#ifdef __LOCAL
#include <mytemplate.hpp>  // プリコンパイル済みヘッダ ~/local/include/mytemplate.hpp.gch
#else
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <climits>
#include <cmath>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream> 
#include <iterator>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#endif
using namespace std;
// #include <boost/multiprecision/cpp_int.hpp>
// using bint = boost::multiprecision::cpp_int;
using int128 = __int128_t;
using ll = long long;
using vl = vector<ll>;
using vvl = vector<vl>;
using vb = vector<bool>;
using vvb = vector<vb>;
using vd = vector<double>;
using vvd = vector<vd>;
using vc = vector<char>;
using vvc = vector<vc>;
using pll = pair<ll, ll>;
#define REP1(i, n) REP3(i, 0, n, 1)
#define REP2(i, s, n) REP3(i, s, n, 1)
#define REP3(i, s, n, d) for(ll i = (ll)(s); i < (ll)(n); i += (d))
#define REP_OVERLOAD(e1, e2, e3, e4, NAME,...) NAME
#define rep(...) REP_OVERLOAD(__VA_ARGS__, REP3, REP2, REP1)(__VA_ARGS__)
#define DEP1(i, n) DEP3(i, n, -1, 1)
#define DEP2(i, n, s) DEP3(i, n, s, 1)
#define DEP3(i, n, s, d) for(ll i = (ll)(n); (ll)(s) < i; i -= (d))
#define DEP_OVERLOAD(e1, e2, e3, e4, NAME,...) NAME
#define dep(...) DEP_OVERLOAD(__VA_ARGS__, DEP3, DEP2, DEP1)(__VA_ARGS__)
#define fore(e, a) for (auto&& e: (a))
#define len(a) (ll)(a).size()
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define th third
/*********    C O N S T A N T    **********/
constexpr ll INF = LONG_LONG_MAX / 2 - 10000LL;  // 4,611,686,018,427,377,903  ~= 4.6e+18, 19桁
const double PI = acos(-1);
/*********       P A I R       **********/
template<class T, class U> inline pair<T, U>& operator+=(pair<T, U>& a, const pair<T, U>& b) {a.fi += b.fi; a.se += b.se; return a;}
template<class T, class U> inline pair<T, U>& operator-=(pair<T, U>& a, const pair<T, U>& b) {a.fi -= b.fi; a.se -= b.se; return a;}
template<class T, class U> inline pair<T, U>& operator*=(pair<T, U>& a, const pair<T, U>& b) {a.fi *= b.fi; a.se *= b.se; return a;}
template<class T, class U> inline pair<T, U>& operator/=(pair<T, U>& a, const pair<T, U>& b) {a.fi /= b.fi; a.se /= b.se; return a;}
template<class T, class U> inline pair<T, U>& operator%=(pair<T, U>& a, const pair<T, U>& b) {a.fi %= b.fi; a.se %= b.se; return a;}
template<class T, class U, class V> inline pair<T, U>& operator+=(pair<T, U>& a, const V& b) {a.fi += b; a.se += b; return a;}
template<class T, class U, class V> inline pair<T, U>& operator-=(pair<T, U>& a, const V& b) {a.fi -= b; a.se -= b; return a;}
template<class T, class U, class V> inline pair<T, U>& operator*=(pair<T, U>& a, const V& b) {a.fi *= b; a.se *= b; return a;}
template<class T, class U, class V> inline pair<T, U>& operator/=(pair<T, U>& a, const V& b) {a.fi /= b; a.se /= b; return a;}
template<class T, class U, class V> inline pair<T, U>& operator%=(pair<T, U>& a, const V& b) {a.fi %= b; a.se %= b; return a;}
template<class T, class U, class V> inline pair<T, U> operator+(pair<T, U> a, const V& b) {a += b; return a;}
template<class T, class U, class V> inline pair<T, U> operator-(pair<T, U> a, const V& b) {a -= b; return a;}
template<class T, class U, class V> inline pair<T, U> operator*(pair<T, U> a, const V& b) {a *= b; return a;}
template<class T, class U, class V> inline pair<T, U> operator/(pair<T, U> a, const V& b) {a /= b; return a;}
template<class T, class U, class V> inline pair<T, U> operator%(pair<T, U> a, const V& b) {a %= b; return a;}
template<class T, class U> inline pair<T, U> operator+(pair<T, U> a) {return a;}
template<class T, class U> inline pair<T, U> operator-(pair<T, U> a) {return a * (-1);}
template<class T, class U> istream& operator >>(istream& stream, pair<T, U>& a) {stream >> a.fi >> a.se; return stream;}
template<class T, class U> ostream& operator <<(ostream &stream, const pair<T, U>& a) { stream << a.fi << " " << a.se; return stream; }
/*********       V E C T O R      **********/
template<class T> inline vector<T>& operator+=(vector<T>& a, const vector<T>& b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] += b[i]; return a;}
template<class T> inline vector<T>& operator-=(vector<T>& a, const vector<T>& b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] -= b[i]; return a;}
