Submission #25160111

---

Source Code Expand

#include <bits/stdc++.h>
#include <cassert>
typedef long long int ll;
using namespace std;

// @@ !! LIM(perm mod debug f:updMaxMin coordCompr cmpNaive)

// ---- inserted library file perm.cc

template<typename T>
class IterPerm {
  int cand_size;
  int seq_size;
  T perm;
  vector<T> cands;
  vector<int> idx;
  
  void construct(const T& orig, int ss) {
    cand_size = orig.size();
    seq_size = ss;
    perm = T(orig.begin(), orig.begin() + seq_size);
    cands = vector<T>(seq_size);
    if (seq_size > 0) cands.at(0) = orig;
    idx = vector<int>(seq_size);
    init();
  }

  void init() {
    for (int i = 0; i < seq_size; i++) {
      perm.at(i) = cands.at(0).at(i);
      if (i > 0) {
	cands.at(i) = T(cands.at(0).begin() + i, cands.at(0).end());
      }
      idx.at(i) = 0;
    }
  }

  // IntPerm is implemented using IterPerm<vector<int>>, and
  // it needs a constructor without parameter.
  friend class IntPerm;
  IterPerm() {}

public:
  
  IterPerm(const T& orig, int ss) { construct(orig, ss); }
  IterPerm(const T& orig) { construct(orig, orig.size()); }
  
  const T& get() { return perm; }

  bool next() {
    int i = seq_size - 1;
    while (i >= 0 && ++idx.at(i) >= cand_size - i) i--;
    if (i < 0) {
      init();
      return false;
    }
    perm.at(i) = cands.at(i).at(idx.at(i));
    for (int k = i + 1; k < seq_size; k++) {
      for (int m = 0; m < cand_size - k; m++) {
	int shift = m < idx.at(k - 1) ? 0 : 1;
	cands.at(k).at(m) = cands.at(k - 1).at(m + shift);
      }
      idx.at(k) = 0;
      perm.at(k) = cands.at(k).at(0);
    }
    return true;
  }
};

class IntPerm {

  IterPerm<vector<int>> itp;

  void construct(int ns, int ss) {
    vector<int> vec(ns);
    iota(vec.begin(), vec.end(), 0);
    itp = IterPerm(vec, ss);
  }

public:

  IntPerm(int ns, int ss) { construct(ns, ss); }
  IntPerm(int ns) { construct(ns, ns); }
  const vector<int>& get() { return itp.get(); }
  bool next() { return itp.next(); }

};

template<typename T>
class IterComb {

  vector<T> orig;
  int c_size;
  vector<T> comb;
  vector<int> idx;

  void init() {
    for (int i = 0; i < c_size; i++) {
      idx.at(i) = i;
      comb.at(i) = orig.at(i);
    }
  }


public:

  IterComb() {}

  IterComb(vector<T> orig_, int c_size_)
    : orig(orig_), c_size(c_size_), comb(c_size), idx(c_size) { init(); }

  const vector<T>& get() { return comb; }

  bool next() {
    int n = orig.size();
    int i = c_size - 1;
    while (i >= 0 && ++idx.at(i) > n - (c_size - i)) i--;
    if (i < 0) {
      init();
      return false;
    }

    int k = idx.at(i);
    for ( ; i < c_size; i++, k++) {
      idx.at(i) = k;
      comb.at(i) = orig.at(k);
    }
    return true;

  }

};

class IntComb {
  
  IterComb<int> itc;

public:

  IntComb(int n, int r) {
    vector<int> seq(n);
    iota(seq.begin(), seq.end(), 0);
    itc = IterComb<int>(seq, r);
  }
  const vector<int>& get() { return itc.get(); }
  bool next() { return itc.next(); }
};

class DupIntPerm {
  int n;
  int r;
  vector<int> vec;

public:
  DupIntPerm(int n_, int r_) : n(n_), r(r_), vec(r) {}

  const vector<int>& get() { return vec; }

  bool next() {
    for (int i = r - 1; i >= 0; i--) {
      if (++vec[i] < n) return true;
      vec[i] = 0;
    }
    return false;
  }
};

