return {c2 - c1, Mono::op(Mono::inverse(t1), t2)};
    }
    int lo = IDX(y1), hi = IDX(y2), cnt = 0;
    T t = Mono::unit();
    auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
      assert(b - a == (1 << d));
      if (hi <= a || b <= lo) return;
      if (lo <= a && b <= hi) {
        cnt += R - L, t = Mono::op(t, seg[d].prod(L, R));
        return;
      }
      --d;
      int c = (a + b) / 2;
      int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      dfs(dfs, d, l0, r0, a, c), dfs(dfs, d, l1, r1, c, b);
    };
    dfs(dfs, log, L, R, 0, 1 << log);
    return {cnt, t};
  }

  // [L,R) x [y1,y2)
  T prefix_prod(int L, int R, Y y) { return prefix_count_and_prod(L, R, y).se; }
  // [L,R) x [y1,y2)
  T prod(int L, int R, Y y1, Y y2) { return count_and_prod(L, R, y1, y2).se; }

  Y kth(int L, int R, int k) {
    assert(0 <= k && k < R - L);
    int p = 0;
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (k < r0 - l0) {
        L = l0, R = r0;
      } else {
        k -= r0 - l0, L = l1, R = r1, p |= 1 << d;
      }
    }
    return ItoY[p];
  }

  // y 以上最小 OR infty<Y>
  Y next(int L, int R, Y y) {
    int k = IDX(y);
    int p = K;

    auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
      if (p <= a || L == R || b <= k) return;
      if (d == 0) {
        chmin(p, a);
        return;
      }
      --d;
      int c = (a + b) / 2;
      int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      dfs(dfs, d, l0, r0, a, c), dfs(dfs, d, l1, r1, c, b);
    };
    dfs(dfs, log, L, R, 0, 1 << log);
    return (p == K ? infty<Y> : ItoY[p]);
  }

  // y 以下最大 OR -infty<T>
  Y prev(int L, int R, Y y) {
    int k = IDX(y + 1);
    int p = -1;
    auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
      if (b - 1 <= p || L == R || k <= a) return;
      if (d == 0) {
        chmax(p, a);
        return;
      }
      --d;
      int c = (a + b) / 2;
      int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      dfs(dfs, d, l1, r1, c, b), dfs(dfs, d, l0, r0, a, c);
    };
    dfs(dfs, log, L, R, 0, 1 << log);
    return (p == -1 ? -infty<Y> : ItoY[p]);
  }

  Y median(bool UPPER, int L, int R) {
    assert(0 <= L && L < R && R <= n);
    int k = (UPPER ? (R - L) / 2 : (R - L - 1) / 2);
    return kth(L, R, k);
  }

  pair<Y, T> kth_value_and_prod(int L, int R, int k) {
    assert(0 <= k && k <= R - L);
    if (k == R - L) return {infty<Y>, seg[log].prod(L, R)};
    int p = 0;
    T t = Mono::unit();
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (k < r0 - l0) {
        L = l0, R = r0;
      } else {
        t = Mono::op(t, seg[d].prod(l0, r0)), k -= r0 - l0, L = l1, R = r1,
        p |= 1 << d;
      }
    }
    t = Mono::op(t, seg[0].prod(L, L + k));
    return {ItoY[p], t};
  }

  T prod_index_range(int L, int R, int k1, int k2) {
    static_assert(has_inverse<Mono>::value);
    T t1 = kth_value_and_prod(L, R, k1).se;
    T t2 = kth_value_and_prod(L, R, k2).se;
    return Mono::op(Mono::inverse(t1), t2);
  }

  // [L,R) x [0,y) での check(cnt, prod) が true となる最大の (cnt,prod)
  template <typename F>
  pair<int, T> max_right(F check, int L, int R) {
    int cnt = 0;
    T t = Mono::unit();
    assert(check(0, Mono::unit()));
    if (check(R - L, seg[log].prod(L, R))) {
      return {R - L, seg[log].prod(L, R)};
    }
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      int cnt1 = cnt + r0 - l0, t1 = Mono::op(t, seg[d].prod(l0, r0));
      if (check(cnt1, t1)) {
        cnt = cnt1, t = t1, L = l1, R = r1;
      } else {
        L = l0, R = r0;
      }
    }
    return {cnt, t};
  }

  void set(int i, T t) {
    assert(0 <= i && i < n);
    int L = i, R = i + 1;
    seg[log].set(L, t);
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (l0 < r0) L = l0, R = r0;
      if (l0 == r0) L = l1, R = r1;
      seg[d].set(L, t);
    }
  }
  void multiply(int i, T t) {
    assert(0 <= i && i < n);
    int L = i, R = i + 1;
    seg[log].multiply(L, t);
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (l0 < r0) L = l0, R = r0;
      if (l0 == r0) L = l1, R = r1;
      seg[d].multiply(L, t);
    }
  }
};

