Problem p03173 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
using namespace std;

template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;
template <class T> using VVV = V<VV<T>>;
template <class S, class T> using P = pair<S, T>;
template <class... T> using TP = tuple<T...>;

using ll = long long;
using ull = unsigned long long;
using dbl = double;
using str = string;
using vll = V<ll>;
using vvll = V<vll>;
using vvvll = V<vvll>;
using pl = P<ll, ll>;
using tl = TP<ll, ll, ll>;
using vpl = V<pl>;
using vvpl = V<vpl>;
using vtl = V<tl>;
using vvtl = V<vtl>;
using vs = V<str>;
using vvs = V<vs>;
using vd = V<dbl>;
using vvd = V<vd>;
using vvvd = V<vvd>;
using qll = queue<ll>;
using qpl = queue<pl>;
using stll = stack<ll>;
using stpl = stack<pl>;
using mapll = map<ll, ll>;
using setll = set<ll>;
using pqll = priority_queue<ll>;

// #define int ll
#define fi first
#define se second
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define pob pop_back()
#define pf push_front
#define pof pop_front()
#define sz size()
#define bgn begin()
#define en end()
#define asn assign
#define emp empty()
#define fr front()
#define bk back()
#define clr clear()
#define ins insert
#define ers erase
#define res resize
#define tp top()
#define p_q priority_queue
#define inv inverse()

#define FOR(i, a, b) for (ll i = (a); i <= (ll)(b); i++)
#define rFOR(i, a, b) for (ll i = (b); i >= (ll)(a); i--)
#define REP(i, a) FOR((i), 0, (ll)(a)-1)
#define REP0(i, a) FOR((i), 0, (ll)(a))
#define REP1(i, a) FOR((i), 1, (ll)(a))
#define rREP(i, a) rFOR((i), 0, (ll)(a)-1)
#define rREP0(i, a) rFOR((i), 0, (ll)(a))
#define rREP1(i, a) rFOR((i), 1, (ll)(a))
#define ROR(v, i) for (auto &(i) : (v))
#define IOTA(a, n) iota((a).bgn, (a).en, (n))
#define SORT(a) sort((a).bgn, (a).en)
#define rSORT(a) sort((a).rbegin(), (a).rend())
#define UNIQUE(a) (a).erase(unique((a).bgn, (a).en), (a).en)
#define PREVP(a) prev_permutation((a).bgn, (a).en)
#define NEXTP(a) next_permutation((a).bgn, (a).en)
#define BINS(a, b) binary_search((a).bgn, (a).en, (b))
#define LOWB(a, b) (lower_bound((a).bgn, (a).en, (b)) - (a).bgn)
#define UPB(a, b) (upper_bound((a).bgn, (a).en, (b)) - (a).bgn)
#define CNT(a, b) count((a).bgn, (a).en, b)
#define SUM(a) accumulate((a).bgn, (a).en, 0)
#define REV(a) reverse((a).bgn, (a).en)
#define REGS(a, b) regex_search((a), regex(b))
#define REGM(a, b) regex_match((a), regex(b))
#define yn(a) cout << ((a) ? "yes" : "no") << "\n";
#define Yn(a) cout << ((a) ? "Yes" : "No") << "\n";
#define YN(a) cout << ((a) ? "YES" : "NO") << "\n";
#define imp(a) cout << ((a) ? "possible" : "impossible") << "\n";
#define Imp(a) cout << ((a) ? "Possible" : "Impossible") << "\n";
#define IMP(a) cout << ((a) ? "POSSIBLE" : "IMPOSSIBLE") << "\n";
#define fs(a) cout << ((a) ? "second" : "first") << "\n";
#define Fs(a) cout << ((a) ? "Second" : "First") << "\n";
#define FS(a) cout << ((a) ? "SECOND" : "FIRST") << "\n";
// #define say(a) cout <<(a);
// #define sal(a) cout <<(a)<<"\n";
#define sak cout << "\n";
#define sas cout << " ";
#define sat cout << "\t";
#define dbg(a) cerr << (#a) << ": " << (a) << "\n";
#define dbgs(...)                                                              \
  dal(#__VA_ARGS__);                                                           \
  dal(__VA_ARGS__);
#define c2l(a) ((ll)(a - 48))
#define a2l(a) ((ll)(a - 97))
#define A2l(a) ((ll)(a - 65))
#define l2c(a) ((char)(a + 48))
#define l2a(a) ((char)(a + 97))
#define l2A(a) ((char)(a + 65))
#define DigN2(a) ((llabs(a) == 0) ? (1) : ((ll)(log2(double(llabs(a)))) + 1))
#define DigN10(a) ((llabs(a) == 0) ? (1) : ((ll)(log10(double(llabs(a)))) + 1))
#define Dig2(a, b) (((a) >> (b)) & 1)
#define Dig10(a, b) (ll)(((a) / ((ll)(pow(10.0, (double)(b))))) % 10)
#define Pow2(a) ((ll)(1) << (a))
#define Pow10(a) ((ll)(pow(10.0, double(a))))
#define LSB(a) ((a) & (-(a)))
/*#define llin(a) ll (a);cin >>(a);
#define llin2(a,b) ll (a),(b);cin >>(a)>>(b);
#define llin3(a,b,c) ll (a),(b),(c);cin >>(a)>>(b)>>(c);
#define stin(a) string (a);cin >>(a);*/
#define vin(v)                                                                 \
  ROR((v), (i)) { cin >> (i); };
#define vllin(N, v)                                                            \
  vll(v)((N));                                                                 \
  vin(v);
#define vllin2(N, a, b)                                                        \
  vll(a)(N), (b)(N);                                                           \
  REP(i, N) { cin >> (a)[i] >> (b)[i]; };
#define vsin(N, v)                                                             \
  vs(v)((N));                                                                  \
  vin(v);
#define rdn(a, b) ((a) / (b))
#define rou(a, b)                                                              \
  ((((double(a) / double(b)) - ((a) / (b))) < 0.5) ? ((a) / (b))               \
                                                   : (((a) / (b)) + 1))
#define rup(a, b) ((((a) % (b)) == 0) ? ((a) / (b)) : (((a) / (b)) + 1))
#define powll(a, b) (ll)(pow((double)(a), (double)(b)))
#define Triangle(x1, y1, x2, y2, x3, y3)                                       \
  (((x1) - (x2)) * ((y1) - (y3)) - ((x1) - (x3)) * ((y1) - (y2)))
#define tg(t, i) get<i>(t)