// ---- end perm.cc

// ---- inserted function f:gcd from util.cc

tuple<ll, ll, ll> mut_div(ll a, ll b, ll c, bool eff_c = true) {
  // auto [g, s, t] = mut_div(a, b, c, eff_c)
  //    If eff_c is true (default),
  //        g == gcd(|a|, |b|) and as + bt == c, if such s,t exists
  //        (g, s, t) == (-1, -1, -1)            otherwise
  //    If eff_c is false,                                 
  //        g == gcd(|a|, |b|) and as + bt == g           
  //    N.b.  gcd(0, t) == gcd(t, 0) == t.
  if (a == 0) {
    if (eff_c) {
      if (c % b != 0) return {-1, -1, -1};
      else            return {abs(b), 0, c / b};
    }else {
      if (b < 0) return {-b, 0, -1};
      else       return { b, 0,  1};
    }
  }else {
    auto [g, t, u] = mut_div(b % a, a, c, eff_c);
    // DLOGK(b%a, a, c, g, t, u);
    if (g == -1) return {-1, -1, -1};
    return {g, u - (b / a) * t, t};
  }
}

// auto [g, s, t] = eGCD(a, b)  --->  sa + tb == g == gcd(|a|, |b|)
//    N.b.  gcd(0, t) == gcd(t, 0) == t.
tuple<ll, ll, ll> eGCD(ll a, ll b) { return mut_div(a, b, 0, false); }

pair<ll, ll> crt_sub(ll a1, ll x1, ll a2, ll x2) {
  // DLOGKL("crt_sub", a1, x1, a2, x2);
  a1 = a1 % x1;
  a2 = a2 % x2;
  auto [g, s, t] = mut_div(x1, -x2, a2 - a1);
  // DLOGK(g, s, t);
  if (g == -1) return {-1, -1};
  ll z = x1 / g * x2;
  // DLOGK(z);
  s = s % (x2 / g);
  ll r = (x1 * s + a1) % z;
  // DLOGK(r);
  if (r < 0) r += z;
  // DLOGK(r);
  return {r, z};
};

// Chinese Remainder Theorem
//
//    r = crt(a1, x1, a2, x2)
//    ==>   r = a1 (mod x1);  r = a2 (mod x2);  0 <= r < lcm(x1, x2)
//    If no such r exists, returns -1
//    Note: x1 and x2 should >= 1.  a1 and a2 can be negative or zero.
//
//    r = crt(as, xs)
//    ==>   for all i. r = as[i] (mod xs[i]); 0 <= r < lcm(xs)
//    If no such r exists, returns -1
//    Note: xs[i] should >= 1.  as[i] can be negative or zero.
//          It should hold: len(xs) == len(as) > 0

ll crt(ll a1, ll x1, ll a2, ll x2) { return crt_sub(a1, x1, a2, x2).first; }

ll crt(vector<ll> as, vector<ll> xs) {
  // DLOGKL("crt", as, xs);
  assert(xs.size() == as.size() && xs.size() > 0);
  ll r = as[0];
  ll z = xs[0];
  for (size_t i = 1; i < xs.size(); i++) {
    // DLOGK(i, r, z, as[i], xs[i]);
    tie(r, z) = crt_sub(r, z, as[i], xs[i]);
    // DLOGK(r, z);
    if (r == -1) return -1;
  }
  return r;
}

// ---- end f:gcd

// ---- inserted library file mod.cc

template<int mod=0>
struct FpG {   // G for General
  static ll dyn_mod;

  static ll getMod() {
    if (mod == 0) return dyn_mod;
    else          return mod;
  }

  static void setMod(ll _mod) {  // effective only when mod == 0
    dyn_mod = _mod;
  }

  static ll _conv(ll x) {
    if (x >= getMod())  return x % getMod();
    if (x >= 0)         return x;
    if (x >= -getMod()) return x + getMod();
    ll y = x % getMod();
    if (y == 0) return 0;
    return y + getMod();
  }

  ll val;

