Problem p02590 (C++) — buggy submission, verdict: Time Limit Exceeded

#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES
#define _SILENCE_ALL_CXX17_DEPRECATION_WARNINGS
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma comment(linker, "/STACK:526000000")
#include "bits/stdc++.h"

/*
AtCoder STL, licensed under public domain (cc0)
Download: https://img.atcoder.jp/practice2/ac-library.zip
*/

#ifndef ATCODER_INTERNAL_BITOP_HPP
#define ATCODER_INTERNAL_BITOP_HPP 1
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
std::vector<int> sa_naive(const std::vector<int> &s) {
  int n = int(s.size());
  std::vector<int> sa(n);
  std::iota(sa.begin(), sa.end(), 0);
  std::sort(sa.begin(), sa.end(), [&](int l, int r) {
    if (l == r)
      return false;
    while (l < n && r < n) {
      if (s[l] != s[r])
        return s[l] < s[r];
      l++;
      r++;
    }
    return l == n;
  });
  return sa;
}
std::vector<int> sa_doubling(const std::vector<int> &s) {
  int n = int(s.size());
  std::vector<int> sa(n), rnk = s, tmp(n);
  std::iota(sa.begin(), sa.end(), 0);
  for (int k = 1; k < n; k *= 2) {
    auto cmp = [&](int x, int y) {
      if (rnk[x] != rnk[y])
        return rnk[x] < rnk[y];
      int rx = x + k < n ? rnk[x + k] : -1;
      int ry = y + k < n ? rnk[y + k] : -1;
      return rx < ry;
    };
    std::sort(sa.begin(), sa.end(), cmp);
    tmp[sa[0]] = 0;
    for (int i = 1; i < n; i++) {
      tmp[sa[i]] = tmp[sa[i - 1]] + (cmp(sa[i - 1], sa[i]) ? 1 : 0);
    }
    std::swap(tmp, rnk);
  }
  return sa;
}
template <int THRESHOLD_NAIVE = 10, int THRESHOLD_DOUBLING = 40>
std::vector<int> sa_is(const std::vector<int> &s, int upper) {
  int n = int(s.size());
  if (n == 0)
    return {};
  if (n == 1)
    return {0};
  if (n == 2) {
    if (s[0] < s[1]) {
      return {0, 1};
    } else {
      return {1, 0};
    }
  }
  if (n < THRESHOLD_NAIVE) {
    return sa_naive(s);
  }
  if (n < THRESHOLD_DOUBLING) {
    return sa_doubling(s);
  }
  std::vector<int> sa(n);
  std::vector<bool> ls(n);
  for (int i = n - 2; i >= 0; i--) {
    ls[i] = (s[i] == s[i + 1]) ? ls[i + 1] : (s[i] < s[i + 1]);
  }
  std::vector<int> sum_l(upper + 1), sum_s(upper + 1);
  for (int i = 0; i < n; i++) {
    if (!ls[i]) {
      sum_s[s[i]]++;
    } else {
      sum_l[s[i] + 1]++;
    }
  }
  for (int i = 0; i <= upper; i++) {
    sum_s[i] += sum_l[i];
    if (i < upper)
      sum_l[i + 1] += sum_s[i];
  }
  auto induce = [&](const std::vector<int> &lms) {
    std::fill(sa.begin(), sa.end(), -1);
    std::vector<int> buf(upper + 1);
    std::copy(sum_s.begin(), sum_s.end(), buf.begin());
    for (auto d : lms) {
      if (d == n)
        continue;
      sa[buf[s[d]]++] = d;
    }
    std::copy(sum_l.begin(), sum_l.end(), buf.begin());
    sa[buf[s[n - 1]]++] = n - 1;
    for (int i = 0; i < n; i++) {
      int v = sa[i];
      if (v >= 1 && !ls[v - 1]) {
        sa[buf[s[v - 1]]++] = v - 1;
      }
    }
    std::copy(sum_l.begin(), sum_l.end(), buf.begin());
    for (int i = n - 1; i >= 0; i--) {
      int v = sa[i];
      if (v >= 1 && ls[v - 1]) {
        sa[--buf[s[v - 1] + 1]] = v - 1;
      }
    }
  };
  std::vector<int> lms_map(n + 1, -1);
  int m = 0;
  for (int i = 1; i < n; i++) {
    if (!ls[i - 1] && ls[i]) {
      lms_map[i] = m++;
    }
  }
  std::vector<int> lms;
  lms.reserve(m);
  for (int i = 1; i < n; i++) {
    if (!ls[i - 1] && ls[i]) {
      lms.push_back(i);
    }
  }
  induce(lms);
  if (m) {
    std::vector<int> sorted_lms;
    sorted_lms.reserve(m);
    for (int v : sa) {
      if (lms_map[v] != -1)
        sorted_lms.push_back(v);
    }
    std::vector<int> rec_s(m);
    int rec_upper = 0;
    rec_s[lms_map[sorted_lms[0]]] = 0;
    for (int i = 1; i < m; i++) {
      int l = sorted_lms[i - 1], r = sorted_lms[i];
      int end_l = (lms_map[l] + 1 < m) ? lms[lms_map[l] + 1] : n;
      int end_r = (lms_map[r] + 1 < m) ? lms[lms_map[r] + 1] : n;
      bool same = true;
      if (end_l - l != end_r - r) {
        same = false;
      } else {
        while (l < end_l) {
          if (s[l] != s[r]) {
            break;
          }
          l++;
          r++;
        }
        if (l == n || s[l] != s[r])
          same = false;
      }
      if (!same)
        rec_upper++;
      rec_s[lms_map[sorted_lms[i]]] = rec_upper;
    }
    auto rec_sa = sa_is<THRESHOLD_NAIVE, THRESHOLD_DOUBLING>(rec_s, rec_upper);
    for (int i = 0; i < m; i++) {
      sorted_lms[i] = lms[rec_sa[i]];
    }
    induce(sorted_lms);
  }
  return sa;
}
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
int ceil_pow2(int n) {
  int x = 0;
  while ((1U << x) < (unsigned int)(n))
    x++;
  return x;
}
int bsf(unsigned int n) {
#ifdef _MSC_VER
  unsigned long index;
  _BitScanForward(&index, n);
  return index;
#else
  return __builtin_ctz(n);
#endif
}
constexpr long long safe_mod(long long x, long long m) {
  x %= m;
  if (x < 0)
    x += m;
  return x;
}
struct barrett {
  unsigned int _m;
  unsigned long long im;
  barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
  unsigned int umod() const { return _m; }
  unsigned int mul(unsigned int a, unsigned int b) const {
    unsigned long long z = a;
    z *= b;
#ifdef _MSC_VER
    unsigned long long x;
    _umul128(z, im, &x);
#else
    unsigned long long x =
        (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
    unsigned int v = (unsigned int)(z - x * _m);
    if (_m <= v)
      v += _m;
    return v;
  }
};
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
  if (m == 1)
    return 0;
  unsigned int _m = (unsigned int)(m);
  unsigned long long r = 1;
  unsigned long long y = safe_mod(x, m);
  while (n) {
    if (n & 1)
      r = (r * y) % _m;
    y = (y * y) % _m;
    n >>= 1;
  }
  return r;
}
constexpr bool is_prime_constexpr(int n) {
  if (n <= 1)
    return false;
  if (n == 2 || n == 7 || n == 61)
    return true;
  if (n % 2 == 0)
    return false;
  long long d = n - 1;
  while (d % 2 == 0)
    d /= 2;
  {
    long long a = 2;
    long long t = d;
    long long y = pow_mod_constexpr(a, t, n);
    while (t != n - 1 && y != 1 && y != n - 1) {
      y = y * y % n;
      t <<= 1;
    }
    if (y != n - 1 && t % 2 == 0) {
      return false;
    }
  }
  {
    long long a = 7;
    long long t = d;
    long long y = pow_mod_constexpr(a, t, n);
    while (t != n - 1 && y != 1 && y != n - 1) {
      y = y * y % n;
      t <<= 1;
    }
    if (y != n - 1 && t % 2 == 0) {
      return false;
    }
  }
  {
    long long a = 61;
    long long t = d;
    long long y = pow_mod_constexpr(a, t, n);
    while (t != n - 1 && y != 1 && y != n - 1) {
      y = y * y % n;
      t <<= 1;
    }
    if (y != n - 1 && t % 2 == 0) {
      return false;
    }
  }
  return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
  a = safe_mod(a, b);
  if (a == 0)
    return {b, 0};
  long long s = b, t = a;
  long long m0 = 0, m1 = 1;
  while (t) {
    long long u = s / t;
    s -= t * u;
    m0 -= m1 * u;
    auto tmp = s;
    s = t;
    t = tmp;
    tmp = m0;
    m0 = m1;
    m1 = tmp;
  }
  if (m0 < 0)
    m0 += b / s;
  return {s, m0};
}
constexpr int primitive_root_constexpr(int m) {
  if (m == 2)
    return 1;
  if (m == 167772161)
    return 3;
  if (m == 469762049)
    return 3;
  if (m == 754974721)
    return 11;
  if (m == 998244353)
    return 3;
  int divs[20] = {};
  divs[0] = 2;
  int cnt = 1;
  int x = (m - 1) / 2;
  while (x % 2 == 0)
    x /= 2;
  for (int i = 3; (long long)(i)*i <= x; i += 2) {
    if (x % i == 0) {
      divs[cnt++] = i;
      while (x % i == 0) {
        x /= i;
      }
    }
  }
  if (x > 1) {
    divs[cnt++] = x;
  }
  for (int g = 2;; g++) {
    bool ok = true;
    for (int i = 0; i < cnt; i++) {
      if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
        ok = false;
        break;
      }
    }
    if (ok)
      return g;
  }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
template <class T> struct simple_queue {
  std::vector<T> payload;
  int pos = 0;
  void reserve(int n) { payload.reserve(n); }
  int size() const { return int(payload.size()) - pos; }
  bool empty() const { return pos == int(payload.size()); }
  void push(const T &t) { payload.push_back(t); }
  T &front() { return payload[pos]; }
  void clear() {
    payload.clear();
    pos = 0;
  }
  void pop() { pos++; }
};
template <class E> struct csr {
  std::vector<int> start;
  std::vector<E> elist;
  csr(int n, const std::vector<std::pair<int, E>> &edges)
      : start(n + 1), elist(edges.size()) {
    for (auto e : edges) {
      start[e.first + 1]++;
    }
    for (int i = 1; i <= n; i++) {
      start[i] += start[i - 1];
    }
    auto counter = start;
    for (auto e : edges) {
      elist[counter[e.first]++] = e.second;
    }
  }
};
struct scc_graph {
public:
  scc_graph(int n) : _n(n) {}
  int num_vertices() { return _n; }
  void add_edge(int from, int to) { edges.push_back({from, {to}}); }
  std::pair<int, std::vector<int>> scc_ids() {
    auto g = csr<edge>(_n, edges);
    int now_ord = 0, group_num = 0;
    std::vector<int> visited, low(_n), ord(_n, -1), ids(_n);
    visited.reserve(_n);
    auto dfs = [&](auto self, int v) -> void {
      low[v] = ord[v] = now_ord++;
      visited.push_back(v);
      for (int i = g.start[v]; i < g.start[v + 1]; i++) {
        auto to = g.elist[i].to;
        if (ord[to] == -1) {
          self(self, to);
          low[v] = std::min(low[v], low[to]);
        } else {
          low[v] = std::min(low[v], ord[to]);
        }
      }
      if (low[v] == ord[v]) {
        while (true) {
          int u = visited.back();
          visited.pop_back();
          ord[u] = _n;
          ids[u] = group_num;
          if (u == v)
            break;
        }
        group_num++;
      }
    };
    for (int i = 0; i < _n; i++) {
      if (ord[i] == -1)
        dfs(dfs, i);
    }
    for (auto &x : ids) {
      x = group_num - 1 - x;
    }
    return {group_num, ids};
  }
  std::vector<std::vector<int>> scc() {
    auto ids = scc_ids();
    int group_num = ids.first;
    std::vector<int> counts(group_num);
    for (auto x : ids.second)
      counts[x]++;
    std::vector<std::vector<int>> groups(ids.first);
    for (int i = 0; i < group_num; i++) {
      groups[i].reserve(counts[i]);
    }
    for (int i = 0; i < _n; i++) {
      groups[ids.second[i]].push_back(i);
    }
    return groups;
  }