#define Id(x) get<0>(x)
#define Act(x) get<1>(x)
#define InvAct(x) get<2>(x)
#define mg(id, act) mt(id, act, lam(l))
// #define MonoidSet(T) TP<T, function<T(T, T)>>
#define GroupSet(T) TP<T, function<T(T, T)>, function<T(T, T)>>
#define CompareSet(T) TP<T, function<bool(T, T)>>
#define lam(lr) ([](auto l, auto r) { return (lr); })
#define elam(lr) ([=](auto l, auto r) { return (lr); })
#define clam(lr) ([&](auto l, auto r) { return (lr); })
#define lamr(lr) ([](auto l, auto r) { lr })
#define elamr(lr) ([=](auto l, auto r) { lr })
#define clamr(lr) ([&](auto l, auto r) { lr })
#define min(...) Operation(MIN, __VA_ARGS__)
#define max(...) Operation(MAX, __VA_ARGS__)
#define gcd(...) Operation(GCD, __VA_ARGS__)
#define lcm(...) Operation(LCM, __VA_ARGS__)
#define vmin(...) VOperation(MIN, __VA_ARGS__)
#define vmax(...) VOperation(MAX, __VA_ARGS__)
#define vgcd(...) VOperation(GCD, __VA_ARGS__)
#define vlcm(...) VOperation(LCM, __VA_ARGS__)
#define vsum(...) VOperation(ADD, __VA_ARGS__)
#define vpro(...) VOperation(MUL, __VA_ARGS__)
#define emin(a, ...) ((a) = min((a), __VA_ARGS__))
#define emax(a, ...) ((a) = max((a), __VA_ARGS__))
#define egcd(a, ...) ((a) = gcd((a), __VA_ARGS__))
#define elcm(a, ...) ((a) = lcm((a), __VA_ARGS__))
#define ope Operation
#define vope VOperation

#define svll SumV<ll>
#define svvll SumV2<ll>

#define li(...)                                                                \
  ll __VA_ARGS__;                                                              \
  Input(__VA_ARGS__);
#define si(...)                                                                \
  str __VA_ARGS__;                                                             \
  Input(__VA_ARGS__);
// #define vli(size, ...) vll __VA_ARGS__;vInitInput(size,__VA_ARGS__);
#define vlr(size, ...)                                                         \
  vll __VA_ARGS__;                                                             \
  vInitInputR(size, __VA_ARGS__);
#define vlc(size, ...)                                                         \
  vll __VA_ARGS__;                                                             \
  vInitInputC(size, __VA_ARGS__);
#define vli(size, ...)                                                         \
  vll __VA_ARGS__;                                                             \
  vInitInputR(size, __VA_ARGS__);
#define vsr(size, ...)                                                         \
  vs __VA_ARGS__;                                                              \
  vInitInputR(size, __VA_ARGS__);
#define vsc(size, ...)                                                         \
  vs __VA_ARGS__;                                                              \
  vInitInputC(size, __VA_ARGS__);
#define vsi(size, ...)                                                         \
  vs __VA_ARGS__;                                                              \
  vInitInputR(size, __VA_ARGS__);
#define vli2(rowSize, columnSize, ...)                                         \
  vvll __VA_ARGS__;                                                            \
  vInitInput2(rowSize, columnSize, __VA_ARGS__);
#define vplr(size, ...)                                                        \
  vpl __VA_ARGS__;                                                             \
  vInitInputR(size, __VA_ARGS__);
#define vplc(size, ...)                                                        \
  vpl __VA_ARGS__;                                                             \
  vInitInputC(size, __VA_ARGS__);
#define vpli(size, ...)                                                        \
  vpl __VA_ARGS__;                                                             \
  vInitInputR(size, __VA_ARGS__);

const ll MOD = 1e9 + 7;
// const ll MOD = 998244353;
// const ll MOD = 924844033;
// const ll MOD = 9007199254740881;
const ll INF = 1LL << 60; // 1.15e18
const double PI = acos(-1.0);
const vll DX = {0, -1, 0, 1, 0, -1, 1, 1, -1};
const vll DY = {0, 0, -1, 0, 1, -1, -1, 1, 1};
const str alp = "abcdefghijklmnopqrstuvwxyz";
const str ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";

template <class T> auto GetVectorValueType(T v) { return v; }
template <class T> auto GetVectorValueType(V<T> v) {
  return GetVectorValueType(T());
}

template <class S, class T> istream &operator>>(istream &in, P<S, T> &p) {
  return in >> p.fi >> p.se;
}
template <class T> istream &operator>>(istream &in, V<T> &v) {
  REP(i, v.sz) in >> v[i];
  return in;
}

void Input() {}
template <class Var, class... Args> void Input(Var &var, Args &...args) {
  cin >> var;
  Input(args...);
}

