#line 1 "main.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1077"
#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

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

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

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

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

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

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

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

#define stoi stoll

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

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

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

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

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

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

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

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

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

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

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}

template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
  vc<T> &res = first;
  (res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 1 "/home/maspy/compro/library/other/io.hpp"
#define FASTIO
#include <unistd.h>

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

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

inline void load() {
  memcpy(ibuf, ibuf + pil, pir - pil);
  pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
  pil = 0;
  if (pir < SZ) ibuf[pir++] = '\n';
}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

#if defined(LOCAL)
#define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush()
#define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), flush()
#else
#define SHOW(...)
#endif

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

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

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 1 "/home/maspy/compro/library/convex/slope_trick/slope_trick_1.hpp"

#line 1 "/home/maspy/compro/library/ds/double_end_queue_const_add.hpp"
// 全体加算もできるようにしよう
// Monoid_Add<T> を渡す感じで. T は operator< が定義されている必要あり.
template <typename Monoid>
struct Double_End_Queue_Const_Add {
  using MX = Monoid;
  using T = typename MX::value_type;
  vector<T> dat;
  T add;

  Double_End_Queue_Const_Add() : add(MX::unit()) {}
  Double_End_Queue_Const_Add(vc<T>& A) : add(MX::unit()) { build(A); }

  int size() { return dat.size(); }
  bool empty() { return dat.empty(); }
  T min() { return MX::op(dat[0], add); }
  T max() { return MX::op(add, (len(dat) == 1 ? dat[0] : dat[1])); }

  void build(vc<T>& A) {
    add = MX::unit();
    dat = A;
    int n = len(dat);
    FOR_R(i, n) { down(i); }
  }
  void clear() {
    dat.clear(), dat.shrink_to_fit();
    add = 0;
  }

  void push(T x) { dat.eb(x - add), up(); }

  T pop_min() {
    assert(!dat.empty());
    swap(dat[0], dat.back());
    T res = POP(dat);
    down(0);
    return res + add;
  }

  T pop_max() {
    assert(!dat.empty());
    if (len(dat) <= 2) { return POP(dat) + add; }
    swap(dat[1], dat.back());
    T res = POP(dat);
    down(1);
    return res + add;
  }

  template <typename F>
  void enumerate_all(F f) {
    for (auto& x: dat) f(x + add);
  }

private:
  inline int parent(int i) { return (i - 4 + (i & 3)) / 2; }

  void down(int i) {
    int n = len(dat);
    if (i % 2 == 0) {
      while (1) {
        if (i + 1 < n && dat[i + 1] < dat[i]) swap(dat[i], dat[i + 1]);
        int j = i, l = 2 * i + 2, r = 2 * i + 4;
        if (l < n && dat[l] < dat[j]) j = l;
        if (r < n && dat[r] < dat[j]) j = r;
        if (i == j) break;
        swap(dat[i], dat[j]), i = j;
      }
    } else {
      while (1) {
        if (dat[i] < dat[i - 1]) swap(dat[i - 1], dat[i]);
        int j = i, l = 2 * i + 1, r = 2 * i + 3;
        if (r >= n) --r;
        if (l >= n) --l;
        if (l < n && dat[j] < dat[l]) j = l;
        if (r < n && dat[j] < dat[r]) j = r;
        if (i == j) break;
        swap(dat[i], dat[j]), i = j;
        if (i % 2 == 0) break;
      }
    }
  }

  void up() {
    int i = len(dat) - 1;
    if (2 <= i && i % 2 == 0) {
      int p = parent(i) ^ 1;
      if (dat[p] < dat[i]) { swap(dat[i], dat[p]), i = p; }
    }
    if (i % 2 == 1 && dat[i] < dat[i - 1]) { swap(dat[i - 1], dat[i]), --i; }
    if (i % 2 == 0) {
      while (i >= 2) {
        int p = parent(i);
        if (!(dat[i] < dat[p])) break;
        swap(dat[p], dat[i]), i = p;
      }
      return;
    }
    while (i >= 3) {
      int p = parent(i);
      if (!(dat[p] < dat[i])) break;
      swap(dat[p], dat[i]), i = p;
    }
  }
};
#line 2 "/home/maspy/compro/library/alg/monoid/add.hpp"

template <typename E>
struct Monoid_Add {
  using X = E;
  using value_type = X;
  static constexpr X op(const X &x, const X &y) noexcept { return x + y; }
  static constexpr X inverse(const X &x) noexcept { return -x; }
  static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; }
  static constexpr X unit() { return X(0); }
  static constexpr bool commute = true;
};
#line 4 "/home/maspy/compro/library/convex/slope_trick/slope_trick_1.hpp"

struct Slope_Trick_1 {
  struct FUNC {
    // 定義域の両端は que に入れることにして que が空でない状態を保つ
    Double_End_Queue_Const_Add<Monoid_Add<ll>> que_l, que_r;
    i128 min_f = 0;
    int size() { return que_l.size() + que_r.size(); }
  };