private:
  int _n;
  struct edge {
    int to;
  };
  std::vector<std::pair<int, edge>> edges;
};
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type, std::false_type>::type;
template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t,
                              unsigned __int128>;
template <class T>
using is_integral =
    typename std::conditional<std::is_integral<T>::value ||
                                  is_signed_int128<T>::value ||
                                  is_unsigned_int128<T>::value,
                              std::true_type, std::false_type>::type;
template <class T>
using is_signed_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_signed<T>::value) ||
                                  is_signed_int128<T>::value,
                              std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type, std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value, make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type, std::false_type>::type;
template <class T>
using to_unsigned =
    typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>,
                              std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)> * = nullptr>
struct static_modint : internal::static_modint_base {
  using mint = static_modint;

public:
  static constexpr int mod() { return m; }
  static mint raw(int v) {
    mint x;
    x._v = v;
    return x;
  }
  static_modint() : _v(0) {}
  template <class T, internal::is_signed_int_t<T> * = nullptr>
  static_modint(T v) {
    long long x = (long long)(v % (long long)(umod()));
    if (x < 0)
      x += umod();
    _v = (unsigned int)(x);
  }
  template <class T, internal::is_unsigned_int_t<T> * = nullptr>
  static_modint(T v) {
    _v = (unsigned int)(v % umod());
  }
  static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }
  unsigned int val() const { return _v; }
  mint &operator++() {
    _v++;
    if (_v == umod())
      _v = 0;
    return *this;
  }
  mint &operator--() {
    if (_v == 0)
      _v = umod();
    _v--;
    return *this;
  }
  mint operator++(int) {
    mint result = *this;
    ++*this;
    return result;
  }
  mint operator--(int) {
    mint result = *this;
    --*this;
    return result;
  }
  mint &operator+=(const mint &rhs) {
    _v += rhs._v;
    if (_v >= umod())
      _v -= umod();
    return *this;
  }
  mint &operator-=(const mint &rhs) {
    _v -= rhs._v;
    if (_v >= umod())
      _v += umod();
    return *this;
  }
  mint &operator*=(const mint &rhs) {
    unsigned long long z = _v;
    z *= rhs._v;
    _v = (unsigned int)(z % umod());
    return *this;
  }
  mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }
  mint operator+() const { return *this; }
  mint operator-() const { return mint() - *this; }
  mint pow(long long n) const {
    assert(0 <= n);
    mint x = *this, r = 1;
    while (n) {
      if (n & 1)
        r *= x;
      x *= x;
      n >>= 1;
    }
    return r;
  }
  mint inv() const {
    if (prime) {
      assert(_v);
      return pow(umod() - 2);
    } else {
      auto eg = internal::inv_gcd(_v, m);
      assert(eg.first == 1);
      return eg.second;
    }
  }
  friend mint operator+(const mint &lhs, const mint &rhs) {
    return mint(lhs) += rhs;
  }
  friend mint operator-(const mint &lhs, const mint &rhs) {
    return mint(lhs) -= rhs;
  }
  friend mint operator*(const mint &lhs, const mint &rhs) {
    return mint(lhs) *= rhs;
  }
  friend mint operator/(const mint &lhs, const mint &rhs) {
    return mint(lhs) /= rhs;
  }
  friend bool operator==(const mint &lhs, const mint &rhs) {
    return lhs._v == rhs._v;
  }
  friend bool operator!=(const mint &lhs, const mint &rhs) {
    return lhs._v != rhs._v;
  }

private:
  unsigned int _v;
  static constexpr unsigned int umod() { return m; }
  static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
  using mint = dynamic_modint;

public:
  static int mod() { return (int)(bt.umod()); }
  static void set_mod(int m) {
    assert(1 <= m);
    bt = internal::barrett(m);
  }
  static mint raw(int v) {
    mint x;
    x._v = v;
    return x;
  }
  dynamic_modint() : _v(0) {}
  template <class T, internal::is_signed_int_t<T> * = nullptr>
  dynamic_modint(T v) {
    long long x = (long long)(v % (long long)(mod()));
    if (x < 0)
      x += mod();
    _v = (unsigned int)(x);
  }
  template <class T, internal::is_unsigned_int_t<T> * = nullptr>
  dynamic_modint(T v) {
    _v = (unsigned int)(v % mod());
  }
  dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }
  unsigned int val() const { return _v; }
  mint &operator++() {
    _v++;
    if (_v == umod())
      _v = 0;
    return *this;
  }
  mint &operator--() {
    if (_v == 0)
      _v = umod();
    _v--;
    return *this;
  }
  mint operator++(int) {
    mint result = *this;
    ++*this;
    return result;
  }
  mint operator--(int) {
    mint result = *this;
    --*this;
    return result;
  }
  mint &operator+=(const mint &rhs) {
    _v += rhs._v;
    if (_v >= umod())
      _v -= umod();
    return *this;
  }
  mint &operator-=(const mint &rhs) {
    _v += mod() - rhs._v;
    if (_v >= umod())
      _v -= umod();
    return *this;
  }
  mint &operator*=(const mint &rhs) {
    _v = bt.mul(_v, rhs._v);
    return *this;
  }
  mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }
  mint operator+() const { return *this; }
  mint operator-() const { return mint() - *this; }
  mint pow(long long n) const {
    assert(0 <= n);
    mint x = *this, r = 1;
    while (n) {
      if (n & 1)
        r *= x;
      x *= x;
      n >>= 1;
    }
    return r;
  }
  mint inv() const {
    auto eg = internal::inv_gcd(_v, mod());
    assert(eg.first == 1);
    return eg.second;
  }
  friend mint operator+(const mint &lhs, const mint &rhs) {
    return mint(lhs) += rhs;
  }
  friend mint operator-(const mint &lhs, const mint &rhs) {
    return mint(lhs) -= rhs;
  }
  friend mint operator*(const mint &lhs, const mint &rhs) {
    return mint(lhs) *= rhs;
  }
  friend mint operator/(const mint &lhs, const mint &rhs) {
    return mint(lhs) /= rhs;
  }
  friend bool operator==(const mint &lhs, const mint &rhs) {
    return lhs._v == rhs._v;
  }
  friend bool operator!=(const mint &lhs, const mint &rhs) {
    return lhs._v != rhs._v;
  }

private:
  unsigned int _v;
  static internal::barrett bt;
  static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
}; // namespace internal
struct dsu {
public:
  dsu() : _n(0) {}
  dsu(int n) : _n(n), parent_or_size(n, -1) {}
  int merge(int a, int b) {
    assert(0 <= a && a < _n);
    assert(0 <= b && b < _n);
    int x = leader(a), y = leader(b);
    if (x == y)
      return x;
    if (-parent_or_size[x] < -parent_or_size[y])
      std::swap(x, y);
    parent_or_size[x] += parent_or_size[y];
    parent_or_size[y] = x;
    return x;
  }
  bool same(int a, int b) {
    assert(0 <= a && a < _n);
    assert(0 <= b && b < _n);
    return leader(a) == leader(b);
  }
  int leader(int a) {
    assert(0 <= a && a < _n);
    if (parent_or_size[a] < 0)
      return a;
    return parent_or_size[a] = leader(parent_or_size[a]);
  }
  int size(int a) {
    assert(0 <= a && a < _n);
    return -parent_or_size[leader(a)];
  }
  std::vector<std::vector<int>> groups() {
    std::vector<int> leader_buf(_n), group_size(_n);
    for (int i = 0; i < _n; i++) {
      leader_buf[i] = leader(i);
      group_size[leader_buf[i]]++;
    }
    std::vector<std::vector<int>> result(_n);
    for (int i = 0; i < _n; i++) {
      result[i].reserve(group_size[i]);
    }
    for (int i = 0; i < _n; i++) {
      result[leader_buf[i]].push_back(i);
    }
    result.erase(
        std::remove_if(result.begin(), result.end(),
                       [&](const std::vector<int> &v) { return v.empty(); }),
        result.end());
    return result;
  }

private:
  int _n;
  std::vector<int> parent_or_size;
};
template <class T> struct fenwick_tree {
  using U = internal::to_unsigned_t<T>;

public:
  fenwick_tree() : _n(0) {}
  fenwick_tree(int n) : _n(n), data(n) {}
  void add(int p, T x) {
    assert(0 <= p && p < _n);
    p++;
    while (p <= _n) {
      data[p - 1] += U(x);
      p += p & -p;
    }
  }
  T sum(int l, int r) {
    assert(0 <= l && l <= r && r <= _n);
    return sum(r) - sum(l);
  }