/*
// 座圧するかどうかを COMPRESS で指定する
// xor 的な使い方をする場合には、コンストラクタで log を渡すこと
template <typename T, bool COMPRESS, bool USE_SUM>
struct Wavelet_Matrix_Old {
  static_assert(is_same_v<T, int> || is_same_v<T, ll>);
  int N, lg;
  vector<int> mid;
  vector<Bit_Vector> bv;
  vc<T> key;
  bool set_log;
  vvc<T> cumsum;

  Wavelet_Matrix_Old() {}

  // 和を使わないなら、SUM_data は空でよい
  Wavelet_Matrix_Old(vc<T> A, vc<T> SUM_data = {}, int log = -1) {
    build(A, SUM_data, log);
  }

  void build(vc<T> A, vc<T> SUM_data = {}, int log = -1) {
    if constexpr (USE_SUM) { assert(len(SUM_data) == len(A)); }
    N = len(A), lg = log, set_log = (log != -1);
    if (N == 0) {
      lg = 0;
      cumsum.resize(1);
      cumsum[0] = {0};
      return;
    }
    vc<T>& S = SUM_data;
    if (COMPRESS) {
      assert(!set_log);
      key.reserve(N);
      vc<int> I = argsort(A);
      for (auto&& i: I) {
        if (key.empty() || key.back() != A[i]) key.eb(A[i]);
        A[i] = len(key) - 1;
      }
      key.shrink_to_fit();
    }
    if (lg == -1) lg = __lg(max<ll>(MAX(A), 1)) + 1;
    mid.resize(lg), bv.assign(lg, Bit_Vector(N));
    if constexpr (USE_SUM) cumsum.assign(1 + lg, vc<T>(N + 1, 0));
    S.resize(N);
    vc<T> A0(N), A1(N);
    vc<T> S0(N), S1(N);
    FOR_R(d, -1, lg) {
      int p0 = 0, p1 = 0;
      if constexpr (USE_SUM) {
        FOR(i, N) { cumsum[d + 1][i + 1] = cumsum[d + 1][i] + S[i]; }
      }
      if (d == -1) break;
      FOR(i, N) {
        bool f = (A[i] >> d & 1);
        if (!f) {
          if constexpr (USE_SUM) S0[p0] = S[i];
          A0[p0++] = A[i];
        } else {
          if constexpr (USE_SUM) S1[p1] = S[i];
          bv[d].set(i), A1[p1++] = A[i];
        }
      }
      mid[d] = p0;
      bv[d].build();
      swap(A, A0), swap(S, S0);
      FOR(i, p1) A[p0 + i] = A1[i], S[p0 + i] = S1[i];
    }
  }

  // [L,R) x [a,b), (cnt, monoid value)
  pair<int, T> range_cnt_sum(int L, int R, T a, T b, T xor_val = 0) {
    if (xor_val != 0) assert(set_log);
    if (a == b) return {0, 0};
    if (COMPRESS) a = LB(key, a), b = LB(key, b);
    int cnt = 0;
    T sm = 0;
    auto dfs = [&](auto& dfs, int d, int L, int R, T lx, T rx) -> void {
      if (rx <= a || b <= lx) return;
      if (a <= lx && rx <= b) {
        cnt += R - L, sm += get(d, L, R);
        return;
      }
      --d;
      T mx = (lx + rx) / 2;
      int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (xor_val >> d & 1) swap(l0, l1), swap(r0, r1);
      dfs(dfs, d, l0, r0, lx, mx), dfs(dfs, d, l1, r1, mx, rx);
    };
    dfs(dfs, lg, L, R, 0, T(1) << lg);
    return {cnt, sm};
  }

  // smallest k, sum of [0,k)
  pair<T, T> kth_value_sum(int L, int R, int k, T xor_val = 0) {
    assert(0 <= k && k <= R - L);
    if (k == R - L) { return {infty<T>, sum_all(L, R)}; }
    if (L == R) return {infty<T>, 0};
    if (xor_val != 0) assert(set_log);
    T sm = 0, val = 0;
    for (int d = lg - 1; d >= 0; --d) {
      // いま幅 d+1 の trie node に居て, 幅 d のところに行く
      int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (xor_val >> d & 1) swap(l0, l1), swap(r0, r1);
      if (k < r0 - l0) {
        L = l0, R = r0;
      } else {
        k -= r0 - l0, val |= T(1) << d, L = l1, R = r1;
        if constexpr (USE_SUM) sm += get(d, l0, r0);
      }
    }
    if constexpr (USE_SUM) sm += get(0, L, L + k);
    if (COMPRESS) val = key[val];

    return {val, sm};
  }

  int count(int L, int R, T a, T b, T xor_val = 0) {
    return range_cnt_sum(L, R, a, b, xor_val).fi;
  }
  T sum(int L, int R, T a, T b, T xor_val = 0) {
    static_assert(USE_SUM);
    return range_cnt_sum(L, R, a, b, xor_val).se;
  }