template<class T> inline vector<T>& operator*=(vector<T>& a, const vector<T>& b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] *= b[i]; return a;}
template<class T> inline vector<T>& operator/=(vector<T>& a, const vector<T>& b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] /= b[i]; return a;}
template<class T> inline vector<T>& operator%=(vector<T>& a, const vector<T>& b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] %= b[i]; return a;}
template<class T, class U> inline vector<T>& operator+=(vector<T>& a, const U& b) {fore(e, a) e += b; return a;}
template<class T, class U> inline vector<T>& operator-=(vector<T>& a, const U& b) {fore(e, a) e -= b; return a;}
template<class T, class U> inline vector<T>& operator*=(vector<T>& a, const U& b) {fore(e, a) e *= b; return a;}
template<class T, class U> inline vector<T>& operator/=(vector<T>& a, const U& b) {fore(e, a) e /= b; return a;}
template<class T, class U> inline vector<T>& operator%=(vector<T>& a, const U& b) {fore(e, a) e %= b; return a;}
template<class T, class U> inline vector<T> operator+(vector<T> a, const U& b) {a += b; return a;}
template<class T, class U> inline vector<T> operator-(vector<T> a, const U& b) {a -= b; return a;}
template<class T, class U> inline vector<T> operator*(vector<T> a, const U& b) {a *= b; return a;}
template<class T, class U> inline vector<T> operator/(vector<T> a, const U& b) {a /= b; return a;}
template<class T, class U> inline vector<T> operator%(vector<T> a, const U& b) {a %= b; return a;}
template<class T> inline vector<T> operator+(vector<T> a) {return a;}
template<class T> inline vector<T> operator-(vector<T> a) {return a * (-1);}
template<class T> istream& operator >>(istream& stream, vector<T>& a) {fore(e, a) stream >> e; return stream;}
template<class T> ostream& operator <<(ostream& stream, const vector<T>& v) {if(v.size()){stream << v[0]; rep(i, 1, v.size()) cout << " " << v[i];} return stream;}
template<class T> ostream& operator <<(ostream& stream, const vector<vector<T>>& vv) {if(vv.size()){stream << vv[0]; rep(i, 1, vv.size()) cout << '\n' << vv[i];} return stream;}
template<class T> inline T Sum(const vector<T>& v) {return reduce(all(v));}  // v.size() == 0 のとき T() を返す
template<class T> inline T Max(const vector<T>& v) {assert(v.size()); return *max_element(all(v));}
template<class T> inline T Min(const vector<T>& v) {assert(v.size()); return *min_element(all(v));}
template<class T> inline ll Argmax(const vector<T>& v) {assert(v.size()); return max_element(all(v)) - v.begin();}
template<class T> inline ll Argmin(const vector<T>& v) {assert(v.size()); return min_element(all(v)) - v.begin();}
template<class T, class U> inline bool Contains(const vector<T>& v, const U& a) {return find(all(v), a) != v.end();}
template<class T, class U> vector<T> make_vector(int n, U v) { return vector<T>(n, v); }
template <class T, class... Args> auto make_vector(int n, Args... args) {auto val = make_vector<T>(args...); return make_vector<decltype(val)>(n, move(val));}
/*********        S E T        **********/
template<class T> istream& operator >>(istream& stream, set<T>& st) {T e; stream >> e; st.insert(e); return stream;}
template<class T> ostream& operator <<(ostream& stream, const set<T>& st) {if(st.size()){auto it=st.begin(); stream << *it++; for(; it!=st.end(); it++) cout << " " << *it;} return stream;}
template<class T> inline T Max(const set<T>& st) {assert(st.size()); return *prev(st.end());}
template<class T> inline T Min(const set<T>& st) {assert(st.size()); return *st.begin();}
template<class T> inline bool Contains(const set<T>& st, T x) {return st.find(x) != st.end();}
/*********   M U L T I S E T   **********/
template<class T> istream& operator >>(istream& stream, multiset<T>& st) {T e; stream >> e; st.insert(e); return stream;}
template<class T> ostream& operator <<(ostream& stream, const multiset<T>& st) {if(st.size()){auto it=st.begin(); stream << *it++; for(; it!=st.end(); it++) cout << " " << *it;} return stream;}
template<class T> inline T Max(const multiset<T>& st) {assert(st.size()); return *prev(st.end());}
template<class T> inline T Min(const multiset<T>& st) {assert(st.size()); return *st.begin();}