  FpG(int t = 0) : val(_conv(t)) {}
  FpG(ll t) : val(_conv(t)) {}
  FpG(const FpG& t) : val(t.val) {}
  FpG& operator =(const FpG& t) { val = t.val; return *this; }
  FpG& operator =(ll t) { val = _conv(t); return *this; }
  FpG& operator =(int t) { val = _conv(t); return *this; }

  FpG& operator +=(const FpG& t) {
    val += t.val;
    if (val >= getMod()) val -= getMod();
    return *this;
  }

  FpG& operator -=(const FpG& t) {
    val -= t.val;
    if (val < 0) val += getMod();
    return *this;
  }

  FpG& operator *=(const FpG& t) {
    val = (val * t.val) % getMod();
    return *this;
  }

  FpG inv() const {
    if (val == 0) {
      throw runtime_error("FpG::inv(): called for zero.");
    }
    auto [g, u, v] = eGCD(val, getMod());
    return FpG(u);
  }

  FpG& operator /=(const FpG& t) {
    return (*this) *= t.inv();
  }

  FpG operator +(const FpG& t) const { return FpG(val) += t; }
  FpG operator -(const FpG& t) const { return FpG(val) -= t; }
  FpG operator *(const FpG& t) const { return FpG(val) *= t; }
  FpG operator /(const FpG& t) const { return FpG(val) /= t; }
  FpG operator -() const { return FpG(-val); }

  bool operator ==(const FpG& t) const { return val == t.val; }
  bool operator !=(const FpG& t) const { return val != t.val; }
  
  operator ll() const { return val; }

  friend FpG operator +(int x, const FpG& y) { return FpG(x) + y; }
  friend FpG operator -(int x, const FpG& y) { return FpG(x) - y; }
  friend FpG operator *(int x, const FpG& y) { return FpG(x) * y; }
  friend FpG operator /(int x, const FpG& y) { return FpG(x) / y; }
  friend bool operator ==(int x, const FpG& y) { return FpG(x) == y; }
  friend bool operator !=(int x, const FpG& y) { return FpG(x) != y; }
  friend FpG operator +(ll x, const FpG& y) { return FpG(x) + y; }
  friend FpG operator -(ll x, const FpG& y) { return FpG(x) - y; }
  friend FpG operator *(ll x, const FpG& y) { return FpG(x) * y; }
  friend FpG operator /(ll x, const FpG& y) { return FpG(x) / y; }
  friend bool operator ==(ll x, const FpG& y) { return FpG(x) == y; }
  friend bool operator !=(ll x, const FpG& y) { return FpG(x) != y; }
  friend FpG operator +(const FpG& x, int y) { return x + FpG(y); }
  friend FpG operator -(const FpG& x, int y) { return x - FpG(y); }
  friend FpG operator *(const FpG& x, int y) { return x * FpG(y); }
  friend FpG operator /(const FpG& x, int y) { return x / FpG(y); }
  friend bool operator ==(const FpG& x, int y) { return x == FpG(y); }
  friend bool operator !=(const FpG& x, int y) { return x != FpG(y); }
  friend FpG operator +(const FpG& x, ll y) { return x + FpG(y); }
  friend FpG operator -(const FpG& x, ll y) { return x - FpG(y); }
  friend FpG operator *(const FpG& x, ll y) { return x * FpG(y); }
  friend FpG operator /(const FpG& x, ll y) { return x / FpG(y); }
  friend bool operator ==(const FpG& x, ll y) { return x == FpG(y); }
  friend bool operator !=(const FpG& x, ll y) { return x != FpG(y); }

  friend istream& operator>> (istream& is, FpG& t) {
    ll x; is >> x;
    t = x;
    return is;
  }

  friend ostream& operator<< (ostream& os, const FpG& t) {
    os << t.val;
    return os;
  }