  // O(|a|)
  FUNC segment_func(ll L, ll R, ll a, ll b) {
    FUNC f;
    if (a >= 0) {
      f.min_f = i128(a) * L + b;
      f.que_l.push(L);
      FOR(a) f.que_r.push(L);
      f.que_r.push(R);
    } else {
      f.min_f = i128(a) * R + b;
      f.que_r.push(R);
      FOR(-a) f.que_l.push(R);
      f.que_l.push(L);
    }
    return f;
  }

  pair<ll, ll> domain(FUNC &f) { return {f.que_l.min(), f.que_r.max()}; }

  // O(N)
  i128 eval(FUNC &f, ll x) {
    auto [x0, x1] = domain(f);
    assert(x0 <= x && x <= x1);
    i128 ans = f.min_f;
    f.que_l.enumerate_all([&](ll l) -> void { ans += max<ll>(l - x, 0); });
    f.que_r.enumerate_all([&](ll r) -> void { ans += max<ll>(x - r, 0); });
    return ans;
  }

  // もとの min_f と定義域が交わる場合だけ実装した
  FUNC restrict_domain(FUNC &f, ll L, ll R) {
    auto [x0, x1] = domain(f);
    chmax(L, x0), chmin(R, x1);
    while (!f.que_l.empty() && f.que_l.min() <= L) { f.que_l.pop_min(); }
    while (!f.que_r.empty() && f.que_r.max() >= R) { f.que_r.pop_max(); }
    f.que_l.push(L);
    f.que_r.push(R);
    return f;
  }

  // +(ax+b), O(|a|*log)
  FUNC add_linear(FUNC &f, ll a, ll b) {
    auto [x0, x1] = domain(f);
    f.min_f += b;
    while (a > 0) {
      f.min_f += f.que_l.pop_max();
      f.que_r.push(f.que_l.pop_max());
      if (f.que_l.empty()) f.que_l.push(x0);
      --a;
    }
    while (a < 0) {
      f.min_f -= f.que_r.pop_min();
      f.que_l.push(f.que_r.pop_min());
      if (f.que_r.empty()) f.que_r.push(x0);
      ++a;
    }
    return f;
  }

  // (a-x)+
  FUNC add_a_minus_x(FUNC &f, ll a) {
    auto [x0, x1] = domain(f);
    assert(x0 <= x1);
    if (a <= x0) return f;
    if (x1 <= a) return add_linear(f, -1, a);
    ll x = f.que_r.min();
    f.min_f += max<ll>(a - x, 0);
    if (a <= x) {
      f.que_l.push(a);
    } else {
      f.que_l.push(f.que_r.pop_min());
      f.que_r.push(a);
    }
    return f;
  }

  // (x-a)+
  FUNC add_x_minus_a(FUNC &f, ll a) {
    auto [x0, x1] = domain(f);
    assert(x0 <= x1);
    if (a <= x0) return add_linear(f, 1, -a);
    if (x1 <= a) return f;
    ll x = f.que_l.max();
    f.min_f += max<ll>(x - a, 0);
    if (a >= x) {
      f.que_r.push(a);
    } else {
      f.que_r.push(f.que_l.pop_max());
      f.que_l.push(a);
    }
    return f;
  }

  // (x-a)+
  FUNC add_abs(FUNC &f, ll a) {
    f = add_a_minus_x(f, a);
    f = add_x_minus_a(f, a);
    return f;
  }

  FUNC clear_inc(FUNC &f) {
    auto [x0, x1] = domain(f);
    f.que_r.clear();
    f.que_r.push(x1);
    return f;
  }