private:
  int _n;
  std::vector<U> data;
  U sum(int r) {
    U s = 0;
    while (r > 0) {
      s += data[r - 1];
      r -= r & -r;
    }
    return s;
  }
};
long long pow_mod(long long x, long long n, int m) {
  assert(0 <= n && 1 <= m);
  if (m == 1)
    return 0;
  internal::barrett bt((unsigned int)(m));
  unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m));
  while (n) {
    if (n & 1)
      r = bt.mul(r, y);
    y = bt.mul(y, y);
    n >>= 1;
  }
  return r;
}
long long inv_mod(long long x, long long m) {
  assert(1 <= m);
  auto z = internal::inv_gcd(x, m);
  assert(z.first == 1);
  return z.second;
}
std::pair<long long, long long> crt(const std::vector<long long> &r,
                                    const std::vector<long long> &m) {
  assert(r.size() == m.size());
  int n = int(r.size());
  long long r0 = 0, m0 = 1;
  for (int i = 0; i < n; i++) {
    assert(1 <= m[i]);
    long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i];
    if (m0 < m1) {
      std::swap(r0, r1);
      std::swap(m0, m1);
    }
    if (m0 % m1 == 0) {
      if (r0 % m1 != r1)
        return {0, 0};
      continue;
    }
    long long g, im;
    std::tie(g, im) = internal::inv_gcd(m0, m1);
    long long u1 = (m1 / g);
    if ((r1 - r0) % g)
      return {0, 0};
    long long x = (r1 - r0) / g % u1 * im % u1;
    r0 += x * m0;
    m0 *= u1;
    if (r0 < 0)
      r0 += m0;
  }
  return {r0, m0};
}
long long floor_sum(long long n, long long m, long long a, long long b) {
  long long ans = 0;
  if (a >= m) {
    ans += (n - 1) * n * (a / m) / 2;
    a %= m;
  }
  if (b >= m) {
    ans += n * (b / m);
    b %= m;
  }
  long long y_max = (a * n + b) / m, x_max = (y_max * m - b);
  if (y_max == 0)
    return ans;
  ans += (n - (x_max + a - 1) / a) * y_max;
  ans += floor_sum(y_max, a, m, (a - x_max % a) % a);
  return ans;
}
template <class Cap> struct mf_graph {
public:
  mf_graph() : _n(0) {}
  mf_graph(int n) : _n(n), g(n) {}
  int add_edge(int from, int to, Cap cap) {
    assert(0 <= from && from < _n);
    assert(0 <= to && to < _n);
    assert(0 <= cap);
    int m = int(pos.size());
    pos.push_back({from, int(g[from].size())});
    g[from].push_back(_edge{to, int(g[to].size()), cap});
    g[to].push_back(_edge{from, int(g[from].size()) - 1, 0});
    return m;
  }
  struct edge {
    int from, to;
    Cap cap, flow;
  };
  edge get_edge(int i) {
    int m = int(pos.size());
    assert(0 <= i && i < m);
    auto _e = g[pos[i].first][pos[i].second];
    auto _re = g[_e.to][_e.rev];
    return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap};
  }
  std::vector<edge> edges() {
    int m = int(pos.size());
    std::vector<edge> result;
    for (int i = 0; i < m; i++) {
      result.push_back(get_edge(i));
    }
    return result;
  }
  void change_edge(int i, Cap new_cap, Cap new_flow) {
    int m = int(pos.size());
    assert(0 <= i && i < m);
    assert(0 <= new_flow && new_flow <= new_cap);
    auto &_e = g[pos[i].first][pos[i].second];
    auto &_re = g[_e.to][_e.rev];
    _e.cap = new_cap - new_flow;
    _re.cap = new_flow;
  }
  Cap flow(int s, int t) { return flow(s, t, std::numeric_limits<Cap>::max()); }
  Cap flow(int s, int t, Cap flow_limit) {
    assert(0 <= s && s < _n);
    assert(0 <= t && t < _n);
    std::vector<int> level(_n), iter(_n);
    internal::simple_queue<int> que;
    auto bfs = [&]() {
      std::fill(level.begin(), level.end(), -1);
      level[s] = 0;
      que.clear();
      que.push(s);
      while (!que.empty()) {
        int v = que.front();
        que.pop();
        for (auto e : g[v]) {
          if (e.cap == 0 || level[e.to] >= 0)
            continue;
          level[e.to] = level[v] + 1;
          if (e.to == t)
            return;
          que.push(e.to);
        }
      }
    };
    auto dfs = [&](auto self, int v, Cap up) {
      if (v == s)
        return up;
      Cap res = 0;
      int level_v = level[v];
      for (int &i = iter[v]; i < int(g[v].size()); i++) {
        _edge &e = g[v][i];
        if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0)
          continue;
        Cap d = self(self, e.to, std::min(up - res, g[e.to][e.rev].cap));
        if (d <= 0)
          continue;
        g[v][i].cap += d;
        g[e.to][e.rev].cap -= d;
        res += d;
        if (res == up)
          break;
      }
      return res;
    };
    Cap flow = 0;
    while (flow < flow_limit) {
      bfs();
      if (level[t] == -1)
        break;
      std::fill(iter.begin(), iter.end(), 0);
      while (flow < flow_limit) {
        Cap f = dfs(dfs, t, flow_limit - flow);
        if (!f)
          break;
        flow += f;
      }
    }
    return flow;
  }
  std::vector<bool> min_cut(int s) {
    std::vector<bool> visited(_n);
    internal::simple_queue<int> que;
    que.push(s);
    while (!que.empty()) {
      int p = que.front();
      que.pop();
      visited[p] = true;
      for (auto e : g[p]) {
        if (e.cap && !visited[e.to]) {
          visited[e.to] = true;
          que.push(e.to);
        }
      }
    }
    return visited;
  }

private:
  int _n;
  struct _edge {
    int to, rev;
    Cap cap;
  };
  std::vector<std::pair<int, int>> pos;
  std::vector<std::vector<_edge>> g;
};
struct scc_graph {
public:
  scc_graph() : internal(0) {}
  scc_graph(int n) : internal(n) {}
  void add_edge(int from, int to) {
    int n = internal.num_vertices();
    assert(0 <= from && from < n);
    assert(0 <= to && to < n);
    internal.add_edge(from, to);
  }
  std::vector<std::vector<int>> scc() { return internal.scc(); }

private:
  internal::scc_graph internal;
};
template <class Cap, class Cost> struct mcf_graph {
public:
  mcf_graph() {}
  mcf_graph(int n) : _n(n), g(n) {}
  int add_edge(int from, int to, Cap cap, Cost cost) {
    assert(0 <= from && from < _n);
    assert(0 <= to && to < _n);
    int m = int(pos.size());
    pos.push_back({from, int(g[from].size())});
    g[from].push_back(_edge{to, int(g[to].size()), cap, cost});
    g[to].push_back(_edge{from, int(g[from].size()) - 1, 0, -cost});
    return m;
  }
  struct edge {
    int from, to;
    Cap cap, flow;
    Cost cost;
  };
  edge get_edge(int i) {
    int m = int(pos.size());
    assert(0 <= i && i < m);
    auto _e = g[pos[i].first][pos[i].second];
    auto _re = g[_e.to][_e.rev];
    return edge{
        pos[i].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost,
    };
  }
  std::vector<edge> edges() {
    int m = int(pos.size());
    std::vector<edge> result(m);
    for (int i = 0; i < m; i++) {
      result[i] = get_edge(i);
    }
    return result;
  }
  std::pair<Cap, Cost> flow(int s, int t) {
    return flow(s, t, std::numeric_limits<Cap>::max());
  }
  std::pair<Cap, Cost> flow(int s, int t, Cap flow_limit) {
    return slope(s, t, flow_limit).back();
  }
  std::vector<std::pair<Cap, Cost>> slope(int s, int t) {
    return slope(s, t, std::numeric_limits<Cap>::max());
  }
  std::vector<std::pair<Cap, Cost>> slope(int s, int t, Cap flow_limit) {
    assert(0 <= s && s < _n);
    assert(0 <= t && t < _n);
    assert(s != t);
    std::vector<Cost> dual(_n, 0), dist(_n);
    std::vector<int> pv(_n), pe(_n);
    std::vector<bool> vis(_n);
    auto dual_ref = [&]() {
      std::fill(dist.begin(), dist.end(), std::numeric_limits<Cost>::max());
      std::fill(pv.begin(), pv.end(), -1);
      std::fill(pe.begin(), pe.end(), -1);
      std::fill(vis.begin(), vis.end(), false);
      struct Q {
        Cost key;
        int to;
        bool operator<(Q r) const { return key > r.key; }
      };
      std::priority_queue<Q> que;
      dist[s] = 0;
      que.push(Q{0, s});
      while (!que.empty()) {
        int v = que.top().to;
        que.pop();
        if (vis[v])
          continue;
        vis[v] = true;
        if (v == t)
          break;
        for (int i = 0; i < int(g[v].size()); i++) {
          auto e = g[v][i];
          if (vis[e.to] || !e.cap)
            continue;
          Cost cost = e.cost - dual[e.to] + dual[v];
          if (dist[e.to] - dist[v] > cost) {
            dist[e.to] = dist[v] + cost;
            pv[e.to] = v;
            pe[e.to] = i;
            que.push(Q{dist[e.to], e.to});
          }
        }
      }
      if (!vis[t]) {
        return false;
      }
      for (int v = 0; v < _n; v++) {
        if (!vis[v])
          continue;
        dual[v] -= dist[t] - dist[v];
      }
      return true;
    };
    Cap flow = 0;
    Cost cost = 0, prev_cost = -1;
    std::vector<std::pair<Cap, Cost>> result;
    result.push_back({flow, cost});
    while (flow < flow_limit) {
      if (!dual_ref())
        break;
      Cap c = flow_limit - flow;
      for (int v = t; v != s; v = pv[v]) {
        c = std::min(c, g[pv[v]][pe[v]].cap);
      }
      for (int v = t; v != s; v = pv[v]) {
        auto &e = g[pv[v]][pe[v]];
        e.cap -= c;
        g[v][e.rev].cap += c;
      }
      Cost d = -dual[s];
      flow += c;
      cost += c * d;
      if (prev_cost == d) {
        result.pop_back();
      }
      result.push_back({flow, cost});
      prev_cost = cost;
    }
    return result;
  }

private:
  int _n;
  struct _edge {
    int to, rev;
    Cap cap;
    Cost cost;
  };
  std::vector<std::pair<int, int>> pos;
  std::vector<std::vector<_edge>> g;
};
template <class S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S),
          F (*composition)(F, F), F (*id)()>
struct lazy_segtree {
public:
  lazy_segtree() : lazy_segtree(0) {}
  lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
  lazy_segtree(const std::vector<S> &v) : _n(int(v.size())) {
    log = internal::ceil_pow2(_n);
    size = 1 << log;
    d = std::vector<S>(2 * size, e());
    lz = std::vector<F>(size, id());
    for (int i = 0; i < _n; i++)
      d[size + i] = v[i];
    for (int i = size - 1; i >= 1; i--) {
      update(i);
    }
  }
  void set(int p, S x) {
    assert(0 <= p && p < _n);
    p += size;
    for (int i = log; i >= 1; i--)
      push(p >> i);
    d[p] = x;
    for (int i = 1; i <= log; i++)
      update(p >> i);
  }
  S get(int p) {
    assert(0 <= p && p < _n);
    p += size;
    for (int i = log; i >= 1; i--)
      push(p >> i);
    return d[p];
  }
  S prod(int l, int r) {
    assert(0 <= l && l <= r && r <= _n);
    if (l == r)
      return e();
    l += size;
    r += size;
    for (int i = log; i >= 1; i--) {
      if (((l >> i) << i) != l)
        push(l >> i);
      if (((r >> i) << i) != r)
        push(r >> i);
    }
    S sml = e(), smr = e();
    while (l < r) {
      if (l & 1)
        sml = op(sml, d[l++]);
      if (r & 1)
        smr = op(d[--r], smr);
      l >>= 1;
      r >>= 1;
    }
    return op(sml, smr);
  }
  S all_prod() { return d[1]; }
  void apply(int p, F f) {
    assert(0 <= p && p < _n);
    p += size;
    for (int i = log; i >= 1; i--)
      push(p >> i);
    d[p] = mapping(f, d[p]);
    for (int i = 1; i <= log; i++)
      update(p >> i);
  }
  void apply(int l, int r, F f) {
    assert(0 <= l && l <= r && r <= _n);
    if (l == r)
      return;
    l += size;
    r += size;
    for (int i = log; i >= 1; i--) {
      if (((l >> i) << i) != l)
        push(l >> i);
      if (((r >> i) << i) != r)
        push((r - 1) >> i);
    }
    {
      int l2 = l, r2 = r;
      while (l < r) {
        if (l & 1)
          all_apply(l++, f);
        if (r & 1)
          all_apply(--r, f);
        l >>= 1;
        r >>= 1;
      }
      l = l2;
      r = r2;
    }
    for (int i = 1; i <= log; i++) {
      if (((l >> i) << i) != l)
        update(l >> i);
      if (((r >> i) << i) != r)
        update((r - 1) >> i);
    }
  }
  template <bool (*g)(S)> int max_right(int l) {
    return max_right(l, [](S x) { return g(x); });
  }
  template <class G> int max_right(int l, G g) {
    assert(0 <= l && l <= _n);
    assert(g(e()));
    if (l == _n)
      return _n;
    l += size;
    for (int i = log; i >= 1; i--)
      push(l >> i);
    S sm = e();
    do {
      while (l % 2 == 0)
        l >>= 1;
      if (!g(op(sm, d[l]))) {
        while (l < size) {
          push(l);
          l = (2 * l);
          if (g(op(sm, d[l]))) {
            sm = op(sm, d[l]);
            l++;
          }
        }
        return l - size;
      }
      sm = op(sm, d[l]);
      l++;
    } while ((l & -l) != l);
    return _n;
  }
  template <bool (*g)(S)> int min_left(int r) {
    return min_left(r, [](S x) { return g(x); });
  }
  template <class G> int min_left(int r, G g) {
    assert(0 <= r && r <= _n);
    assert(g(e()));
    if (r == 0)
      return 0;
    r += size;
    for (int i = log; i >= 1; i--)
      push((r - 1) >> i);
    S sm = e();
    do {
      r--;
      while (r > 1 && (r % 2))
        r >>= 1;
      if (!g(op(d[r], sm))) {
        while (r < size) {
          push(r);
          r = (2 * r + 1);
          if (g(op(d[r], sm))) {
            sm = op(d[r], sm);
            r--;
          }
        }
        return r + 1 - size;
      }
      sm = op(d[r], sm);
    } while ((r & -r) != r);
    return 0;
  }