};
template<int mod>
ll FpG<mod>::dyn_mod;

template<int mod=0>
class CombG {
  int nMax;
  vector<FpG<mod>> vFact;
  vector<FpG<mod>> vInvFact;
public:
  CombG(int nm) : nMax(nm), vFact(nm+1), vInvFact(nm+1) {
    vFact.at(0) = 1;
    for (int i = 1; i <= nMax; i++) vFact.at(i) = i * vFact.at(i-1);
    vInvFact.at(nMax) = vFact.at(nMax).inv();
    for (int i = nMax; i >= 1; i--) vInvFact.at(i-1) = i * vInvFact.at(i);
  }
  FpG<mod> fact(int n) { return vFact.at(n); }
  FpG<mod> comb(int n, int r) {
    return vFact.at(n) * vInvFact.at(r) * vInvFact.at(n-r);
  }
  // The number of permutation extracting r from n.
  FpG<mod> perm(int n, int r) {
    return vFact.at(n) * vInvFact.at(n-r);
  }
};

constexpr int primeA = 1'000'000'007;
constexpr int primeB = 998'244'353;          // '
using FpA = FpG<primeA>;
using FpB = FpG<primeB>;
using CombA = CombG<primeA>;
using CombB = CombG<primeB>;

// ---- end mod.cc

// ---- inserted function f:<< from util.cc
template <typename T1, typename T2>
ostream& operator<< (ostream& os, const pair<T1,T2>& p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}

template <typename T1, typename T2, typename T3>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3>& t) {
  os << "(" << get<0>(t) << ", " << get<1>(t)
     << ", " << get<2>(t) << ")";
  return os;
}

template <typename T1, typename T2, typename T3, typename T4>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3,T4>& t) {
  os << "(" << get<0>(t) << ", " << get<1>(t)
     << ", " << get<2>(t) << ", " << get<3>(t) << ")";
  return os;
}

template <typename T>
ostream& operator<< (ostream& os, const vector<T>& v) {
  os << '[';
  for (auto it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  os << ']';

  return os;
}

template <typename T, typename C>
ostream& operator<< (ostream& os, const set<T, C>& v) {
  os << '{';
  for (auto it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  os << '}';

  return os;
}

template <typename T, typename C>
ostream& operator<< (ostream& os, const unordered_set<T, C>& v) {
  os << '{';
  for (auto it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  os << '}';

  return os;
}

template <typename T, typename C>
ostream& operator<< (ostream& os, const multiset<T, C>& v) {
  os << '{';
  for (auto it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  os << '}';

  return os;
}

template <typename T1, typename T2, typename C>
ostream& operator<< (ostream& os, const map<T1, T2, C>& mp) {
  os << '[';
  for (auto it = mp.begin(); it != mp.end(); it++) {
    if (it != mp.begin()) os << ", ";
    os << it->first << ": " << it->second;
  }
  os << ']';

  return os;
}

template <typename T1, typename T2, typename C>
ostream& operator<< (ostream& os, const unordered_map<T1, T2, C>& mp) {
  os << '[';
  for (auto it = mp.begin(); it != mp.end(); it++) {
    if (it != mp.begin()) os << ", ";
    os << it->first << ": " << it->second;
  }
  os << ']';

  return os;
}

template <typename T, typename T2>
ostream& operator<< (ostream& os, const queue<T, T2>& orig) {
  queue<T, T2> que(orig);
  bool first = true;
  os << '[';
  while (!que.empty()) {
    T x = que.front(); que.pop();
    if (!first) os << ", ";
    os << x;
    first = false;
  }
  return os << ']';
}

template <typename T, typename T2>
ostream& operator<< (ostream& os, const deque<T, T2>& orig) {
  deque<T, T2> que(orig);
  bool first = true;
  os << '[';
  while (!que.empty()) {
    T x = que.front(); que.pop_front();
    if (!first) os << ", ";
    os << x;
    first = false;
  }
  return os << ']';
}

template <typename T, typename T2, typename T3>
ostream& operator<< (ostream& os, const priority_queue<T, T2, T3>& orig) {
  priority_queue<T, T2, T3> pq(orig);
  bool first = true;
  os << '[';
  while (!pq.empty()) {
    T x = pq.top(); pq.pop();
    if (!first) os << ", ";
    os << x;
    first = false;
  }
  return os << ']';
}

template <typename T>
ostream& operator<< (ostream& os, const stack<T>& st) {
  stack<T> tmp(st);
  os << '[';
  bool first = true;
  while (!tmp.empty()) {
    T& t = tmp.top();
    if (first) first = false;
    else os << ", ";
    os << t;
    tmp.pop();
  }
  os << ']';
  return os;
}