template<class T> inline bool Contains(const multiset<T>& st, T x) {return st.find(x) != st.end();}
template<class T> inline bool EraseOne(multiset<T>& st, T x) {auto it=st.find(x); if (it!=st.end()) {st.erase(it); return true;} else return false;}  // 要素xを1つ削除. 消せたらtrueを返す.
/*********     S T R I N G     **********/
template<class T> inline bool Contains(const string& s, const T& c) {return s.find(c) != string::npos;}  // cはchar, string共に可
inline string ToUpper(const string& s) {string t; t.resize(s.size()); std::transform(all(s), t.begin(), ::toupper); return t; }
inline string ToLower(const string& s) {string t; t.resize(s.size()); std::transform(all(s), t.begin(), ::tolower); return t; }
/*********       T R I O       **********/
template<class T1, class T2, class T3> struct trio {
    T1 first; T2 second; T3 third;
    // コンストラクタ・代入演算子
    trio() {first=T1(); second=T2(); third=T3();}
    trio(const T1& x) : first(x), second(x), third(x) {}
    trio(const T1& x, const T2& y, const T3& z) : first(x), second(y), third(z) {}
    trio(const trio& t) {first=t.first; second=t.second; third=t.third;}  // コピーコンストラクタ
    trio& operator =(const trio& t) {first=t.first; second=t.second; third=t.third; return *this;}
    // 比較演算子
    bool operator <(const trio& t) const {return tie(first, second, third) < tie(t.first, t.second, t.third);}
    bool operator ==(const trio& t) const {return tie(first, second, third) == tie(t.first, t.second, t.third);}
    bool operator !=(const trio& other) const { return !(*this == other); }
    bool operator >(const trio& other) const { return other < *this; }
    bool operator <=(const trio& other) const { return !(*this > other); }
    bool operator >=(const trio& other) const { return !(*this < other); }
    // 単項演算子（+ -）
    trio operator +() const { return *this; }
    trio operator -() const { return (-1) * (*this); }
    // 複合代入演算子
    trio& operator +=(const trio& t) {first += t.first; second += t.second; third += t.third; return *this;}
    trio& operator -=(const trio& t) {first -= t.first; second -= t.second; third -= t.third; return *this;}
    trio& operator *=(const trio& t) {first *= t.first; second *= t.second; third *= t.third; return *this;}
    trio& operator /=(const trio& t) {first /= t.first; second /= t.second; third /= t.third; return *this;}
    trio& operator %=(const trio& t) {first %= t.first; second %= t.second; third %= t.third; return *this;}
    // 算術演算子
    friend trio operator +(const trio& lhs, const trio& rhs) {return trio(lhs) += rhs;}
    friend trio operator -(const trio& lhs, const trio& rhs) {return trio(lhs) -= rhs;}
    friend trio operator *(const trio& lhs, const trio& rhs) {return trio(lhs) *= rhs;}
    friend trio operator /(const trio& lhs, const trio& rhs) {return trio(lhs) /= rhs;}
    friend trio operator %(const trio& lhs, const trio& rhs) {return trio(lhs) %= rhs;}
    // 入出力
    friend istream& operator >>(istream &stream, trio& t) {return stream >> t.first >> t.second >> t.third;}
    friend ostream& operator <<(ostream &stream, const trio& t) {return stream << t.first << " " << t.second << " " << t.third;}
    operator tuple<T1&, T2&, T3&>() {return tie(first, second, third);}
};
using tll = trio<ll, ll, ll>;
/*********     R A N D O M     **********/
struct Random {
    mt19937_64 rnd;
    Random() {
        random_device seed_gen;
        rnd.seed(seed_gen());
    }
    ll randint(ll a, ll b) {  // [a, b]
        uniform_int_distribution<ll> dist(a, b);
        return dist(rnd);
    }
    double randreal(double a, double b) {
        uniform_real_distribution<double> dist(a, b);
        return dist(rnd);
    }
    char randchar(char a, char b) {  // [a, b]
        uniform_int_distribution<ll> dist(a, b);
        return dist(rnd);
    }
};
/*********       P R I N T       **********/
template<class T> inline void print(const T& e) {cout << e << '\n';}
template<class H, class... T> inline void print(const H& h, const T&... t) {cout << h << ' '; print(t...);}
template<class... T> inline void End(const T&... t) {print(t...); exit(0);}
/*********       D E B U G       **********/
#ifdef __LOCAL
#define debug(...) if(DEBUG) do{cout << '[' << #__VA_ARGS__ << "] ";debug_(__VA_ARGS__);}while(0)