private:
  int _n, size, log;
  std::vector<S> d;
  std::vector<F> lz;
  void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
  void all_apply(int k, F f) {
    d[k] = mapping(f, d[k]);
    if (k < size)
      lz[k] = composition(f, lz[k]);
  }
  void push(int k) {
    all_apply(2 * k, lz[k]);
    all_apply(2 * k + 1, lz[k]);
    lz[k] = id();
  }
};
template <class S, S (*op)(S, S), S (*e)()> struct segtree {
public:
  segtree() : segtree(0) {}
  segtree(int n) : segtree(std::vector<S>(n, e())) {}
  segtree(const std::vector<S> &v) : _n(int(v.size())) {
    log = internal::ceil_pow2(_n);
    size = 1 << log;
    d = std::vector<S>(2 * size, e());
    for (int i = 0; i < _n; i++)
      d[size + i] = v[i];
    for (int i = size - 1; i >= 1; i--) {
      update(i);
    }
  }
  void set(int p, S x) {
    assert(0 <= p && p < _n);
    p += size;
    d[p] = x;
    for (int i = 1; i <= log; i++)
      update(p >> i);
  }
  S get(int p) {
    assert(0 <= p && p < _n);
    return d[p + size];
  }
  S prod(int l, int r) {
    assert(0 <= l && l <= r && r <= _n);
    S sml = e(), smr = e();
    l += size;
    r += size;
    while (l < r) {
      if (l & 1)
        sml = op(sml, d[l++]);
      if (r & 1)
        smr = op(d[--r], smr);
      l >>= 1;
      r >>= 1;
    }
    return op(sml, smr);
  }
  S all_prod() { return d[1]; }
  template <bool (*f)(S)> int max_right(int l) {
    return max_right(l, [](S x) { return f(x); });
  }
  template <class F> int max_right(int l, F f) {
    assert(0 <= l && l <= _n);
    assert(f(e()));
    if (l == _n)
      return _n;
    l += size;
    S sm = e();
    do {
      while (l % 2 == 0)
        l >>= 1;
      if (!f(op(sm, d[l]))) {
        while (l < size) {
          l = (2 * l);
          if (f(op(sm, d[l]))) {
            sm = op(sm, d[l]);
            l++;
          }
        }
        return l - size;
      }
      sm = op(sm, d[l]);
      l++;
    } while ((l & -l) != l);
    return _n;
  }
  template <bool (*f)(S)> int min_left(int r) {
    return min_left(r, [](S x) { return f(x); });
  }
  template <class F> int min_left(int r, F f) {
    assert(0 <= r && r <= _n);
    assert(f(e()));
    if (r == 0)
      return 0;
    r += size;
    S sm = e();
    do {
      r--;
      while (r > 1 && (r % 2))
        r >>= 1;
      if (!f(op(d[r], sm))) {
        while (r < size) {
          r = (2 * r + 1);
          if (f(op(d[r], sm))) {
            sm = op(d[r], sm);
            r--;
          }
        }
        return r + 1 - size;
      }
      sm = op(d[r], sm);
    } while ((r & -r) != r);
    return 0;
  }

private:
  int _n, size, log;
  std::vector<S> d;
  void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};
struct two_sat {
public:
  two_sat() : _n(0), scc(0) {}
  two_sat(int n) : _n(n), _answer(n), scc(2 * n) {}
  void add_clause(int i, bool f, int j, bool g) {
    assert(0 <= i && i < _n);
    assert(0 <= j && j < _n);
    scc.add_edge(2 * i + (f ? 0 : 1), 2 * j + (g ? 1 : 0));
    scc.add_edge(2 * j + (g ? 0 : 1), 2 * i + (f ? 1 : 0));
  }
  bool satisfiable() {
    auto id = scc.scc_ids().second;
    for (int i = 0; i < _n; i++) {
      if (id[2 * i] == id[2 * i + 1])
        return false;
      _answer[i] = id[2 * i] < id[2 * i + 1];
    }
    return true;
  }
  std::vector<bool> answer() { return _answer; }

private:
  int _n;
  std::vector<bool> _answer;
  internal::scc_graph scc;
};
std::vector<int> suffix_array(const std::vector<int> &s, int upper) {
  assert(0 <= upper);
  for (int d : s) {
    assert(0 <= d && d <= upper);
  }
  auto sa = internal::sa_is(s, upper);
  return sa;
}
template <class T> std::vector<int> suffix_array(const std::vector<T> &s) {
  int n = int(s.size());
  std::vector<int> idx(n);
  iota(idx.begin(), idx.end(), 0);
  sort(idx.begin(), idx.end(), [&](int l, int r) { return s[l] < s[r]; });
  std::vector<int> s2(n);
  int now = 0;
  for (int i = 0; i < n; i++) {
    if (i && s[idx[i - 1]] != s[idx[i]])
      now++;
    s2[idx[i]] = now;
  }
  return internal::sa_is(s2, now);
}
std::vector<int> suffix_array(const std::string &s) {
  int n = int(s.size());
  std::vector<int> s2(n);
  for (int i = 0; i < n; i++) {
    s2[i] = s[i];
  }
  return internal::sa_is(s2, 255);
}
template <class T>
std::vector<int> lcp_array(const std::vector<T> &s,
                           const std::vector<int> &sa) {
  int n = int(s.size());
  assert(n >= 1);
  std::vector<int> rnk(n);
  for (int i = 0; i < n; i++) {
    rnk[sa[i]] = i;
  }
  std::vector<int> lcp(n - 1);
  int h = 0;
  for (int i = 0; i < n; i++) {
    if (h > 0)
      h--;
    if (rnk[i] == 0)
      continue;
    int j = sa[rnk[i] - 1];
    for (; j + h < n && i + h < n; h++) {
      if (s[j + h] != s[i + h])
        break;
    }
    lcp[rnk[i] - 1] = h;
  }
  return lcp;
}
std::vector<int> lcp_array(const std::string &s, const std::vector<int> &sa) {
  int n = int(s.size());
  std::vector<int> s2(n);
  for (int i = 0; i < n; i++) {
    s2[i] = s[i];
  }
  return lcp_array(s2, sa);
}
template <class T> std::vector<int> z_algorithm(const std::vector<T> &s) {
  int n = int(s.size());
  if (n == 0)
    return {};
  std::vector<int> z(n);
  z[0] = 0;
  for (int i = 1, j = 0; i < n; i++) {
    int &k = z[i];
    k = (j + z[j] <= i) ? 0 : std::min(j + z[j] - i, z[i - j]);
    while (i + k < n && s[k] == s[i + k])
      k++;
    if (j + z[j] < i + z[i])
      j = i;
  }
  z[0] = n;
  return z;
}
std::vector<int> z_algorithm(const std::string &s) {
  int n = int(s.size());
  std::vector<int> s2(n);
  for (int i = 0; i < n; i++) {
    s2[i] = s[i];
  }
  return z_algorithm(s2);
}
namespace internal {
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
void butterfly(std::vector<mint> &a) {
  static constexpr int g = internal::primitive_root<mint::mod()>;
  int n = int(a.size());
  int h = internal::ceil_pow2(n);
  static bool first = true;
  static mint sum_e[30];
  if (first) {
    first = false;
    mint es[30], ies[30];
    int cnt2 = bsf(mint::mod() - 1);
    mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
    for (int i = cnt2; i >= 2; i--) {
      es[i - 2] = e;
      ies[i - 2] = ie;
      e *= e;
      ie *= ie;
    }
    mint now = 1;
    for (int i = 0; i < cnt2 - 2; i++) {
      sum_e[i] = es[i] * now;
      now *= ies[i];
    }
  }
  for (int ph = 1; ph <= h; ph++) {
    int w = 1 << (ph - 1), p = 1 << (h - ph);
    mint now = 1;
    for (int s = 0; s < w; s++) {
      int offset = s << (h - ph + 1);
      for (int i = 0; i < p; i++) {
        auto l = a[i + offset];
        auto r = a[i + offset + p] * now;
        a[i + offset] = l + r;
        a[i + offset + p] = l - r;
      }
      now *= sum_e[bsf(~(unsigned int)(s))];
    }
  }
}
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
void butterfly_inv(std::vector<mint> &a) {
  static constexpr int g = internal::primitive_root<mint::mod()>;
  int n = int(a.size());
  int h = internal::ceil_pow2(n);
  static bool first = true;
  static mint sum_ie[30];
  if (first) {
    first = false;
    mint es[30], ies[30];
    int cnt2 = bsf(mint::mod() - 1);
    mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
    for (int i = cnt2; i >= 2; i--) {
      es[i - 2] = e;
      ies[i - 2] = ie;
      e *= e;
      ie *= ie;
    }
    mint now = 1;
    for (int i = 0; i < cnt2 - 2; i++) {
      sum_ie[i] = ies[i] * now;
      now *= es[i];
    }
  }
  for (int ph = h; ph >= 1; ph--) {
    int w = 1 << (ph - 1), p = 1 << (h - ph);
    mint inow = 1;
    for (int s = 0; s < w; s++) {
      int offset = s << (h - ph + 1);
      for (int i = 0; i < p; i++) {
        auto l = a[i + offset];
        auto r = a[i + offset + p];
        a[i + offset] = l + r;
        a[i + offset + p] =
            (unsigned long long)(mint::mod() + l.val() - r.val()) * inow.val();
      }
      inow *= sum_ie[bsf(~(unsigned int)(s))];
    }
  }
}
}; // namespace internal
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
  int n = int(a.size()), m = int(b.size());
  if (!n || !m)
    return {};
  if (std::min(n, m) <= 60) {
    if (n < m) {
      std::swap(n, m);
      std::swap(a, b);
    }
    std::vector<mint> ans(n + m - 1);
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        ans[i + j] += a[i] * b[j];
      }
    }
    return ans;
  }
  int z = 1 << internal::ceil_pow2(n + m - 1);
  a.resize(z);
  internal::butterfly(a);
  b.resize(z);
  internal::butterfly(b);
  for (int i = 0; i < z; i++) {
    a[i] *= b[i];
  }
  internal::butterfly_inv(a);
  a.resize(n + m - 1);
  mint iz = mint(z).inv();
  for (int i = 0; i < n + m - 1; i++)
    a[i] *= iz;
  return a;
}
template <unsigned int mod = 998244353, class T,
          std::enable_if_t<internal::is_integral<T>::value> * = nullptr>
std::vector<T> convolution(const std::vector<T> &a, const std::vector<T> &b) {
  int n = int(a.size()), m = int(b.size());
  if (!n || !m)
    return {};
  using mint = static_modint<mod>;
  std::vector<mint> a2(n), b2(m);
  for (int i = 0; i < n; i++) {
    a2[i] = mint(a[i]);
  }
  for (int i = 0; i < m; i++) {
    b2[i] = mint(b[i]);
  }
  auto c2 = convolution(move(a2), move(b2));
  std::vector<T> c(n + m - 1);
  for (int i = 0; i < n + m - 1; i++) {
    c[i] = c2[i].val();
  }
  return c;
}
std::vector<long long> convolution_ll(const std::vector<long long> &a,
                                      const std::vector<long long> &b) {
  int n = int(a.size()), m = int(b.size());
  if (!n || !m)
    return {};
  static constexpr unsigned long long MOD1 = 754974721;
  static constexpr unsigned long long MOD2 = 167772161;
  static constexpr unsigned long long MOD3 = 469762049;
  static constexpr unsigned long long M2M3 = MOD2 * MOD3;
  static constexpr unsigned long long M1M3 = MOD1 * MOD3;
  static constexpr unsigned long long M1M2 = MOD1 * MOD2;
  static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
  static constexpr unsigned long long i1 =
      internal::inv_gcd(MOD2 * MOD3, MOD1).second;
  static constexpr unsigned long long i2 =
      internal::inv_gcd(MOD1 * MOD3, MOD2).second;
  static constexpr unsigned long long i3 =
      internal::inv_gcd(MOD1 * MOD2, MOD3).second;
  auto c1 = convolution<MOD1>(a, b);
  auto c2 = convolution<MOD2>(a, b);
  auto c3 = convolution<MOD3>(a, b);
  std::vector<long long> c(n + m - 1);
  for (int i = 0; i < n + m - 1; i++) {
    unsigned long long x = 0;
    x += (c1[i] * i1) % MOD1 * M2M3;
    x += (c2[i] * i2) % MOD2 * M1M3;
    x += (c3[i] * i3) % MOD3 * M1M2;
    long long diff =
        c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
    if (diff < 0)
      diff += MOD1;
    static constexpr unsigned long long offset[5] = {0, 0, M1M2M3, 2 * M1M2M3,
                                                     3 * M1M2M3};
    x -= offset[diff % 5];
    c[i] = x;
  }
  return c;
}
} // namespace atcoder
#endif