#if __cplusplus >= 201703L
template <typename T>
ostream& operator<< (ostream& os, const optional<T>& t) {
  if (t.has_value()) os << "v(" << t.value() << ")";
  else               os << "nullopt";
  return os;
}
#endif

ostream& operator<< (ostream& os, int8_t x) {
  os << (int32_t)x;
  return os;
}

// ---- end f:<<

// ---- inserted library file debug.cc
template <class... Args>
string dbgFormat(const char* fmt, Args... args) {
  size_t len = snprintf(nullptr, 0, fmt, args...);
  char buf[len + 1];
  snprintf(buf, len + 1, fmt, args...);
  return string(buf);
}

template <class Head>
void dbgLog(bool with_nl, Head&& head) {
  cerr << head;
  if (with_nl) cerr << endl;
}

template <class Head, class... Tail>
void dbgLog(bool with_nl, Head&& head, Tail&&... tail)
{
  cerr << head << " ";
  dbgLog(with_nl, forward<Tail>(tail)...);
}

#if DEBUG
  #define DLOG(...)        dbgLog(true, __VA_ARGS__)
  #define DLOGNNL(...)     dbgLog(false, __VA_ARGS__)
  #define DFMT(...)        cerr << dbgFormat(__VA_ARGS__) << endl
  #define DCALL(func, ...) func(__VA_ARGS__)
#else
  #define DLOG(...)
  #define DLOGNNL(...)
  #define DFMT(...)
  #define DCALL(func, ...)
#endif

/*
#if DEBUG_LIB
  #define DLOG_LIB(...)        dbgLog(true, __VA_ARGS__)
  #define DLOGNNL_LIB(...)     dbgLog(false, __VA_ARGS__)
  #define DFMT_LIB(...)        cerr << dbgFormat(__VA_ARGS__) << endl
  #define DCALL_LIB(func, ...) func(__VA_ARGS__)
#else
  #define DLOG_LIB(...)
  #define DFMT_LIB(...)
  #define DCALL_LIB(func, ...)
#endif
*/

#define DUP1(E1)       #E1 "=", E1
#define DUP2(E1,E2)    DUP1(E1), DUP1(E2)
#define DUP3(E1,...)   DUP1(E1), DUP2(__VA_ARGS__)
#define DUP4(E1,...)   DUP1(E1), DUP3(__VA_ARGS__)
#define DUP5(E1,...)   DUP1(E1), DUP4(__VA_ARGS__)
#define DUP6(E1,...)   DUP1(E1), DUP5(__VA_ARGS__)
#define DUP7(E1,...)   DUP1(E1), DUP6(__VA_ARGS__)
#define DUP8(E1,...)   DUP1(E1), DUP7(__VA_ARGS__)
#define DUP9(E1,...)   DUP1(E1), DUP8(__VA_ARGS__)
#define DUP10(E1,...)   DUP1(E1), DUP9(__VA_ARGS__)
#define DUP11(E1,...)   DUP1(E1), DUP10(__VA_ARGS__)
#define DUP12(E1,...)   DUP1(E1), DUP11(__VA_ARGS__)
#define GET_MACRO(_1,_2,_3,_4,_5,_6,_7,_8,_9,_10,_11,_12,NAME,...) NAME
#define DUP(...)          GET_MACRO(__VA_ARGS__, DUP12, DUP11, DUP10, DUP9, DUP8, DUP7, DUP6, DUP5, DUP4, DUP3, DUP2, DUP1)(__VA_ARGS__)
#define DLOGK(...)        DLOG(DUP(__VA_ARGS__))
#define DLOGKL(lab, ...)  DLOG(lab, DUP(__VA_ARGS__))