void vInit(ll size) {}
template <class T, class... Args> void vInit(ll size, V<T> &v, Args &...args) {
  v.res(size);
  vInit(size, args...);
}
void vInput(ll size) {}
template <class T, class... Args> void vInput(ll size, V<T> &v, Args &...args) {
  REP(i, size) cin >> v[i];
  vInput(size, args...);
}
void vInputR(ll size) {}
template <class T, class... Args>
void vInputR(ll size, V<T> &v, Args &...args) {
  REP(i, size) cin >> v[i];
  vInputR(size, args...);
}
void vInputNumC(ll num) {}
template <class T, class... Args>
void vInputNumC(ll num, V<T> &v, Args &...args) {
  cin >> v[num];
  vInputNumC(num, args...);
}
void vInputC(ll size) {}
template <class... Args> void vInputC(ll size, Args &...args) {
  REP(i, size) vInputNumC(i, args...);
}
void vInitInputR(ll size) {}
template <class... Args> void vInitInputR(ll size, Args &...args) {
  vInit(size, args...);
  vInputR(size, args...);
}
void vInitInputC(ll size) {}
template <class... Args> void vInitInputC(ll size, Args &...args) {
  vInit(size, args...);
  vInputC(size, args...);
}
void vInit2(ll rowSize, ll columnSize) {}
template <class T, class... Args>
void vInit2(ll rowSize, ll columnSize, VV<T> &v, Args &...args) {
  v.asn(rowSize, V<T>(columnSize));
  vInit2(rowSize, columnSize, args...);
}
void vInput2(ll rowSize, ll columnSize) {}
template <class T, class... Args>
void vInput2(ll rowSize, ll columnSize, VV<T> &v, Args &...args) {
  REP(r, rowSize) {
    REP(c, columnSize) { cin >> v[r][c]; }
  }
  vInput2(rowSize, columnSize, args...);
}
void vInitInput2(ll rowSize, ll columnSize) {}
template <class... Args>
void vInitInput2(ll rowSize, ll columnSize, Args &...args) {
  vInit2(rowSize, columnSize, args...);
  vInput2(rowSize, columnSize, args...);
}

template <class S, class T>
ostream &operator<<(ostream &out, const P<S, T> &p) {
  return out << "[" << p.fi << ", " << p.se << "]";
}
template <class T> ostream &operator<<(ostream &out, V<T> &v) {
  if (v.emp)
    return out << "{}";
  else {
    auto itr = v.bgn;
    out << "{" << *itr;
    itr++;
    while (itr != v.en) {
      out << ", " << *itr;
      itr++;
    }
    out << "}";
    return out;
  }
}
template <class S, class T>
ostream &operator<<(ostream &out, const map<S, T> &m) {
  if (m.emp)
    return out << "<[]>";
  else {
    auto itr = m.bgn;
    out << "< [" << (itr->fi) << ": " << (itr->se);
    itr++;
    while (itr != m.en) {
      out << "], [" << (itr->fi) << ": " << (itr->se);
      itr++;
    }
    out << "] >";
    return out;
  }
}
template <class T> ostream &operator<<(ostream &out, const set<T> &s) {
  if (s.emp)
    return out << "<>";
  else {
    auto itr = s.bgn;
    out << "<" << *itr;
    itr++;
    while (itr != s.en) {
      out << ", " << *itr;
      itr++;
    }
    out << ">";
    return out;
  }
}

void say() {}
template <class T> void say(T t) { cout << t; }
template <class Head, class... Body> void say(Head head, Body... body) {
  cout << head << " ";
  say(body...);
}
void sal() { cout << "\n"; }
template <class... Args> void sal(Args... args) {
  say(args...);
  cout << "\n";
}

void day() {}
template <class T> void day(T t) { cerr << t; }
template <class Head, class... Body> void day(Head head, Body... body) {
  cerr << head << " ";
  day(body...);
}
void dal() { cerr << "\n"; }
template <class... Args> void dal(Args... args) {
  day(args...);
  cerr << "\n";
}

void salv() {}
template <class T> void salv(V<T> v) {
  if (v.emp)
    sal();
  else {
    auto itr = v.bgn;
    say(*itr);
    itr++;
    while (itr != v.en) {
      sas;
      say(*itr);
      itr++;
    }
    sak;
  }
}
template <class T> void salv(VV<T> v) {
  if (v.emp)
    sal();
  else {
    ROR(v, i) salv(i);
  }
}
template <class T, class... Args> void salv(T v, Args... args) {
  salv(v);
  salv(args...);
}

template <class L, class R> auto Gcd(L l, R r) -> decltype(l + r) {
  if (l < r)
    swap(l, r);
  return r ? Gcd(r, l % r) : l;
}
template <class L, class R> auto Lcm(L l, R r) {
  if (!l || !r)
    return 0;
  return l / Gcd(l, r) * r;
}