/*
end of AtCoder STL
*/

#define int ll
using namespace std;
using namespace atcoder;
typedef string::const_iterator State;
#define eps 1e-8L
#define MAX_MOD 1000000007LL
#define GYAKU 500000004LL
#define MOD 998244353LL
#define pb push_back
#define mp make_pair
typedef long long ll;
typedef long double ld;
#define REP(a, b) for (long long(a) = 0; (a) < (b); ++(a))
#define ALL(x) (x).begin(), (x).end()
unsigned long xor128() {
  static unsigned long x = 123456789, y = 362436069, z = 521288629,
                       w = 88675123;
  unsigned long t = (x ^ (x << 11));
  x = y;
  y = z;
  z = w;
  return (w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)));
};
typedef complex<long double> Point;
typedef pair<complex<long double>, complex<long double>> Line;
typedef struct Circle {
  complex<long double> center;
  long double r;
} Circle;
long double dot(Point a, Point b) {
  return (a.real() * b.real() + a.imag() * b.imag());
}
long double cross(Point a, Point b) {
  return (a.real() * b.imag() - a.imag() * b.real());
}
long double Dist_Line_Point(Line a, Point b) {
  if (dot(a.second - a.first, b - a.first) < eps)
    return abs(b - a.first);
  if (dot(a.first - a.second, b - a.second) < eps)
    return abs(b - a.second);
  return abs(cross(a.second - a.first, b - a.first)) / abs(a.second - a.first);
}
int is_intersected_ls(Line a, Line b) {
  return (cross(a.second - a.first, b.first - a.first) *
              cross(a.second - a.first, b.second - a.first) <
          eps) &&
         (cross(b.second - b.first, a.first - b.first) *
              cross(b.second - b.first, a.second - b.first) <
          eps);
}
Point intersection_l(Line a, Line b) {
  Point da = a.second - a.first;
  Point db = b.second - b.first;
  return a.first + da * cross(db, b.first - a.first) / cross(db, da);
}
long double Dist_Line_Line(Line a, Line b) {
  if (is_intersected_ls(a, b) == 1) {
    return 0;
  }
  return min({Dist_Line_Point(a, b.first), Dist_Line_Point(a, b.second),
              Dist_Line_Point(b, a.first), Dist_Line_Point(b, a.second)});
}
pair<Point, Point> intersection_Circle_Circle(Circle a, Circle b) {
  long double dist = abs(a.center - b.center);
  assert(dist <= eps + a.r + b.r);
  assert(dist + eps >= abs(a.r - b.r));
  Point target = b.center - a.center;
  long double pointer =
      target.real() * target.real() + target.imag() * target.imag();
  long double aa = pointer + a.r * a.r - b.r * b.r;
  aa /= 2.0L;
  Point l{(aa * target.real() +
           target.imag() * sqrt(pointer * a.r * a.r - aa * aa)) /
              pointer,
          (aa * target.imag() -
           target.real() * sqrt(pointer * a.r * a.r - aa * aa)) /
              pointer};
  Point r{(aa * target.real() -
           target.imag() * sqrt(pointer * a.r * a.r - aa * aa)) /
              pointer,
          (aa * target.imag() +
           target.real() * sqrt(pointer * a.r * a.r - aa * aa)) /
              pointer};
  r = r + a.center;
  l = l + a.center;
  return mp(l, r);
}
ll gcd(ll a, ll b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}
template <typename A> A pows(A val, ll b) {
  assert(b >= 1);
  A ans = val;
  b--;
  while (b) {
    if (b % 2) {
      ans *= val;
    }
    val *= val;
    b /= 2LL;
  }
  return ans;
}
template <typename A> class Compressor {
public:
  bool is_zipped = false;
  map<A, ll> zipper;
  map<ll, A> unzipper;
  queue<A> fetcher;
  Compressor() {
    is_zipped = false;
    zipper.clear();
    unzipper.clear();
  }
  void add(A now) {
    assert(is_zipped == false);
    zipper[now] = 1;
    fetcher.push(now);
  }
  void exec() {
    assert(is_zipped == false);
    int cnt = 0;
    for (auto i = zipper.begin(); i != zipper.end(); ++i) {
      i->second = cnt;
      unzipper[cnt] = i->first;
      cnt++;
    }
    is_zipped = true;
  }
  ll fetch() {
    assert(is_zipped == true);
    A hoge = fetcher.front();
    fetcher.pop();
    return zipper[hoge];
  }
  ll zip(A now) {
    assert(is_zipped == true);
    assert(zipper.find(now) != zipper.end());
    return zipper[now];
  }
  A unzip(ll a) {
    assert(is_zipped == true);
    assert(a < unzipper.size());
    return unzipper[a];
  }
  ll next(A now) {
    auto x = zipper.upper_bound(now);
    if (x == zipper.end())
      return zipper.size();
    return (ll)((*x).second);
  }
  ll back(A now) {
    auto x = zipper.lower_bound(now);
    if (x == zipper.begin())
      return -1;
    x--;
    return (ll)((*x).second);
  }
};
template <typename A> class Matrix {
public:
  vector<vector<A>> data;
  Matrix(vector<vector<A>> a) : data(a) {}
  Matrix operator+(const Matrix obj) {
    vector<vector<A>> ans;
    assert(obj.data.size() == this->data.size());
    assert(obj.data[0].size() == this->data[0].size());
    REP(i, obj.data.size()) {
      ans.push_back(vector<A>());
      REP(q, obj.data[i].size()) {
        A hoge = obj.data[i][q] + (this->data[i][q]);
        ans.back().push_back(hoge);
      }
    }
    return Matrix(ans);
  }
  Matrix operator-(const Matrix obj) {
    vector<vector<A>> ans;
    assert(obj.data.size() == this->data.size());
    assert(obj.data[0].size() == this->data[0].size());
    REP(i, obj.data.size()) {
      ans.push_back(vector<A>());
      REP(q, obj.data[i].size()) {
        A hoge = this->data[i][q] - obj.data[i][q];
        ans.back().push_back(hoge);
      }
    }
    return Matrix(ans);
  }
  Matrix operator*(const Matrix obj) {
    vector<vector<A>> ans;
    assert(obj.data.size() == this->data[0].size());
    REP(i, this->data.size()) {
      ans.push_back(vector<A>());
      REP(q, obj.data[0].size()) {
        A hoge = ((this->data[i][0]) * (obj.data[0][q]));
        for (int t = 1; t < obj.data.size(); ++t) {
          hoge += ((this->data[i][t]) * obj.data[t][q]);
        }
        ans.back().push_back(hoge);
      }
    }
    return Matrix(ans);
  }
  Matrix &operator*=(const Matrix obj) {
    *this = (*this * obj);
    return *this;
  }
  Matrix &operator+=(const Matrix obj) {
    *this = (*this + obj);
    return *this;
  }
  Matrix &operator-=(const Matrix obj) {
    *this = (*this - obj);
    return *this;
  }
};
struct Fraction {
  ll a;
  ll b;
  Fraction() : a(0LL), b(1LL) {}
  Fraction(ll c, ll d) {
    int hoge = gcd(llabs(c), llabs(d));
    if (hoge != 0) {
      c /= hoge;
      d /= hoge;
      if (d < 0 or (d == 0 and c < 0)) {
        d *= -1;
        c *= -1;
      }
    }
    a = c;
    b = d;
  }
  bool operator<(Fraction rhs) const {
    if (a < 0 and rhs.a > 0)
      return 1;
    if (a > 0 and rhs.a < 0)
      return 0;
    return a * rhs.b < rhs.a * b;
  }
  bool operator==(Fraction rhs) const { return a == rhs.a and b == rhs.b; }
};
class Dice {
public:
  vector<ll> vertexs;
  Dice(vector<ll> init) : vertexs(init) {}
  void RtoL() {
    for (int q = 1; q < 4; ++q) {
      swap(vertexs[q], vertexs[q + 1]);
    }
  }
  void LtoR() {
    for (int q = 3; q >= 1; --q) {
      swap(vertexs[q], vertexs[q + 1]);
    }
  }
  void UtoD() {
    swap(vertexs[5], vertexs[4]);
    swap(vertexs[2], vertexs[5]);
    swap(vertexs[0], vertexs[2]);
  }
  void DtoU() {
    swap(vertexs[0], vertexs[2]);
    swap(vertexs[2], vertexs[5]);
    swap(vertexs[5], vertexs[4]);
  }
  bool ReachAble(Dice now) {
    set<Dice> hoge;
    queue<Dice> next;
    next.push(now);
    hoge.insert(now);
    while (next.empty() == false) {
      Dice seeing = next.front();
      next.pop();
      if (seeing == *this)
        return true;
      seeing.RtoL();
      if (hoge.count(seeing) == 0) {
        hoge.insert(seeing);
        next.push(seeing);
      }
      seeing.LtoR();
      seeing.LtoR();
      if (hoge.count(seeing) == 0) {
        hoge.insert(seeing);
        next.push(seeing);
      }
      seeing.RtoL();
      seeing.UtoD();
      if (hoge.count(seeing) == 0) {
        hoge.insert(seeing);
        next.push(seeing);
      }
      seeing.DtoU();
      seeing.DtoU();
      if (hoge.count(seeing) == 0) {
        hoge.insert(seeing);
        next.push(seeing);
      }
    }
    return false;
  }
  bool operator==(const Dice &a) {
    for (int q = 0; q < 6; ++q) {
      if (a.vertexs[q] != (*this).vertexs[q]) {
        return false;
      }
    }
    return true;
  }
  bool operator<(const Dice &a) const { return (*this).vertexs < a.vertexs; }
};
pair<Dice, Dice> TwoDimDice(int center, int up) {
  int target = 1;
  while (true) {
    if (center != target && 7 - center != target && up != target &&
        7 - up != target) {
      break;
    }
    target++;
  }
  return mp(
      Dice(vector<ll>{up, target, center, 7 - target, 7 - center, 7 - up}),
      Dice(vector<ll>{up, 7 - target, center, target, 7 - center, 7 - up}));
}
tuple<Dice, Dice, Dice, Dice> OneDimDice(int center) {
  int bo = min(center, 7 - center);
  pair<int, int> goa;
  if (bo == 1) {
    goa = mp(2, 3);
  } else if (bo == 2) {
    goa = mp(1, 3);
  } else if (bo == 3) {
    goa = mp(1, 2);
  }
  tuple<Dice, Dice, Dice, Dice> now =
      make_tuple(Dice(vector<ll>{goa.first, goa.second, center, 7 - goa.second,
                                 7 - center, 7 - goa.first}),
                 Dice(vector<ll>{goa.first, 7 - goa.second, center, goa.second,
                                 7 - center, 7 - goa.first}),
                 Dice(vector<ll>{7 - goa.first, goa.second, center,
                                 7 - goa.second, 7 - center, goa.first}),
                 Dice(vector<ll>{7 - goa.first, 7 - goa.second, center,
                                 goa.second, 7 - center, goa.first}));
  return now;
}
class HLDecomposition {
public:
  vector<vector<int>> vertexs;
  vector<int> depth;
  vector<int> backs;
  vector<int> connections;
  vector<int> zip, unzip;
  HLDecomposition(int n) {
    vertexs = vector<vector<int>>(n, vector<int>());
    depth = vector<int>(n);
    zip = vector<int>(n);
    unzip = zip;
  }
  void add_edge(int a, int b) {
    vertexs[a].push_back(b);
    vertexs[b].push_back(a);
  }
  int depth_dfs(int now, int back) {
    depth[now] = 0;
    for (auto x : vertexs[now]) {
      if (x == back)
        continue;
      depth[now] = max(depth[now], 1 + depth_dfs(x, now));
    }
    return depth[now];
  }
  void dfs(int now, int backing) {
    zip[now] = backs.size();
    unzip[backs.size()] = now;
    backs.push_back(backing);
    int now_max = -1;
    int itr = -1;
    for (auto x : vertexs[now]) {
      if (depth[x] > depth[now])
        continue;
      if (now_max < depth[x]) {
        now_max = depth[x];
        itr = x;
      }
    }
    if (itr == -1)
      return;
    connections.push_back(connections.back());
    dfs(itr, backing);
    for (auto x : vertexs[now]) {
      if (depth[x] > depth[now])
        continue;
      if (x == itr)
        continue;
      connections.push_back(zip[now]);
      dfs(x, backs.size());
    }
    return;
  }
  void build() {
    depth_dfs(0, -1);
    connections.push_back(-1);
    dfs(0, -1);
  }
  vector<pair<int, int>> query(int a, int b) {
    a = zip[a];
    b = zip[b];
    vector<pair<int, int>> ans;
    while (backs[a] != backs[b]) {
      if (a < b)
        swap(a, b);
      ans.push_back(mp(backs[a], a + 1));
      a = connections[a];
    }
    if (a > b)
      swap(a, b);
    ans.push_back(mp(a, b + 1));
    return ans;
  }
  int lca(int a, int b) {
    a = zip[a];
    b = zip[b];
    while (backs[a] != backs[b]) {
      if (a < b)
        swap(a, b);
      a = connections[a];
    }
    return unzip[min(a, b)];
  }
};
void init() {
  iostream::sync_with_stdio(false);
  cout << fixed << setprecision(20);
}
#undef int
int cnter[300000];
void solve() {
  int n;
  cin >> n;
  const int P = 200003;
  int now = 1;
  for (int q = 1; q < 300000; ++q) {
    now *= 2;
    now %= P;
    if (cnter[now] == 0) {
      cnter[now] = q;
    }
  }
  cnter[1] = 0;
  vector<ll> A(P, 0);
  REP(i, n) {
    int a;
    cin >> a;
    if (a == 0)
      continue;
    A[cnter[a]]++;
  }
  vector<ll> B = A;
  vector<ll> hoge = convolution_ll(A, B);
  REP(i, A.size()) { hoge[i * 2] -= A[i]; }
  ll ans = 0;
  now = 1;
  REP(i, hoge.size()) {
    ans += hoge[i] * now;
    now *= 2;
    now %= P;
  }
  cout << ans / 2LL << endl;
}
#undef int
int main() {
  init();
  int t = 1;
  REP(tea, t)
  solve();
}