#else
#define debug(...)
#endif
void dbg_(const long long& e) {if (e == INF) cout << "INF"; else if (e == -INF) cout << "-INF"; else cout << e;}
template<class T> void dbg_(const T& e) {cout << e;}
template<class T, class U> void dbg_(const pair<T, U>& p) {cout << '('; dbg_(p.first); cout << ' '; dbg_(p.second); cout << ')';}
template<class T1, class T2, class T3> void dbg_(const trio<T1, T2, T3>& t) {cout << '('; dbg_(t.first); cout << ' '; dbg_(t.second); cout << ' '; dbg_(t.third); cout << ')';}
template<class T> void debug_(const T& e) {dbg_(e); cout << '\n';}
template<class T> void debug_(const vector<T>& v) {if (v.size()){auto it=v.begin(); dbg_(*it++); for(; it!=v.end(); ++it){cout << ' '; dbg_(*it);}} cout << '\n';}
template<class T> void debug_(const vector<vector<T>>& vv) {cout << '\n'; ll cnt=0; for(auto&& v : vv){cout << cnt++ << ": "; debug_(v);}}
template<class T, class U> void debug_(const map<T, U>& mp) {if (mp.size()) {auto it = mp.begin(); dbg_(*it++); for(; it != mp.end(); ++it) {cout << ' '; dbg_(*it);}} cout << '\n';}
template<class T, class U> void debug_(const vector<map<T, U>>& vm){cout << '\n'; ll cnt=0; for(auto&& mp : vm){cout << cnt++ << ": "; debug_(mp);}}
template<class T> void debug_(const set<T>& st) {if(st.size()){auto it=st.begin(); dbg_(*it++); for(; it!=st.end(); ++it) {cout << ' '; dbg_(*it);}}cout << '\n';}
template<class T> void debug_(const multiset<T>& st) {if(st.size()) {auto it=st.begin(); dbg_(*it++); for(; it != st.end(); ++it) {cout << ' '; dbg_(*it);}} cout << '\n';}
template<class T> void debug_(const vector<set<T>>& vs) {cout << '\n'; ll cnt=0; for(auto&& st : vs){cout << cnt++ << ": "; debug_(st);}}
template<class T> void debug_(const vector<multiset<T>>& vs) {cout << '\n'; ll cnt=0;for(auto&& st : vs){cout << cnt++ << ": "; debug_(st);}}
template<class H, class... T> void debug_(const H& h, const T&... t) {dbg_(h); cout << ", "; debug_(t...);}
/*********       O T H E R S       **********/
template<class T, class U> inline bool chmin(T& a, U b) {if (a > b) {a = b; return true;} return false;}  // bは値渡し!
template<class T, class U> inline bool chmax(T& a, U b) {if (a < b) {a = b; return true;} return false;}
template<class T, class U> inline auto Mod(const T& a, const U& m) {return (a % m + m) % m;}  // 負もOK
template<class T, class U> inline auto Ceil(const T& x, const U& y) {return x < 0 ? x/y : (x + y - 1) / y;}  // 負もOK
template<class T, class U> inline auto Floor(const T& x, const U& y) {return -(Ceil(-x, y)); }  // 負もOK
inline ll Isqrt(ll n) {assert(n >= 0); ll x = round(sqrt(n)); while(x * x > n) --x; return x;}
inline ll Comb(ll n, ll r) {if (r < 0 || n < r) return 0; r = min(r, n - r); ll ret = 1; rep(i, r) {ret *= n - i; ret /= i + 1;} return ret;}  // n=60, r=30までOK
template<class T> inline T Pow(T x, ll n) {assert(n >= 0); T ret = 1; while(1) {if (n % 2) ret *= x; n /= 2; if(!n) return ret; x = x * x;}}  // べき乗 mintもOK
template<class T> inline T Aseries(T a, T d, ll n) {assert(n >= 0); return a * n + n * (n - 1) / 2 * d;}  // 等差級数 mintもOK
template<class T> inline T Gseries(T a, T r, ll n) {assert(n >= 0); if (r == 1) return a * n; else return a * (1 - Pow(r, n)) / (1 - r);}  // 等比級数 mintもOK
template<class T> using min_priority_queue = priority_queue<T, vector<T>, greater<T>>;
inline bool Bit(ll b, int i) {assert(0 <= i && i < 64); return (b >> i) & 1;}
inline ll Popcount(ll b) {return __builtin_popcountll(b);}
inline ll Mask(ll n) {assert(0 <= n && n < 63); return (1LL << n) - 1LL;}  // [0, n)のbitが立った64bit整数を返す。
inline ll Mask(ll n, ll m) {assert(n >= m); return Mask(n) ^ Mask(m);}  // [m, n)のbitが立った64bit整数を返す。
/*********       M  O  D       **********/
// #include <atcoder/modint>  // https://atcoder.github.io/ac-library/production/document_ja/
// using namespace atcoder;
// using mint = modint998244353;     // modint1000000007;
// istream& operator >>(istream& stream, mint& e) {ll n; stream >> n; e = n; return stream; }
// ostream& operator <<(ostream& stream, const mint& e) { stream << e.val(); return stream; }
// using vm = vector<mint>;
// using vvm = vector<vm>;
/***************************************/
constexpr bool DEBUG = true;