/*
auto LES = mp(INF, lam(return l < r;));
auto GRT = mp(-INF, lam(return l > r;));
auto EQ = mp(0, lam(return l == r;));

auto ADD = mp(0, lam(return l + r;));
auto SUB = mp(0, lam(return l - r;));
auto MUL = mp(1, lam(return l * r;));
auto DIV = mp(1, lam(return l / r;));
auto MDL = mp(1, lam(return l % r;));
auto XOR = mp(0, lam(return l ^ r;));
auto OR = mp(0, lam(return l | r;));
auto AND = mp(((ll)(1) << 63) - 1, lam(return l & r;));
auto MIN = mp(INF, lam(return (l < r) ? l : r;));
auto MAX = mp(-INF, lam(return (l > r) ? l : r;));
auto GCD = mp(0, lam(return Gcd(l, r);));
auto LCM = mp(1, lam(return Lcm(l, r);));
*/

auto LES = mp(INF, lam(l < r));
auto GRT = mp(-INF, lam(l > r));
auto EQ = mp(0, lam(l == r));

auto ADD = mt(0, lam(l + r), lam(l - r));
auto MUL = mt(1, lam(l *r), lam(l / r));
auto XOR = mt(0, lam(l ^ r), lam(l ^ r));
auto OR = mg(0, lam(l | r));
auto AND = mg(((ll)(1) << 63) - 1, lam(l &r));
auto MIN = mg(0, lam((l < r) ? l : r));
auto MAX = mg(0, lam((l > r) ? l : r));
auto GCD = mg(0, lam(Gcd(l, r)));
auto LCM = mg(0, lam(Lcm(l, r)));

template <class OperationType> auto Operation(OperationType A) { return Id(A); }
template <class OperationType, class T> auto Operation(OperationType A, T x) {
  return x;
}
template <class OperationType, class T, class... Args>
auto Operation(OperationType A, T x, Args... args) {
  auto tmp = Operation(A, args...);
  return Act(A)(x, tmp);
}

template <class OperationType> auto VOperation(OperationType A) {
  return Id(A);
}
template <class OperationType, class T> auto VOperation(OperationType A, T x) {
  return x;
}
template <class OperationType, class T>
auto VOperation(OperationType A, V<T> v) {
  if (v.emp) {
    decltype(GetVectorValueType(T())) tmp = Id(A);
    return tmp;
  }
  auto tmp = VOperation(A, v[0]);
  FOR(i, 1, v.sz - 1) tmp = Act(A)(tmp, VOperation(A, v[i]));
  return tmp;
}
template <class OperationType, class T, class... Args>
auto VOperation(OperationType A, T x, Args... args) {
  auto xResult = VOperation(A, x);
  auto tmp = VOperation(A, args...);
  return Act(A)(xResult, tmp);
}

ll Bset(ll a, ll b, ll c) {
  if (c)
    a |= b;
  else
    a &= ~b;
  return a;
}

struct UFT {

public:
  ll tsize;
  ll mode;
  vll par;
  vll rank;
  UFT(ll tsizeget, ll modeget = 0) {
    tsize = tsizeget;
    mode = modeget;
    par.asn(tsize, -1);
    if (!mode)
      rank.res(tsize, 0);
  }
  ll root(ll x) { return par[x] < 0 ? x : par[x] = root(par[x]); }
  bool isRoot(ll x) { return x == root(x); }
  bool same(ll x, ll y) { return root(x) == root(y); }
  void merge(ll x, ll y) {
    x = root(x);
    y = root(y);
    if (x == y)
      return;
    if (mode) {
      par[x] += par[y];
      par[y] = x;
    } else {
      if (rank[x] < rank[y]) {
        par[y] += par[x];
        par[x] = y;
      } else {
        par[x] += par[y];
        par[y] = x;
        if (rank[x] == rank[y])
          rank[x]++;
      }
    }
  }
  ll size(ll x) { return -par[root(x)]; }
};

template <class T> struct pUFT {

public:
  ll tsize;
  ll now;
  vll par;
  vll rank;
  vll mtime;
  vvll sizepi;
  VV<T> sizepv;
  V<T> elm;
  GroupSet(T) Add;

  pUFT(ll tsize, GroupSet(T) Add = ADD) : tsize(tsize), Add(Add) { init(); }
  void init() {
    now = 0;
    par.asn(tsize, -1);
    rank.asn(tsize, 0);
    mtime.asn(tsize, INF);
    sizepi.asn(tsize, {0});
    sizepv.asn(tsize, {});
  }
  void set(ll x, T s) {
    elm[x] = s;
    sizepv[x] = {s};
  }
  ll root(ll x, ll t) { return (mtime[x] > t) ? x : root(par[x], t); }
  bool same(ll x, ll y, ll t) { return root(x, t) == root(y, t); }
  ll merge(ll x, ll y) {
    now++;
    x = root(x, now);
    y = root(y, now);
    if (x != y) {
      if (rank[x] < rank[y]) {
        elm[y] = Act(Add)(elm[x], elm[y]);
        sizepi[y].pb(now);
        sizepv[y].pb(elm[y]);
        par[x] = y;
        mtime[x] = now;
      } else {
        elm[x] = Act(Add)(elm[x], elm[y]);
        sizepi[x].pb(now);
        sizepv[x].pb(elm[x]);
        par[y] = x;
        mtime[y] = now;
        if (rank[x] == rank[y])
          rank[x]++;
      }
    }
    return now;
  }
  T size(ll x, ll t) {
    x = root(x, t);
    return sizepv[x][UPB(sizepi[x], t) - 1];
  }
};

struct wUFT {
public:
  ll tsize;
  ll mode;
  vll par;
  vll rank;
  vll dweight;
  wUFT(ll tsizeget, ll modeget = 0) {
    tsize = tsizeget;
    mode = modeget;
    par.asn(tsize, -1);
    if (!mode)
      rank.res(tsize, 0);
    dweight.asn(tsize, 0);
  }
  ll root(ll x) {
    if (par[x] < 0)
      return x;
    else {
      ll r = root(par[x]);
      dweight[x] += dweight[par[x]];
      return par[x] = r;
    }
  }
  ll weight(ll x) {
    root(x);
    return dweight[x];
  }
  ll diff(ll x, ll y) { return weight(y) - weight(x); }
  bool isRoot(ll x) { return x == root(x); }
  bool same(ll x, ll y) { return root(x) == root(y); }
  void merge(ll x, ll y, ll w) {
    w += weight(x);
    w -= weight(y);
    x = root(x);
    y = root(y);
    if (x == y)
      return;
    if (mode) {
      par[x] += par[y];
      par[y] = x;
    } else {
      if (rank[x] < rank[y]) {
        par[y] += par[x];
        par[x] = y;
        dweight[x] = -w;
      } else {
        par[x] += par[y];
        par[y] = x;
        if (rank[x] == rank[y])
          rank[x]++;
        dweight[y] = w;
      }
    }
  }
  ll size(ll x) { return -par[root(x)]; }
};