Error: TLE

Fixed submission:

#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES

#pragma comment(linker, "/STACK:526000000")

#include "bits/stdc++.h"
#define int ll

using namespace std;
typedef string::const_iterator State;
#define eps 1e-8L
#define MAX_MOD 1000000007LL
#define GYAKU 500000004LL
#define MOD 998244353LL
#define pb push_back
#define mp make_pair
typedef long long ll;
typedef long double ld;
#define REP(a, b) for (long long(a) = 0; (a) < (b); ++(a))
#define ALL(x) (x).begin(), (x).end()
#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES

#pragma comment(linker, "/STACK:526000000")

#include "bits/stdc++.h"

#define int ll

using namespace std;
typedef long long ll;
typedef long double ld;
#define REP(a, b) for (long long(a) = 0; (a) < (b); ++(a))
#define ALL(x) (x).begin(), (x).end()

typedef complex<long double> Point;
typedef pair<complex<long double>, complex<long double>> Line;

typedef struct Circle {
  complex<long double> center;
  long double r;
} Circle;

long double dot(Point a, Point b) {
  return (a.real() * b.real() + a.imag() * b.imag());
}
long double cross(Point a, Point b) {
  return (a.real() * b.imag() - a.imag() * b.real());
}

long double Dist_Line_Point(Line a, Point b) {
  if (dot(a.second - a.first, b - a.first) < eps)
    return abs(b - a.first);
  if (dot(a.first - a.second, b - a.second) < eps)
    return abs(b - a.second);
  return abs(cross(a.second - a.first, b - a.first)) / abs(a.second - a.first);
}

int is_intersected_ls(Line a, Line b) {
  return (cross(a.second - a.first, b.first - a.first) *
              cross(a.second - a.first, b.second - a.first) <
          eps) &&
         (cross(b.second - b.first, a.first - b.first) *
              cross(b.second - b.first, a.second - b.first) <
          eps);
}

Point intersection_l(Line a, Line b) {
  Point da = a.second - a.first;
  Point db = b.second - b.first;
  return a.first + da * cross(db, b.first - a.first) / cross(db, da);
}

long double Dist_Line_Line(Line a, Line b) {
  if (is_intersected_ls(a, b) == 1) {
    return 0;
  }
  return min({Dist_Line_Point(a, b.first), Dist_Line_Point(a, b.second),
              Dist_Line_Point(b, a.first), Dist_Line_Point(b, a.second)});
}

pair<Point, Point> intersection_Circle_Circle(Circle a, Circle b) {
  long double dist = abs(a.center - b.center);
  assert(dist <= eps + a.r + b.r);
  assert(dist + eps >= abs(a.r - b.r));
  Point target = b.center - a.center;
  long double pointer =
      target.real() * target.real() + target.imag() * target.imag();
  long double aa = pointer + a.r * a.r - b.r * b.r;
  aa /= 2.0L;
  Point l{(aa * target.real() +
           target.imag() * sqrt(pointer * a.r * a.r - aa * aa)) /
              pointer,
          (aa * target.imag() -
           target.real() * sqrt(pointer * a.r * a.r - aa * aa)) /
              pointer};
  Point r{(aa * target.real() -
           target.imag() * sqrt(pointer * a.r * a.r - aa * aa)) /
              pointer,
          (aa * target.imag() +
           target.real() * sqrt(pointer * a.r * a.r - aa * aa)) /
              pointer};
  r = r + a.center;
  l = l + a.center;
  return mp(l, r);
}

// end of geometry

ll gcd(ll a, ll b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}

template <typename A> A pows(A val, ll b) {
  assert(b >= 1);
  A ans = val;
  b--;
  while (b) {
    if (b % 2) {
      ans *= val;
    }
    val *= val;
    b /= 2LL;
  }
  return ans;
}

template <typename A> class Compressor {
public:
  bool is_zipped = false;
  map<A, ll> zipper;
  map<ll, A> unzipper;
  queue<A> fetcher;
  Compressor() {
    is_zipped = false;
    zipper.clear();
    unzipper.clear();
  }
  void add(A now) {
    assert(is_zipped == false);
    zipper[now] = 1;
    fetcher.push(now);
  }
  void exec() {
    assert(is_zipped == false);
    int cnt = 0;
    for (auto i = zipper.begin(); i != zipper.end(); ++i) {
      i->second = cnt;
      unzipper[cnt] = i->first;
      cnt++;
    }
    is_zipped = true;
  }
  ll fetch() {
    assert(is_zipped == true);
    A hoge = fetcher.front();
    fetcher.pop();
    return zipper[hoge];
  }
  ll zip(A now) {
    assert(is_zipped == true);
    assert(zipper.find(now) != zipper.end());
    return zipper[now];
  }
  A unzip(ll a) {
    assert(is_zipped == true);
    assert(a < unzipper.size());
    return unzipper[a];
  }
  ll next(A now) {
    auto x = zipper.upper_bound(now);
    if (x == zipper.end())
      return zipper.size();
    return (ll)((*x).second);
  }
  ll back(A now) {
    auto x = zipper.lower_bound(now);
    if (x == zipper.begin())
      return -1;
    x--;
    return (ll)((*x).second);
  }
};

template <typename A> class Matrix {
public:
  vector<vector<A>> data;
  Matrix(vector<vector<A>> a) : data(a) {}
  Matrix operator+(const Matrix obj) {
    vector<vector<A>> ans;
    assert(obj.data.size() == this->data.size());
    assert(obj.data[0].size() == this->data[0].size());
    REP(i, obj.data.size()) {
      ans.push_back(vector<A>());
      REP(q, obj.data[i].size()) {
        A hoge = obj.data[i][q] + (this->data[i][q]);
        ans.back().push_back(hoge);
      }
    }
    return Matrix(ans);
  }
  Matrix operator-(const Matrix obj) {
    vector<vector<A>> ans;
    assert(obj.data.size() == this->data.size());
    assert(obj.data[0].size() == this->data[0].size());
    REP(i, obj.data.size()) {
      ans.push_back(vector<A>());
      REP(q, obj.data[i].size()) {
        A hoge = this->data[i][q] - obj.data[i][q];
        ans.back().push_back(hoge);
      }
    }
    return Matrix(ans);
  }
  Matrix operator*(const Matrix obj) {
    vector<vector<A>> ans;
    assert(obj.data.size() == this->data[0].size());
    REP(i, this->data.size()) {
      ans.push_back(vector<A>());
      REP(q, obj.data[0].size()) {
        A hoge = ((this->data[i][0]) * (obj.data[0][q]));
        for (int t = 1; t < obj.data.size(); ++t) {
          hoge += ((this->data[i][t]) * obj.data[t][q]);
        }
        ans.back().push_back(hoge);
      }
    }
    return Matrix(ans);
  }
  Matrix &operator*=(const Matrix obj) {
    *this = (*this * obj);
    return *this;
  }
  Matrix &operator+=(const Matrix obj) {
    *this = (*this + obj);
    return *this;
  }
  Matrix &operator-=(const Matrix obj) {
    *this = (*this - obj);
    return *this;
  }
};