#if DEBUG_LIB
  #define DLOG_LIB   DLOG
  #define DLOGK_LIB  DLOGK
  #define DLOGKL_LIB DLOGKL
#endif

// ---- end debug.cc

// ---- inserted function f:updMaxMin from util.cc
template<typename T>
bool updMax(T& tmax, const T& x) {
  if (x > tmax) { tmax = x; return true;  }
  else          {           return false; }
}
template<typename T>
bool updMin(T& tmin, const T& x) {
  if (x < tmin) { tmin = x; return true;  }
  else          {           return false; }
}
// ---- end f:updMaxMin

// ---- inserted library file coordCompr.cc

class CoordCompr {
  bool built;
  map<ll, int> mp;     // map from an original value to a compressed value
  vector<ll> rev;      // vector of original values

  void build() {
    built = true;
    sort(rev.begin(), rev.end());
    rev.erase(unique(rev.begin(), rev.end()), rev.end());
    mp = map<ll, int>();
    for (size_t i = 0; i < rev.size(); i++) mp[rev[i]] = i;
  }

public:

  CoordCompr() : built(false) {}
  CoordCompr(const vector<ll>& vec) : built(false), rev(vec) {}
  CoordCompr(vector<ll>&& vec) : built(false), rev(move(vec)) {}

  void add(ll x) {
    rev.push_back(x);
    built = false;
  }

  void add(const vector<ll>& vec) {
    for (ll x : vec) rev.push_back(x);
    built = false;
  }

  int c(ll x) {
    if (! built) build();
    return mp[x];
  }

  ll d(int i) {
    if (! built) build();
    return rev[i];
  }

  int size() {
    if (! built) build();
    return rev.size();
  }

};

// ---- end coordCompr.cc

// ---- inserted library file cmpNaive.cc

const string end_mark("^__=end=__^");

int naive(istream& cin, ostream& cout);
int body(istream& cin, ostream& cout);

void cmpNaive() {
  while (true) {
    string s;
    getline(cin, s);
    bool run_body;
    if (s.at(0) == 'Q') {
      return;
    }else if (s.at(0) == 'B') {
      run_body = true;
    }else if (s.at(0) == 'N') {
      run_body = false;
    }else {
      cerr << "Unknown body/naive specifier.\n";
      exit(1);
    }
    string input_s;
    while (true) {
      getline(cin, s);
      if (s == end_mark) break;
      input_s += s;
      input_s += "\n";
    }
    stringstream ss_in(move(input_s));
    stringstream ss_out;
    if (run_body) {
      body(ss_in, ss_out);
    }else {
      naive(ss_in, ss_out);
    }
    cout << ss_out.str() << end_mark << endl;
  }
}

int main(int argc, char *argv[]) {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout << setprecision(20);

#if CMPNAIVE
  if (argc == 2) {
    if (strcmp(argv[1], "cmpNaive") == 0) {
      cmpNaive();
    }else if (strcmp(argv[1], "naive") == 0) {
      naive(cin, cout);
    }else if (strcmp(argv[1], "skip") == 0) {
      exit(0);
    }else {
      cerr << "Unknown argument.\n";
      exit(1);
    }
  }else {
#endif
    body(cin, cout);
#if CMPNAIVE
  }
#endif
  return 0;
}

/*
int naive(istream& cin, ostream& cout) {
  return 0;
}
int body(istream& cin, ostream& cout) {
  return 0;
}
*/