template <class T> struct sUFT {

public:
  ll tsize;
  ll mode;
  vll par;
  vll rank;
  GroupSet(T) Add;
  V<T> elm;
  sUFT(ll tsize, GroupSet(T) Add = ADD, ll mode = 0)
      : tsize(tsize), Add(Add), mode(mode) {
    init();
  }
  void init() {
    par.asn(tsize, -1);
    if (!mode)
      rank.res(tsize, 0);
    elm.asn(tsize, Id(Add));
  }
  ll root(ll x) { return par[x] < 0 ? x : par[x] = root(par[x]); }
  bool isRoot(ll x) { return x == root(x); }
  bool same(ll x, ll y) { return root(x) == root(y); }
  void merge(ll x, ll y) {
    x = root(x);
    y = root(y);
    if (x == y)
      return;
    if (mode) {
      elm[x] = Act(Add)(elm[x], elm[y]);
      par[y] = x;
    } else {
      if (rank[x] < rank[y]) {
        elm[y] = Act(Add)(elm[x], elm[y]);
        par[x] = y;
      } else {
        elm[x] = Act(Add)(elm[x], elm[y]);
        par[y] = x;
        if (rank[x] == rank[y])
          rank[x]++;
      }
    }
  }
  T size(ll x) { return elm[root(x)]; }
  T &operator[](ll x) { return elm[x]; }
};

template <typename valtype> class SegT {

public:
  ll size;
  vector<valtype> v;

  valtype initv;
  function<valtype(valtype x, valtype y)> calc;

  SegT() {}
  SegT(const SegT &segt) {}

  SegT(ll sizeget, ll modeget = 0) {
    sizeset(sizeget);
    modeset(modeget);
    init();
  }
  SegT(vector<valtype> cpyvec, ll modeget = 0) {
    sizeset(cpyvec.sz);
    modeset(modeget);
    init();
    copy(cpyvec);
  }
  SegT(ll sizeget, valtype initvget,
       function<valtype(valtype x, valtype y)> calcget) {
    sizeset(sizeget);
    initv = initvget;
    calc = calcget;
    init();
  }
  SegT(vector<valtype> cpyvec, valtype initvget,
       function<valtype(valtype x, valtype y)> calcget) {
    sizeset(cpyvec.sz);
    initv = initvget;
    calc = calcget;
    init();
    copy(cpyvec);
  }
  void sizeset(ll rsize) {
    size = DigN2(rsize);
    if (rsize == Pow2(size - 1))
      size--;
    return;
  }
  void modeset(ll mode) {
    switch (mode) {
    case 0:
      initv = 0;
      calc = [](valtype x, valtype y) { return x + y; };
      break;
    case 1:
      initv = INF;
      calc = [](valtype x, valtype y) { return min(x, y); };
      break;
    case 2:
      initv = -INF;
      calc = [](valtype x, valtype y) { return max(x, y); };
      break;
    }
    return;
  }
  void init() { v.asn(Pow2(size + 1) - 1, initv); }
  void copy(vector<valtype> cpyvec) {
    REP(i, min(cpyvec.sz, Pow2(size))) set(i, cpyvec[i]);
  }
  ll i2v(ll i) const {
    if (i < 0 || i >= Pow2(size))
      return -1;
    return Pow2(size) + i - 1;
  }
  ll top(ll i) const {
    if (i == 0)
      return -1;
    return (i - 1) / 2;
  }
  pl bot(ll i) const {
    if (i + 1 >= Pow2(size))
      return mp(-1, -1);
    return mp(2 * i + 1, 2 * i + 2);
  }
  void set(ll i, valtype x) {
    i = i2v(i);
    v[i] = x;
    while (i > 0) {
      i = top(i);
      v[i] = calc(v[bot(i).fi], v[bot(i).se]);
    }
    return;
  }
  void add(ll i, valtype x) {
    set(i, v[i2v(i)] + x);
    return;
  }
  valtype operator[](const ll &i) const { return v[i2v(i)]; }
  //	valtype que(ll a = 0, ll b = Pow2(size) - 1) {
  valtype que(ll a, ll b) {
    if (a == b)
      return v[i2v(a)];
    if (a > b)
      return initv; // swap(a, b);
    valtype ans = initv;
    ll ai = i2v(a);
    ll bi = i2v(b);
    FOR(i, 1, size + 1) {
      if (a > b)
        break;
      if (a % Pow2(i)) {
        ans = calc(ans, v[ai]);
        a += Pow2(i - 1);
        ai = top(ai) + 1;
      } else {
        ai = top(ai);
      }
      if (a > b)
        break;
      if ((b + 1) % Pow2(i)) {
        ans = calc(ans, v[bi]);
        b -= Pow2(i - 1);
        bi = top(bi) - 1;
      } else {
        bi = top(bi);
      }
      if (a > b)
        break;
    }
    return ans;
  }
  valtype que(ll b) { return que(0, b); }
  valtype que() { return que(0, Pow2(size) - 1); }
};

/*template <class Type> class DP {

public:

        vector<Type> v;
        Type initv;
        vll size, block;