// 参考:   https://pages.soi.ch/soiminar/treap.pdf
// verify: https://atcoder.jp/contests/past202112-open/tasks/past202112_m
//         https://atcoder.jp/contests/abc217/tasks/abc217_d
template <class T> struct TreapSet {
  private:
    struct Node {
        int priority;
        T key;
        ll size = 1;
        unique_ptr<Node> left, right;

        Node(T key) : priority(rand()), key(key) {}
    };

    using upn = unique_ptr<Node>;
    upn root;

    // 分離。keyの値が含まれるとき、eq2rightがfalseならl, trueならrに行く。
    pair<upn, upn> split(upn current, const T &key, bool eq2right = false) {
        upn l, r;

        if (!current) return {move(l), move(r)};
        if (key < current->key || (key == current->key && eq2right)) {
            r = move(current);
            tie(l, r->left) = split(move(r->left), key, eq2right);
            r->size -= (!l ? 0 : l->size);
        } else {
            l = move(current);
            tie(l->right, r) = split(move(l->right), key, eq2right);
            l->size -= (!r ? 0 : r->size);
        }
        return {move(l), move(r)};
    }

    // 結合。必要条件: l->key <= r->key
    upn merge(upn l, upn r) {
        if (!l || !r) return l ? move(l) : move(r);
        if (l->priority > r->priority) {
            l->size += r->size;
            l->right = merge(move(l->right), move(r));
            return l;
        } else {
            r->size += l->size;
            r->left = merge(move(l), move(r->left));
            return r;
        }
    }

    // x未満の要素数, eq = trueならx以下
    ll index_(const T &x, bool eq) {
        if (!root) return 0;
        Node *current = root.get();

        ll cnt = 0;
        while (current) {
            int left_size = !current->left ? 0 : current->left->size;
            if (current->key == x) {
                cnt += left_size + eq;
                break;
            } else if (current->key < x) {
                cnt += left_size + 1; // +1はrootの分
                current = current->right.get();
            } else {
                current = current->left.get();
            }
        }
        return cnt;
    }

    // x未満の最大値, eq = trueならkey以下.
    optional<T> less_(const T &x, bool eq) {
        if (!root) return nullopt;
        Node *current = root.get();

        T ret = T();
        bool exists = false;
        while (current) {
            if (eq && current->key == x) return x;
            if (current->key < x) {
                ret = current->key;
                exists = true;
                current = current->right.get();
            } else {
                current = current->left.get();
            }
        }
        if (exists)
            return ret;
        else
            return nullopt;
    }

    // x超過の最小値, eq = trueならkey以上.
    optional<T> greater_(const T &x, bool eq) {
        if (!root) return nullopt;
        Node *current = root.get();