  FUNC add(FUNC &f, FUNC &g) {
    auto [a0, a1] = domain(f);
    auto [b0, b1] = domain(g);
    ll x0 = max(a0, b0);
    ll x1 = min(a1, b1);
    assert(x0 <= x1);
    restrict_domain(f, x0, x1), restrict_domain(g, x0, x1);
    if (len(f) < len(g)) swap(f, g);
    f.min_f += g.min_f;
    for (auto l: g.que_l.dat) {
      l += g.que_l.add;
      // (l-x)+
      if (l <= f.que_r.min()) {
        f.que_l.push(l);
      } else {
        f.que_l.push(f.que_r.pop_min());
        f.que_r.push(l);
      }
      ll x = f.que_r.min();
      f.min_f += max<ll>(0, l - x);
    }
    return f;
  }

  // FUNC sum_all(vc<FUNC> &funcs) {}

  // FUNC shift(FUNC &f, T add_x, T add_y) {
  //   ST.apply(f.root, add_x);
  //   f.x0 += add_x, f.x1 += add_x, f.y0 += add_y;
  //   return f;
  // }

  // h[z]=min(x+y==z)f(x)+g(y)
  // FUNC convolve(FUNC &f, FUNC &g) {
  //   if (f.x0 > f.x1 || g.x0 > g.x1) { return {nullptr, infty<T>, -infty<T>, 0, 0}; }
  //   if (len(f) < len(g)) swap(f, g);
  //   shift(f, g.x0, g.y0), shift(g, -g.x0, -g.y0);
  //   if (len(g) == 0) { return convolve_segment(f, 0, g.x1, g.a0, 0); }
  //   auto tmp = ST.get_all(g.root);
  //   ST.free_subtree(g.root);
  //   f = convolve_segment(f, 0, tmp[0].fi, g.a0, 0);
  //   T a = g.a0;
  //   FOR(i, len(tmp)) {
  //     T nx = (i + 1 < len(tmp) ? tmp[i + 1].fi : g.x1);
  //     a += tmp[i].se;
  //     f = convolve_segment(f, 0, nx - tmp[i].fi, a, 0);
  //     for (auto &[x, a]: ST.get_all(f.root)) {
  //       assert(f.x0 <= x && x <= f.x1);
  //       if (f.root) assert(!f.root->p);
  //     }
  //   }
  //   return f;
  // }

  // [x0,x1], y=ax+b
  // FUNC convolve_segment(FUNC &f, T x0, T x1, T a, T b) {
  //   assert(x0 <= x1);
  //   if (f.x0 > f.x1) { return {nullptr, infty<T>, -infty<T>, 0, 0}; }
  //   f = shift(f, x0, a * x0 + b);
  //   T d = x1 - x0;
  //   if (d == 0) return f;
  //   // (0,0) から (x1,ax1) への線分をどこかに挿入する
  //   // 特に x0, y0 はこのままでよい
  //   if (f.x0 == f.x1) { return {nullptr, f.x0, f.x0 + d, a, f.y0}; }
  //   // 先頭に挿入できる場合
  //   if (a <= f.a0) {
  //     ST.apply(f.root, d);
  //     f.root = ST.merge(ST.new_node({f.x0 + d, f.a0 - a}), f.root);
  //     f.x1 += d, f.a0 = a;
  //     return f;
  //   }
  //   // 末尾に挿入できる場合
  //   T a_last = f.a0 + ST.prod(f.root).fi;
  //   if (a_last <= a) {
  //     f.root = ST.merge(f.root, ST.new_node({f.x1, a - a_last}));
  //     f.x1 += d;
  //     return f;
  //   }
  //   // 間のどこかに挿入
  //   auto [l, r] = ST.split_max_right_prod(f.root, [&](auto prod) -> bool { return f.a0 + prod.fi < a; });
  //   T asum = ST.prod(l).fi;
  //   T a1 = a - (asum + f.a0);
  //   auto [xx, aa] = ST.get(r, 0);
  //   ST.apply(r, d);
  //   ST.set(r, 0, {xx + d, aa - a1});
  //   f.root = ST.merge3(l, ST.new_node({xx, a1}), r);
  //   f.x1 += d;
  //   return f;
  // }

  // fx,x
  tuple<i128, ll, ll> get_min(FUNC &f) { return {f.min_f, f.que_l.max(), f.que_r.min()}; }
};
#line 5 "main.cpp"

void solve() {
  LL(N);
  Slope_Trick_1 X;
  using F = decltype(X)::FUNC;
  F f = X.segment_func(-infty<int>, infty<int>, 0, 0);

  FOR(N) {
    LL(x);
    f = X.add_abs(f, x);
    f = X.clear_inc(f);
  }

  auto [fx, lx, rx] = X.get_min(f);
  print(fx);
}

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