        DP() {}
        DP(const DP &dp) {}

        template<class... Args> DP(Args... args) {
                block.asn(1, 1);
                Initialize(args...);
        }

        void Initialize(Type initv_) {
                initv = initv_;
                v.asn(block.bk, initv);
        }
        template<class... Args> void Initialize(ll val, Args... args) {
                size.pb(val);
                block.pb(block.bk*val);
                Initialize(args...);
        }



};*/

pl Bezout(ll a, ll b) {
  if (b != 0) {
    pl xy;
    xy = Bezout(b, a % b);
    return mp(xy.se, xy.fi - ((a / b) * xy.se));
  } else {
    return mp(1, 0);
  }
}
pl Bez(ll a, ll b, ll c) {
  pl xy;
  ll x, y, z, gc;
  xy = Bezout(a, b);
  gc = gcd(a, b);
  if (c % gc != 0)
    return mp(-1, -1);
  x = xy.fi * (c / gc);
  y = xy.se * (c / gc);
  if (x < 0)
    z = rup(-x, (b / gc));
  if (x >= 0)
    z = -x / (b / gc);
  x += z * (b / gc);
  y -= z * (a / gc);
  return mp(x, y);
}

ll DigS10(ll n) {
  ll ans = 0;
  while (1) {
    ans += n % 10;
    n /= 10;
    if (!n)
      break;
  }
  return ans;
}

ll isP(ll n) {
  if (n <= 1)
    return 0;
  FOR(i, 2, (ll)sqrt(n) + 1) {
    if (n % i == 0)
      return 0;
  }
  return 1;
}

ll Tot(ll n) {
  if (n <= 0)
    return 0;
  ll ans = n, x = 2;
  while (x * x <= n) {
    if (n % x == 0) {
      ans -= ans / x;
      while (n % x == 0)
        n /= x;
    }
    x++;
  }
  if (n > 1)
    ans -= ans / n;
  return ans;
}

template <class T> struct Graph {
public:
  ll vSize;
  ll eMode;
  ll mapMode;
  GroupSet(T) Add;
  CompareSet(T) Less;
  CompareSet(T) Equal;
  VV<P<T, ll>> adj;
  map<pl, T> len;
  Graph(ll vSize, ll eMode = 0, ll mapMode = 0, GroupSet(T) Add = ADD,
        CompareSet(T) Less = LES, CompareSet(T) Equal = EQ)
      : vSize(vSize), eMode(eMode), mapMode(mapMode), Add(Add), Less(Less),
        Equal(Equal) {}
  void Init() { adj.asn(vSize, V<P<T, ll>>()); }
  void AddE(ll x, ll y, T cost) {
    iAddE(x, y, cost);
    if (!eMode)
      iAddE(y, x, cost);
  }
  void iAddE(ll x, ll y, T cost) {
    adj[x].pb(mp(cost, y));
    if (mapMode)
      len[mp(x, y)] = cost;
  }
  P<bool, T> getE(ll x, ll y) {
    if (!len.count(mp(x, y)))
      return mp(false, Id(Less));
    return mp(true, len[mp(x, y)]);
  }
  V<T> Dijk(ll x) {
    V<T> ans(vSize, Id(Less));
    if (x < 0 || x >= vSize)
      return ans;
    SegT<P<T, ll>> segt(vSize, mp(Id(Less), -1),
                        clamr(if (l.se < 0) return r; if (r.se < 0) return l;
                              return Act(Less)(l.fi, r.fi) ? l : r;));
    segt.set(x, mp(Id(Add), x));
    P<T, ll> now;
    while ((now = segt.que(0, vSize - 1)).se >= 0) {
      ans[now.se] = segt[now.se].fi;
      segt.set(now.se, mp(Id(Less), -2));
      ROR(adj[now.se], i) {
        if (segt[i.se].se == -2)
          continue;
        if (segt[i.se].se == -1) {
          segt.set(i.se, mp(Act(Add)(ans[now.se], i.fi), i.se));
          continue;
        }
        if (Act(Less)(Act(Add)(ans[now.se], i.fi), segt[i.se].fi)) {
          segt.set(i.se, mp(Act(Add)(ans[now.se], i.fi), i.se));
          continue;
        }
      }
    }
    return ans;
  }
  V<P<T, vll>> rDijk(ll x) {
    V<P<T, vll>> ans(vSize, mp(Id(Less), vll()));
    if (x < 0 || x >= vSize)
      return ans;
    SegT<P<T, ll>> segt(vSize, mp(Id(Less), -1),
                        clamr(if (l.se < 0) return r; if (r.se < 0) return l;
                              return Act(Less)(l.fi, r.fi) ? l : r;));
    segt.set(x, mp(Id(Add), x));
    P<T, ll> now;
    while ((now = segt.que(0, vSize - 1)).se >= 0) {
      ans[now.se].fi = segt[now.se].fi;
      segt.set(now.se, mp(Id(Less), -2));
      ROR(adj[now.se], i) {
        if (segt[i.se].se == -2)
          continue;
        if (segt[i.se].se == -1) {
          segt.set(i.se, mp(Act(Add)(ans[now.se].fi, i.fi), i.se));
          ans[i.se].se = {now.se};
          continue;
        }
        if (Act(Less)(Act(Add)(ans[now.se].fi, i.fi), segt[i.se].fi)) {
          segt.set(i.se, mp(Act(Add)(ans[now.se].fi, i.fi), i.se));
          ans[i.se].se = {now.se};
          continue;
        }
        if (Act(Equal)(Act(Add)(ans[now.se].fi, i.fi), segt[i.se].fi)) {
          ans[i.se].se.pb(now.se);
          continue;
        }
      }
    }
    return ans;
  }