// ---- end cmpNaive.cc

// @@ !! LIM -- end mark --

using Fp = FpA;

ll lis(const vector<int>& vec) {
  ll big = 1e18;
  ll N = vec.size();
  vector<ll> res(N, big);
  for (ll i = 0; i < N; i++) {
    for (ll p = 0; p < N; p++) {
      if (vec[i] <= res[p]) {
        res[p] = vec[i];
        break;
      }
    }
  }
  ll i = 0;
  for (; i < N && res[i] < big; i++);
  return i;
}

int naive(istream& cin, ostream& cout) {
  ll N; cin >> N;
  vector<ll> A(N);
  ll vmax = 0;
  for (ll i = 0; i < N; i++) {
    cin >> A[i];
    vmax = max(vmax, A[i]);
  }
  DupIntPerm dip(vmax, N);
  const vector<int>& v = dip.get();
  Fp sum = 0;
  Fp cnt = 0;
  do {
    bool ok = true;
    for (ll i = 0; i < N; i++) {
      if (v[i] >= A[i]) {
        ok = false;
        break;
      }
    }
    if (! ok) continue;
    sum += Fp(lis(v));
    cnt += Fp(1);
  }while (dip.next());
  DLOGK(sum, cnt);
  Fp ans = sum / cnt;
  cout << ans << endl;

  return 0;
}
int body(istream& cin, ostream& cout) {

  ll N; cin >> N;
  vector<ll> A(N);
  for (ll i = 0; i < N; i++) {
    cin >> A[i];
    A[i]++;
  }
  CoordCompr cc(A);
  cc.add(0); cc.add(1);

  auto check = [&](const vector<int>& vec) -> bool {
    vector<ll> appear(N);
    for (ll i = 0; i < N; i++) appear[vec[i]] += 1;
    ll cnt = 0;
    for (ll i = 0; i < N && appear[i] > 0; i++) cnt += appear[i];
    return cnt == N;
  };

  auto binom = [&](ll n, ll r) -> Fp {
    // DLOGKL("binom", n, r);
    if (r < 0 || r > n) return Fp(0);
    Fp x = 1;
    Fp y = 1;
    for (ll t = 0; t < r; t++) {
      x *= n - t;
      y *= r - t;
    }
    Fp z = x / y;
    // DLOGK(n, r, x, y, z);
    return z;
  };

  const ll big = 1e18;
  auto num_comb = [&](const vector<int>& vec) -> Fp {
    DLOG(vec);
    vector<ll> B(N, big);
    for (ll i = 0; i < N; i++) updMin(B[vec[i]], A[i]);
    ll K = 0; for (; K < N && B[K] < big; K++);
    ll M = cc.size();
    vector tbl(K + 1, vector<Fp>(M));
    tbl[0][0] = 1;
    for (ll k = 1; k <= K; k++) {
      for (ll m = 1; m+1 < M; m++) {
        ll l = cc.d(m);
        ll r = cc.d(m+1);
        if (B[k-1] < r) continue;
        for (ll i = k-1; i >= 0; i--) {
          Fp cb = binom(r - l, k - i);
          Fp t = 0;
          for (ll p = 0; p < m; p++) t += tbl[i][p];
          // DLOGK(k, m, l, r, i, cb, t);
          tbl[k][m] += cb * t;
          if (i == 0 || B[i-1] < r) break;
        }
      }
      DLOGK(k, tbl[k]);
    }
    Fp ret = 0;
    for (ll m = 0; m < M; m++) ret += tbl[K][m];
    return ret;
  };

  DupIntPerm dip(N, N);
  const vector<int>& v = dip.get();
  Fp sum = 0;
  do {
    if (check(v)) {
      ll len = lis(v);
      Fp c = num_comb(v);
      DLOGK(v, len, c);
      sum += len * c;
    }
  }while (dip.next());
  Fp tot = 1;
  for (ll i = 0; i < N; i++) tot *= Fp(A[i] - 1);
  DLOGK(sum, tot);
  cout << sum / tot << endl;

  return 0;
}

Submission Info

Compile Error

./Main.cpp: In function ‘int main(int, char**)’:
./Main.cpp:734:14: warning: unused parameter ‘argc’ [-Wunused-parameter]
  734 | int main(int argc, char *argv[]) {
      |          ~~~~^~~~
./Main.cpp:734:26: warning: unused parameter ‘argv’ [-Wunused-parameter]
  734 | int main(int argc, char *argv[]) {
      |                    ~~~~~~^~~~~~

Judge Result