struct Fraction {
  ll a;
  ll b;
  Fraction() : a(0LL), b(1LL) {}
  Fraction(ll c, ll d) {
    int hoge = gcd(llabs(c), llabs(d));
    if (hoge != 0) {
      c /= hoge;
      d /= hoge;
      if (d < 0 or (d == 0 and c < 0)) {
        d *= -1;
        c *= -1;
      }
    }
    a = c;
    b = d;
  }
  bool operator<(Fraction rhs) const {
    if (a < 0 and rhs.a > 0)
      return 1;
    if (a > 0 and rhs.a < 0)
      return 0;
    return a * rhs.b < rhs.a * b;
  }
  bool operator==(Fraction rhs) const { return a == rhs.a and b == rhs.b; }
};

template <std::uint_fast64_t mod> class modint {
public:
  using u64 = std::uint_fast64_t;
  u64 value = 0;
  modint() : value(0LL) {}
  modint(ll a) : value(a % mod) {}

  constexpr modint operator+(const modint rhs) const {
    return modint(*this) += rhs;
  }
  constexpr modint operator-(const modint rhs) const {
    return modint(*this) -= rhs;
  }
  constexpr modint operator*(const modint rhs) const {
    return modint(*this) *= rhs;
  }
  constexpr modint operator/(const modint rhs) const {
    return modint(*this) /= rhs;
  }
  constexpr modint &operator+=(const modint rhs) {
    value += rhs.value;
    if (value >= mod) {
      value -= mod;
    }
    return *this;
  }
  constexpr modint &operator-=(const modint rhs) {
    if (value < rhs.value) {
      value += mod;
    }
    value -= rhs.value;
    value += mod;
    value %= mod;
    return *this;
  }
  constexpr modint &operator*=(const modint rhs) {
    value = (value * rhs.value) % mod;
    return *this;
  }
  constexpr modint &operator/=(modint rhs) {
    ll rem = mod - 2;
    while (rem) {
      if (rem % 2) {
        *this *= rhs;
      }
      rhs *= rhs;
      rem /= 2LL;
    }
    return *this;
  }
  bool operator<(modint rhs) const { return value < rhs.value; }
  friend ostream &operator<<(ostream &os, modint &p) {
    os << p.value;
    return (os);
  }
};

class Dice {
public:
  vector<ll> vertexs;
  // Up: 0,Left: 1,Center: 2,Right: 3,Adj: 4, Down: 5
  Dice(vector<ll> init) : vertexs(init) {}
  // Look from Center
  void RtoL() {
    for (int q = 1; q < 4; ++q) {
      swap(vertexs[q], vertexs[q + 1]);
    }
  }
  void LtoR() {
    for (int q = 3; q >= 1; --q) {
      swap(vertexs[q], vertexs[q + 1]);
    }
  }
  void UtoD() {
    swap(vertexs[5], vertexs[4]);
    swap(vertexs[2], vertexs[5]);
    swap(vertexs[0], vertexs[2]);
  }
  void DtoU() {
    swap(vertexs[0], vertexs[2]);
    swap(vertexs[2], vertexs[5]);
    swap(vertexs[5], vertexs[4]);
  }
  bool ReachAble(Dice now) {
    set<Dice> hoge;
    queue<Dice> next;
    next.push(now);
    hoge.insert(now);
    while (next.empty() == false) {
      Dice seeing = next.front();
      next.pop();
      if (seeing == *this)
        return true;
      seeing.RtoL();
      if (hoge.count(seeing) == 0) {
        hoge.insert(seeing);
        next.push(seeing);
      }
      seeing.LtoR();
      seeing.LtoR();
      if (hoge.count(seeing) == 0) {
        hoge.insert(seeing);
        next.push(seeing);
      }
      seeing.RtoL();
      seeing.UtoD();
      if (hoge.count(seeing) == 0) {
        hoge.insert(seeing);
        next.push(seeing);
      }
      seeing.DtoU();
      seeing.DtoU();
      if (hoge.count(seeing) == 0) {
        hoge.insert(seeing);
        next.push(seeing);
      }
    }
    return false;
  }
  bool operator==(const Dice &a) {
    for (int q = 0; q < 6; ++q) {
      if (a.vertexs[q] != (*this).vertexs[q]) {
        return false;
      }
    }
    return true;
  }
  bool operator<(const Dice &a) const { return (*this).vertexs < a.vertexs; }
};

pair<Dice, Dice> TwoDimDice(int center, int up) {
  int target = 1;
  while (true) {
    if (center != target && 7 - center != target && up != target &&
        7 - up != target) {
      break;
    }
    target++;
  }
  return mp(
      Dice(vector<ll>{up, target, center, 7 - target, 7 - center, 7 - up}),
      Dice(vector<ll>{up, 7 - target, center, target, 7 - center, 7 - up}));
}

tuple<Dice, Dice, Dice, Dice> OneDimDice(int center) {
  int bo = min(center, 7 - center);
  pair<int, int> goa;
  if (bo == 1) {
    goa = mp(2, 3);
  } else if (bo == 2) {
    goa = mp(1, 3);
  } else if (bo == 3) {
    goa = mp(1, 2);
  }
  tuple<Dice, Dice, Dice, Dice> now =
      make_tuple(Dice(vector<ll>{goa.first, goa.second, center, 7 - goa.second,
                                 7 - center, 7 - goa.first}),
                 Dice(vector<ll>{goa.first, 7 - goa.second, center, goa.second,
                                 7 - center, 7 - goa.first}),
                 Dice(vector<ll>{7 - goa.first, goa.second, center,
                                 7 - goa.second, 7 - center, goa.first}),
                 Dice(vector<ll>{7 - goa.first, 7 - goa.second, center,
                                 goa.second, 7 - center, goa.first}));
  return now;
}

template <typename A, typename B> class Dijkstra {
public:
  vector<vector<pair<int, A>>> vertexs;
  B Cost_Function;
  Dijkstra(int n, B cost) : Cost_Function(cost) {
    vertexs = vector<vector<pair<int, A>>>(n, vector<pair<int, A>>{});
  }
  ~Dijkstra() { vertexs.clear(); }
  void add_edge(int a, int b, A c) { vertexs[a].push_back(mp(b, c)); }
  vector<ll> build_result(int StartPoint) {
    vector<ll> dist(vertexs.size(), 2e18);
    dist[StartPoint] = 0;
    priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>>
        next;
    next.push(make_pair(0, StartPoint));
    while (next.empty() == false) {
      pair<ll, int> now = next.top();
      next.pop();
      if (dist[now.second] != now.first)
        continue;
      for (auto x : vertexs[now.second]) {
        ll now_cost = now.first + Cost_Function(x.second);
        if (dist[x.first] > now_cost) {
          dist[x.first] = now_cost;
          next.push(mp(now_cost, x.first));
        }
      }
    }
    return dist;
  }
};

class Dinic {
public:
  struct edge {
    int to;
    int cap;
    int rev;
  };
  vector<vector<edge>> Graph;
  vector<int> level;
  vector<int> itr;
  Dinic(int n) { Graph = vector<vector<edge>>(n, vector<edge>()); }
  void add_edge(int a, int b, int cap) {
    Graph[a].push_back(edge{b, cap, (int)Graph[b].size()});
    Graph[b].push_back(edge{a, 0, (int)Graph[a].size() - 1});
  }
  void bfs(int s) {
    level = vector<int>(Graph.size(), -1);
    level[s] = 0;
    queue<int> next;
    next.push(s);
    while (next.empty() == false) {
      int now = next.front();
      next.pop();
      for (auto x : Graph[now]) {
        if (x.cap == 0)
          continue;
        if (level[x.to] == -1) {
          level[x.to] = level[now] + 1;
          next.push(x.to);
        }
      }
    }
  }
  int dfs(int now, int goal, int val) {
    if (goal == now)
      return val;
    for (int &i = itr[now]; i < (int)Graph[now].size(); ++i) {
      edge &target = Graph[now][i];
      if (target.cap > 0 && level[now] < level[target.to]) {
        int d = dfs(target.to, goal, min(val, target.cap));
        if (d > 0) {
          target.cap -= d;
          Graph[target.to][target.rev].cap += d;
          return d;
        }
      }
    }
    return 0;
  }
  int run(int s, int t) {
    int ans = 0;
    int f = 0;
    while (bfs(s), level[t] >= 0) {
      itr = vector<int>(Graph.size(), 0);
      while ((f = dfs(s, t, 1e9)) > 0) {
        ans += f;
      }
    }
    return ans;
  }
};

class HLDecomposition {
public:
  vector<vector<int>> vertexs;
  vector<int> depth;
  vector<int> backs;
  vector<int> connections;
  vector<int> zip, unzip;
  HLDecomposition(int n) {
    vertexs = vector<vector<int>>(n, vector<int>());
    depth = vector<int>(n);
    zip = vector<int>(n);
    unzip = zip;
  }
  void add_edge(int a, int b) {
    vertexs[a].push_back(b);
    vertexs[b].push_back(a);
  }
  int depth_dfs(int now, int back) {
    depth[now] = 0;
    for (auto x : vertexs[now]) {
      if (x == back)
        continue;
      depth[now] = max(depth[now], 1 + depth_dfs(x, now));
    }
    return depth[now];
  }
  void dfs(int now, int backing) {
    zip[now] = backs.size();
    unzip[backs.size()] = now;
    backs.push_back(backing);
    int now_max = -1;
    int itr = -1;
    for (auto x : vertexs[now]) {
      if (depth[x] > depth[now])
        continue;
      if (now_max < depth[x]) {
        now_max = depth[x];
        itr = x;
      }
    }
    if (itr == -1)
      return;
    connections.push_back(connections.back());
    dfs(itr, backing);
    for (auto x : vertexs[now]) {
      if (depth[x] > depth[now])
        continue;
      if (x == itr)
        continue;
      connections.push_back(zip[now]);
      dfs(x, backs.size());
    }
    return;
  }
  void build() {
    depth_dfs(0, -1);
    connections.push_back(-1);
    dfs(0, -1);
  }
  vector<pair<int, int>> query(int a, int b) {
    a = zip[a];
    b = zip[b];
    vector<pair<int, int>> ans;
    while (backs[a] != backs[b]) {
      if (a < b)
        swap(a, b);
      ans.push_back(mp(backs[a], a + 1));
      a = connections[a];
    }
    if (a > b)
      swap(a, b);
    ans.push_back(mp(a, b + 1));
    return ans;
  }
  int lca(int a, int b) {
    a = zip[a];
    b = zip[b];
    while (backs[a] != backs[b]) {
      if (a < b)
        swap(a, b);
      a = connections[a];
    }
    return unzip[min(a, b)];
  }
};
// by ei1333
// https://ei1333.github.io/luzhiled/snippets/structure/segment-tree.html
template <typename Monoid> struct SegmentTree {
  using F = function<Monoid(Monoid, Monoid)>;

  int sz;
  vector<Monoid> seg;

  const F f;
  const Monoid M1;

  SegmentTree(int n, const F f, const Monoid &M1) : f(f), M1(M1) {
    sz = 1;
    while (sz < n)
      sz <<= 1;
    seg.assign(2 * sz + 1, M1);
  }

  void set(int k, const Monoid &x) { seg[k + sz] = x; }

  void build() {
    for (int k = sz - 1; k > 0; k--) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }

  void update(int k, const Monoid &x) {
    k += sz;
    seg[k] = x;
    while (k >>= 1) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }

  Monoid query(int a, int b) {
    Monoid L = M1, R = M1;
    for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if (a & 1)
        L = f(L, seg[a++]);
      if (b & 1)
        R = f(seg[--b], R);
    }
    return f(L, R);
  }

  Monoid operator[](const int &k) const { return seg[k + sz]; }

  template <typename C>
  int find_subtree(int a, const C &check, Monoid &M, bool type) {
    while (a < sz) {
      Monoid nxt = type ? f(seg[2 * a + type], M) : f(M, seg[2 * a + type]);
      if (check(nxt))
        a = 2 * a + type;
      else
        M = nxt, a = 2 * a + 1 - type;
    }
    return a - sz;
  }

  template <typename C> int find_first(int a, const C &check) {
    Monoid L = M1;
    if (a <= 0) {
      if (check(f(L, seg[1])))
        return find_subtree(1, check, L, false);
      return -1;
    }
    int b = sz;
    for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if (a & 1) {
        Monoid nxt = f(L, seg[a]);
        if (check(nxt))
          return find_subtree(a, check, L, false);
        L = nxt;
        ++a;
      }
    }
    return -1;
  }

  template <typename C> int find_last(int b, const C &check) {
    Monoid R = M1;
    if (b >= sz) {
      if (check(f(seg[1], R)))
        return find_subtree(1, check, R, true);
      return -1;
    }
    int a = sz;
    for (b += sz; a < b; a >>= 1, b >>= 1) {
      if (b & 1) {
        Monoid nxt = f(seg[--b], R);
        if (check(nxt))
          return find_subtree(b, check, R, true);
        R = nxt;
      }
    }
    return -1;
  }
};

template <typename Monoid, typename OperatorMonoid = Monoid>
struct LazySegmentTree {
  using F = function<Monoid(Monoid, Monoid)>;
  using G = function<Monoid(Monoid, OperatorMonoid)>;
  using H = function<OperatorMonoid(OperatorMonoid, OperatorMonoid)>;

  int sz, height;
  vector<Monoid> data;
  vector<OperatorMonoid> lazy;
  const F f;
  const G g;
  const H h;
  const Monoid M1;
  const OperatorMonoid OM0;

  LazySegmentTree(int n, const F f, const G g, const H h, const Monoid &M1,
                  const OperatorMonoid OM0)
      : f(f), g(g), h(h), M1(M1), OM0(OM0) {
    sz = 1;
    height = 0;
    while (sz < n)
      sz <<= 1, height++;
    data.assign(2 * sz, M1);
    lazy.assign(2 * sz, OM0);
  }

  void set(int k, const Monoid &x) { data[k + sz] = x; }

  void build() {
    for (int k = sz - 1; k > 0; k--) {
      data[k] = f(data[2 * k + 0], data[2 * k + 1]);
    }
  }

  inline void propagate(int k) {
    if (lazy[k] != OM0) {
      lazy[2 * k + 0] = h(lazy[2 * k + 0], lazy[k]);
      lazy[2 * k + 1] = h(lazy[2 * k + 1], lazy[k]);
      data[k] = reflect(k);
      lazy[k] = OM0;
    }
  }

  inline Monoid reflect(int k) {
    return lazy[k] == OM0 ? data[k] : g(data[k], lazy[k]);
  }

  inline void recalc(int k) {
    while (k >>= 1)
      data[k] = f(reflect(2 * k + 0), reflect(2 * k + 1));
  }

  inline void thrust(int k) {
    for (int i = height; i > 0; i--)
      propagate(k >> i);
  }

  void update(int a, int b, const OperatorMonoid &x) {
    thrust(a += sz);
    thrust(b += sz - 1);
    for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
      if (l & 1)
        lazy[l] = h(lazy[l], x), ++l;
      if (r & 1)
        --r, lazy[r] = h(lazy[r], x);
    }
    recalc(a);
    recalc(b);
  }

  Monoid query(int a, int b) {
    thrust(a += sz);
    thrust(b += sz - 1);
    Monoid L = M1, R = M1;
    for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
      if (l & 1)
        L = f(L, reflect(l++));
      if (r & 1)
        R = f(reflect(--r), R);
    }
    return f(L, R);
  }

  Monoid operator[](const int &k) { return query(k, k + 1); }

  template <typename C>
  int find_subtree(int a, const C &check, Monoid &M, bool type) {
    while (a < sz) {
      propagate(a);
      Monoid nxt =
          type ? f(reflect(2 * a + type), M) : f(M, reflect(2 * a + type));
      if (check(nxt))
        a = 2 * a + type;
      else
        M = nxt, a = 2 * a + 1 - type;
    }
    return a - sz;
  }

  template <typename C> int find_first(int a, const C &check) {
    Monoid L = M1;
    if (a <= 0) {
      if (check(f(L, reflect(1))))
        return find_subtree(1, check, L, false);
      return -1;
    }
    thrust(a + sz);
    int b = sz;
    for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if (a & 1) {
        Monoid nxt = f(L, reflect(a));
        if (check(nxt))
          return find_subtree(a, check, L, false);
        L = nxt;
        ++a;
      }
    }
    return -1;
  }

  template <typename C> int find_last(int b, const C &check) {
    Monoid R = M1;
    if (b >= sz) {
      if (check(f(reflect(1), R)))
        return find_subtree(1, check, R, true);
      return -1;
    }
    thrust(b + sz - 1);
    int a = sz;
    for (b += sz; a < b; a >>= 1, b >>= 1) {
      if (b & 1) {
        Monoid nxt = f(reflect(--b), R);
        if (check(nxt))
          return find_subtree(b, check, R, true);
        R = nxt;
      }
    }
    return -1;
  }
};

class KMP {
public:
  vector<ll> table;
  vector<ll> Pattern;
  KMP(vector<ll> a) { build(a); }
  void build(vector<ll> a) {
    Pattern = a;
    table = vector<ll>(a.size() + 1, -1);
    int j = -1;
    for (int i = 0; i < a.size(); ++i) {
      while (j >= 0 && Pattern[i] != Pattern[j]) {
        j = table[j];
      }
      table[i + 1] = ++j;
    }
    return;
  }
  vector<ll> search(vector<ll> a) {
    vector<ll> ans;
    for (int i = 0, k = 0; i < a.size(); ++i) {
      while (k >= 0 && a[i] != Pattern[k])
        k = table[k];
      ++k;
      if (k >= Pattern.size()) {
        ans.push_back(i - Pattern.size() + 1);
        k = table[k];
      }
    }
    return ans;
  }
};

unsigned long xor128() {
  static unsigned long x = 123456789, y = 362436069, z = 521288629,
                       w = 88675123;
  unsigned long t = (x ^ (x << 11));
  x = y;
  y = z;
  z = w;
  return (w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)));
}

void init() {
  iostream::sync_with_stdio(false);
  cout << fixed << setprecision(20);
}

#define int ll

template <typename flow_t, typename cost_t> struct PrimalDual {
  const cost_t INF;

  struct edge {
    int to;
    flow_t cap;
    cost_t cost;
    int rev;
    bool isrev;
  };
  vector<vector<edge>> graph;
  vector<cost_t> potential, min_cost;
  vector<int> prevv, preve;

  PrimalDual(int V) : graph(V), INF(numeric_limits<cost_t>::max()) {}

  void add_edge(int from, int to, flow_t cap, cost_t cost) {
    graph[from].emplace_back(edge{to, cap, cost, (int)graph[to].size(), false});
    graph[to].emplace_back(
        edge{from, 0, -cost, (int)graph[from].size() - 1, true});
  }

  cost_t min_cost_flow(int s, int t, flow_t f) {
    int V = (int)graph.size();
    cost_t ret = 0;
    using Pi = pair<cost_t, int>;
    priority_queue<Pi, vector<Pi>, greater<Pi>> que;
    potential.assign(V, 0);
    preve.assign(V, -1);
    prevv.assign(V, -1);

    while (f > 0) {
      min_cost.assign(V, INF);
      que.emplace(0, s);
      min_cost[s] = 0;
      while (!que.empty()) {
        Pi p = que.top();
        que.pop();
        if (min_cost[p.second] < p.first)
          continue;
        for (int i = 0; i < graph[p.second].size(); i++) {
          edge &e = graph[p.second][i];
          cost_t nextCost = min_cost[p.second] + e.cost + potential[p.second] -
                            potential[e.to];
          if (e.cap > 0 && min_cost[e.to] > nextCost) {
            min_cost[e.to] = nextCost;
            prevv[e.to] = p.second, preve[e.to] = i;
            que.emplace(min_cost[e.to], e.to);
          }
        }
      }
      if (min_cost[t] == INF)
        return -1;
      for (int v = 0; v < V; v++)
        potential[v] += min_cost[v];
      flow_t addflow = f;
      for (int v = t; v != s; v = prevv[v]) {
        addflow = min(addflow, graph[prevv[v]][preve[v]].cap);
      }
      f -= addflow;
      ret += addflow * potential[t];
      for (int v = t; v != s; v = prevv[v]) {
        edge &e = graph[prevv[v]][preve[v]];
        e.cap -= addflow;
        graph[v][e.rev].cap += addflow;
      }
    }
    return ret;
  }

  void output() {
    for (int i = 0; i < graph.size(); i++) {
      for (auto &e : graph[i]) {
        if (e.isrev)
          continue;
        auto &rev_e = graph[e.to][e.rev];
        cout << i << "->" << e.to << " (flow: " << rev_e.cap << "/"
             << rev_e.cap + e.cap << ")" << endl;
      }
    }
  }
};
int modpow(int a, int b, int p) {
  int ans = 1;
  while (b != 0) {
    if (b % 2) {
      ans *= a;
      ans %= p;
    }
    a *= a;
    a %= p;
    b /= 2;
  }
  return ans;
}
int state = 0;
std::pair<ll, ll> baby[100010];
ll modlog(ll x, ll y, const ll p) {
  ll H = sqrt(p) + 1;
  for (ll b = 0, xby = y; b < H; b++, xby = (xby * x) % p) {
    baby[b] = std::make_pair(xby, b);
  }
  std::sort(baby, baby + H);
  state = 1;
  ll xH = 1;
  for (int i = 0; i < H; ++i) {
    xH = (xH * x) % p;
  }
  for (ll a = 1, xaH = xH; a <= H; a++, xaH = (xaH * xH) % p) {
    auto it = std::lower_bound(baby, baby + H, std::make_pair(xaH + 1, 0LL));
    if (it == baby)
      continue;
    it--;
    if (it->first == xaH)
      return a * H - it->second;
  }
  return -1;
}

int cnter[600000];
int sums[600000];
int findings[600000];

void solve() {
  int n;
  cin >> n;
  REP(i, n) {
    int a;
    cin >> a;
    if (a != 0) {
      cnter[a]++;
      sums[a]++;
      findings[a] += a;
    }
  }
  REP(i, 500000) {
    sums[i + 1] += sums[i];
    findings[i + 1] += findings[i];
  }
  int ans = 0;
  const int p = 200003;
  int geko = p;
  for (int i = 1; i <= geko; ++i) {
    if (cnter[i] == 0)
      continue;
    int l = 1;
    while (l <= geko) {
      int r = ((p - (l * i) % p) - 1) / i + l;
      int kazu = sums[r] - sums[l - 1];
      int value = findings[r] - findings[l - 1];
      if (l <= i and i <= r) {
        kazu -= cnter[i];
        value -= cnter[i] * i;
      }
      ans += (value * i - ((l * i) / p) * p * kazu) * cnter[i];
      l = r + 1;
    }
    ans += ((i * i) % p) * cnter[i] * (cnter[i] - 1LL);
  }
  cout << ans / 2LL << endl;
}
#undef int
int main() {
  init();
  solve();
}