  T Prim(ll x = 0) {
    T ans = Id(Add);
    if (x < 0 || x >= vSize)
      return ans;
    SegT<P<T, ll>> segt(vSize, mp(Id(Less), -1),
                        clamr(if (l.se < 0) return r; if (r.se < 0) return l;
                              return Act(Less)(l.fi, r.fi) ? l : r;));
    segt.set(x, mp(Id(Add), x));
    P<T, ll> now;
    while ((now = segt.que(0, vSize - 1)).se >= 0) {
      ans = Act(Add)(ans, segt[now.se].fi);
      segt.set(now.se, mp(Id(Less), -2));
      ROR(adj[now.se], i) {
        if (segt[i.se].se == -2)
          continue;
        if (segt[i.se].se == -1) {
          segt.set(i.se, i);
          continue;
        }
        if (Act(Less)(i.fi, segt[i.se].fi)) {
          segt.set(i.se, i);
          continue;
        }
      }
    }
    return ans;
  }

  P<T, V<P<T, vll>>> rPrim(ll x = 0) {
    P<T, V<P<T, vll>>> ans =
        mp(Id(Add), V<P<T, vll>>(vSize, mp(Id(Less), vll())));
    if (x < 0 || x >= vSize)
      return ans;
    SegT<P<T, ll>> segt(vSize, mp(Id(Less), -1),
                        clamr(if (l.se < 0) return r; if (r.se < 0) return l;
                              return Act(Less)(l.fi, r.fi) ? l : r;));
    segt.set(x, mp(Id(Add), x));
    P<T, ll> now;
    while ((now = segt.que(0, vSize - 1)).se >= 0) {
      ans.se[now.se].fi = segt[now.se].fi;
      ans.fi = Act(Add)(ans.fi, ans.se[now.se].fi);
      segt.set(now.se, mp(Id(Less), -2));
      ROR(adj[now.se], i) {
        if (segt[i.se].se == -2)
          continue;
        if (segt[i.se].se == -1) {
          segt.set(i.se, i);
          ans.se[i.se].se = {now.se};
          continue;
        }
        if (Act(Less)(i.fi, segt[i.se].fi)) {
          segt.set(i.se, i);
          ans.se[i.se].se = {now.se};
          continue;
        }
        if (Act(Equal)(i.fi, segt[i.se].fi)) {
          ans.se[i.se].se.pb(now.se);
          continue;
        }
      }
    }
    return ans;
  }
};

template <class T> struct Sum {
public:
  V<T> v, s;
  ll size;
  GroupSet(T) Add;
  Sum(V<T> v, GroupSet(T) Add = ADD) : v(v), size(v.sz), Add(Add) {
    Init();
    Calc();
  }
  void Init() { s.asn(size + 1, Id(Add)); }
  void Calc() { REP(i, size) s[i + 1] = Act(Add)(s[i], v[i]); }
  T operator()(ll x) {
    if (x < -1)
      x = -1;
    if (x > size - 1)
      x = size - 1;
    return s[x + 1];
  }
  T operator()(ll l, ll r) {
    if (l < 0)
      l = 0;
    if (r >= size)
      r = size - 1;
    if (l > r)
      return Id(Add);
    return InvAct(Add)(s[r + 1], s[l]);
  }
};
using sumll = Sum<ll>;

template <class T> struct Sum2 {
public:
  VV<T> v, s;
  ll RowSize, ColumnSize;
  GroupSet(T) Add;
  Sum2(VV<T> v, GroupSet(T) Add = ADD)
      : v(v), RowSize(v.sz), ColumnSize(v.sz ? v[0].sz : 0), Add(Add) {
    Init();
    Calc();
  }
  void Init() { s.asn(RowSize + 1, V<T>(ColumnSize + 1, Id(Add))); }
  void Calc() {
    REP1(r, RowSize) {
      REP1(c, ColumnSize) {
        //				s[r][c] = InvAct(Add)(Act(Add)(Act(Add)(v[r -
        //1][c - 1], operator()(r - 1, c - 2)), operator()(r - 2, c - 1)),
        //operator()(r - 2, c - 2));
        s[r][c] = Act(Add)(s[r][c - 1], v[r - 1][c - 1]);
      }
    }
    REP1(r, RowSize) {
      REP1(c, ColumnSize) { s[r][c] = Act(Add)(s[r - 1][c], s[r][c]); }
    }
  }
  T operator()(ll r, ll c) {
    if (r < -1)
      r = -1;
    if (c < -1)
      c = -1;
    if (r > RowSize - 1)
      r = RowSize - 1;
    if (c > ColumnSize - 1)
      c = ColumnSize - 1;
    return s[r + 1][c + 1];
  }
  T operator()(ll r1, ll c1, ll r2, ll c2) {
    if (r1 < 0)
      r1 = 0;
    if (c1 < 0)
      c1 = 0;
    if (r2 >= RowSize)
      r2 = RowSize - 1;
    if (c2 >= ColumnSize)
      c2 = ColumnSize - 1;
    if (r1 > r2)
      return Id(Add);
    if (c1 > c2)
      return Id(Add);
    return InvAct(Add)(Act(Add)(s[r2 + 1][c2 + 1], s[r1][c1]),
                       Act(Add)(s[r2 + 1][c1], s[r1][c2 + 1]));
  }
};
using sumll2 = Sum2<ll>;