        T ret = T();
        bool exists = false;
        while (current) {
            if (eq && current->key == x) return x;
            if (current->key > x) {
                ret = current->key;
                exists = true;
                current = current->left.get();
            } else {
                current = current->right.get();
            }
        }
        if (exists)
            return ret;
        else
            return nullopt;
    }

  public:
    TreapSet() {}

    TreapSet(const vector<T> &vec) {
        fore(e, vec) insert(e);
    }

    // keyを追加。追加前にkeyが存在しなかったかどうかを返す
    bool insert(const T &key) {
        unique_ptr<Node> l, r, eq;
        tie(l, r) = split(move(root), key);
        tie(l, eq) = split(move(l), key, true);

        bool key_exists = (bool)eq;
        if (eq) {
            root = merge(merge(move(l), move(eq)), move(r));
        } else {
            auto node = make_unique<Node>(key);
            root = merge(merge(move(l), move(node)), move(r));
        }

        return !key_exists;
    }

    // keyを消去。消去前にkeyが存在したかを返す
    bool erase(const T &key) {
        unique_ptr<Node> l, r, eq;
        tie(l, r) = split(move(root), key);
        tie(l, eq) = split(move(l), key, true);

        bool key_exists = (bool)eq;
        if (eq) eq = merge(move(eq->left), move(eq->right));
        root = merge(merge(move(l), move(eq)), move(r));

        return key_exists;
    }

    // 値xが含まれるかどうか
    bool contains(const T &x) {
        if (!root) return false;
        Node *current = root.get();

        while (current) {
            if (x == current->key)
                return true;
            else if (x < current->key)
                current = current->left.get();
            else
                current = current->right.get();
        }
        return false;
    }

    // 要素数
    ll size() {
        if (!root) return 0;
        return root->size;
    }

    // index番目の値（0-origin）
    T operator[](ll index) const {
        assert(root);
        assert(0 <= index && index < root->size);
        Node *current = root.get();

        while (current) {
            ll left_size = (!current->left ? 0 : current->left->size);

            if (index < left_size) {
                current = current->left.get();
            } else if (index > left_size) {
                index -= left_size + 1; // +1はrootの分
                current = current->right.get();
            } else {
                break;
            }
        }
        return current->key;
    }

    // x未満の要素数
    ll index(const T &x) {
        return index_(x, false);
    }

    // x以下の要素数
    ll index_right(const T &x) {
        return index_(x, true);
    }

    // x未満の最大値
    optional<T> lt(const T &x) {
        return less_(x, false);
    }

    // x以下の最大値
    optional<T> le(const T &x) {
        return less_(x, true);
    }

    // x超過の最小値（upper_bound）
    optional<T> gt(const T &x) {
        return greater_(x, false);
    }

    // x以上の最小値（lower_bound）
    optional<T> ge(const T &x) {
        return greater_(x, true);
    }
};
// TreapSet<ll> trp = vl{0, 5};         // 0, 5を挿入したインスタンスを得る
// trp.insert(3);                    // 挿入, 重複する値は無視
// bool erased = trp.erase(3);       // 削除
// bool exists = trp.contains(3);    // 存在判定
// ll siz = trp.size();          // 要素数
// ll value = trp[i];                // i番目の値, 0-indexed
// ll num1 = trp.index(5);       // 5未満の要素数
// ll num2 = trp.index_right(5); // 5以下の要素数
// optional<ll> val1 = trp.lt(5);    // 5未満の最大値. 値取り出しは val1.value()
// optional<ll> val2 = trp.le(5);    // 5以下の最大値
// optional<ll> val3 = trp.gt(5);    // 5超過の最小値
// optional<ll> val4 = trp.ge(5);    // 5以上の最小値


int main() {
    cin.tie(nullptr); cout << fixed << setprecision(10);

    ll N;
    cin >> N;
    vl A(N);
    cin >> A;
    ll ans = 0;
    TreapSet<ll> trp;
    fore(a, A) trp.insert(a);
    ll to = N;

    while(1) {
        while(trp.contains(to)) {
            to--;
        }
        ll from = trp.lt(INF).value();
        debug(from, to);
        debug(ans);
        if (from == N) break;
        debug(trp.index(from), trp.index(to));
        ll cnt = trp.index(from) - trp.index(to);
        ans += from - to - cnt;
        trp.erase(from);
        trp.insert(to);
    }
    print(ans);
}