  T sum_index_range(int L, int R, int k1, int k2, T xor_val = 0) {
    static_assert(USE_SUM);
    return kth_value_sum(L, R, k2, xor_val).se
           - kth_value_sum(L, R, k1, xor_val).se;
  }
  T kth(int L, int R, int k, T xor_val = 0) {
    assert(0 <= k && k < R - L);
    return kth_value_sum(L, R, k, xor_val).fi;
  }

  // x 以上最小 OR infty<T>
  T next(int L, int R, T x, T xor_val = 0) {
    if (xor_val != 0) assert(set_log);
    if (L == R) return infty<T>;
    if (COMPRESS) x = LB(key, x);
    T ans = infty<T>;

    auto dfs = [&](auto& dfs, int d, int L, int R, T lx, T rx) -> void {
      if (ans <= lx || L == R || rx <= x) return;
      if (d == 0) {
        chmin(ans, lx);
        return;
      }
      --d;
      T mx = (lx + rx) / 2;
      int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (xor_val >> d & 1) swap(l0, l1), swap(r0, r1);
      dfs(dfs, d, l0, r0, lx, mx), dfs(dfs, d, l1, r1, mx, rx);
    };
    dfs(dfs, lg, L, R, 0, T(1) << lg);
    if (COMPRESS && ans < infty<T>) ans = key[ans];
    return ans;
  }

  // x 以下最大 OR -infty<T>
  T prev(int L, int R, T x, T xor_val = 0) {
    if (xor_val != 0) assert(set_log);
    if (L == R) return -infty<T>;
    T ans = -infty<int>;
    ++x;
    if (COMPRESS) x = LB(key, x);

    auto dfs = [&](auto& dfs, int d, int L, int R, T lx, T rx) -> void {
      if ((rx - 1) <= ans || L == R || x <= lx) return;
      if (d == 0) {
        chmax(ans, lx);
        return;
      }
      --d;
      T mx = (lx + rx) / 2;
      int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (xor_val >> d & 1) swap(l0, l1), swap(r0, r1);
      dfs(dfs, d, l1, r1, mx, rx), dfs(dfs, d, l0, r0, lx, mx);
    };
    dfs(dfs, lg, L, R, 0, T(1) << lg);
    if (COMPRESS && ans != -infty<T>) ans = key[ans];
    return ans;
  }

  // xor した結果で、[L, R) の中で中央値。
  // LOWER = true：下側中央値、false：上側中央値
  T median(bool UPPER, int L, int R, T xor_val = 0) {
    int n = R - L;
    int k = (UPPER ? n / 2 : (n - 1) / 2);
    return kth(L, R, k, xor_val);
  }

  T sum_all(int L, int R) { return get(lg, L, R); }

  // check(cnt, prefix sum) が true となるような最大の (cnt, sum)
  template <typename F>
  pair<int, T> max_right(F check, int L, int R, T xor_val = 0) {
    assert(check(0, 0));
    if (xor_val != 0) assert(set_log);
    if (L == R) return {0, 0};
    if (check(R - L, get(lg, L, R))) return {R - L, get(lg, L, R)};
    int cnt = 0;
    T sm = 0;
    for (int d = lg - 1; d >= 0; --d) {
      int l0 = bv[d].count(L, 0), r0 = bv[d].count(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (xor_val >> d & 1) swap(l0, l1), swap(r0, r1);
      if (check(cnt + r0 - l0, sm + get(d, l0, r0))) {
        cnt += r0 - l0, sm += get(d, l0, r0);
        L = l1, R = r1;
      } else {
        L = l0, R = r0;
      }
    }
    int k = binary_search(
        [&](int k) -> bool { return check(cnt + k, sm + get(0, L, L + k)); }, 0,
        R - L);
    cnt += k, sm += get(0, L, L + k);
    return {cnt, sm};
  }

private:
  inline T get(int d, int L, int R) {
    if constexpr (USE_SUM) return cumsum[d][R] - cumsum[d][L];
    return 0;
  }
};
*/
#line 5 "main.cpp"

void solve() {
  LL(N);
  VEC(ll, A, N);
  Wavelet_Matrix<ll, false> WM(A);
  ll ANS = -infty<ll>;

  auto get = [&](ll L, ll R) -> ll {
    assert(L < R);
    return WM.median(0, L, R);
  };

  FOR3(K, 1, N + 1) {
    // とる最大回数
    ll LIM = N / K;
    vi left(LIM);
    vi right(LIM);
    FOR(i, LIM) left[i] = get(K * i, K * i + K);
    FOR(i, LIM) right[i] = get(N - K * i - K, N - K * i);
    left = cumsum<ll>(left);
    right = cumsum<ll>(right);
    // x 回以下とるときの～
    FOR(i, LIM) chmax(left[i + 1], left[i]);
    FOR(i, LIM) chmax(right[i + 1], right[i]);
    FOR(i, LIM + 1) chmax(ANS, K * (left[i] + right[LIM - i]));
  }
  print(ANS);
}

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