template <class T> struct Point2 {
public:
  VV<T> v;
  ll h, w;
  Point2() : h(0), w(0) {}
  Point2(ll h, ll w) : h(h), w(w) { asn(h, w); }
  Point2(ll h, ll w, T val) : h(h), w(w) { asn(h, w, val); }
  Point2(VV<T> cv) : h(cv.sz), w(cv.sz ? cv[0].sz : 0) {
    asn(h, w);
    copy(cv);
  }
  void assign(ll h, ll w) { v.asn(h, V<T>(w)); }
  void assign(ll h, ll w, ll val) { v.asn(h, V<T>(w, val)); }
  void copy(VV<T> cv) { REP(_h, h) REP(_w, w) v[_h][_w] = cv[_h][_w]; }
  T &operator()(ll h, ll w) { return v[h][w]; }
  T &operator()(pl p) { return v[p.fi][p.se]; }
  T &operator[](pl p) { return v[p.fi][p.se]; }
};
template <class T> using P2 = Point2<T>;

template <ll Mod> struct Modll {
public:
  ll v;
  Modll() : v(0) {}
  Modll(ll _v) { set(_v % Mod + Mod); }
  Modll &set(ll _v) {
    v = (_v < Mod) ? _v : (_v - Mod);
    return *this;
  }
  Modll pow(ll n) const {
    Modll x = *this, ans = 1;
    while (n) {
      if (n & 1)
        ans *= x;
      x *= x;
      n >>= 1;
    }
    return ans;
  }
  Modll inverse() const { return (*this).pow(Mod - 2); }
  Modll operator+(const Modll &m) const { return Modll().set(v + m.v); }
  Modll operator-(const Modll &m) const { return Modll().set(Mod + v - m.v); }
  Modll operator*(const Modll &m) const {
    return Modll().set((ull(v) * m.v) % Mod);
  }
  Modll operator/(const Modll &m) const { return *this * m.inv; }
  Modll &operator+=(const Modll &m) { return *this = *this + m; }
  Modll &operator-=(const Modll &m) { return *this = *this - m; }
  Modll &operator*=(const Modll &m) { return *this = *this * m; }
  Modll &operator/=(const Modll &m) { return *this = *this / m; }
  Modll operator-() const { return Modll(0) - *this; }
  explicit operator bool() const { return v != 0; }
  friend istream &operator>>(istream &in, Modll &m) { return in >> m.v; }
  friend ostream &operator<<(ostream &out, const Modll &m) {
    return out << m.v;
  }
};
using mll = Modll<MOD>;
using vmll = V<mll>;
using vvmll = V<vmll>;
using vvvmll = V<vvmll>;

vmll MFactMemo(2, 1);
vmll MIFactMemo(2, 1);

mll mFact(ll n) {
  if (MFactMemo.sz <= n) {
    ll oldsize = MFactMemo.sz;
    MFactMemo.res(n + 1, 1);
    FOR(i, oldsize, n) MFactMemo[i] = MFactMemo[i - 1] * i;
  }
  return MFactMemo[n];
}
mll miFact(ll n) {
  if (MIFactMemo.sz <= n) {
    ll oldsize = MIFactMemo.sz;
    MIFactMemo.res(n + 1, 1);
    MIFactMemo.bk = mFact(n).inv;
    rFOR(i, oldsize + 1, n) MIFactMemo[i - 1] = MIFactMemo[i] * i;
  }
  return MIFactMemo[n];
}
mll mComb(ll n, ll k) {
  if (n < 0 || k < 0 || n < k)
    return 0;
  return mFact(n) * miFact(k) * miFact(n - k);
}

ll LIS(vll v, ll m = 0) {

  if (v.sz > 0) {
    ll ans = 0;
    vll dp(v.sz, INF);
    FOR(i, 0, v.sz - 1) { dp[m ? UPB(dp, v[i]) : LOWB(dp, v[i])] = v[i]; }
    FOR(i, 0, v.sz - 1) {
      if (dp[i] == INF)
        break;
      ans++;
    }
    return ans;
  } else {
    return 0;
  }
}

ll Bsrch(function<bool(ll x)> f, ll mi, ll ma) {
  ll ng = mi - 1, ok = ma, mid;
  while (ok - ng > 1) {
    mid = (ng + ok) / 2;
    (f(mid) ? ok : ng) = mid;
  }
  return ok;
}

template <class T, class M = decltype(MUL), class S = decltype(ADD)>
VV<T> MultiMatrix(VV<T> A, VV<T> B, M Mul = MUL, S Add = ADD) {
  VV<T> ans;
  ll ii = A.sz;
  if (!ii)
    return ans;
  ll jj = A[0].sz;
  if (!jj)
    return ans;
  ll jj2 = B.sz;
  if (!jj2)
    return ans;
  if (jj != jj2)
    return ans;
  ll kk = B[0].sz;
  if (!kk)
    return ans;
  ans.asn(ii, V<T>(kk, 0));
  REP(i, ii) {
    REP(k, kk) {
      REP(j, jj) {
        ans[i][k] = Act(Add)(ans[i][k], Act(Mul)(A[i][j], B[j][k]));
      }
    }
  }
  return ans;
}

vvll CombMemo(1000, vll(1000, -1));

ll Comb(ll n, ll k) {
  if ((n < 0) || (k < 0))
    return 0;
  if (CombMemo[n][k] == -1) {
    if (n < k)
      CombMemo[n][k] = 0;
    else {
      if (n == 0)
        CombMemo[n][k] = 1;
      else if (k == 0)
        CombMemo[n][k] = 1;
      else if (n == k)
        CombMemo[n][k] = 1;
      else
        CombMemo[n][k] = Comb(n - 1, k - 1) + Comb(n - 1, k);
    }
  }
  return CombMemo[n][k];
}

template <class T> map<T, ll> Dict(V<T> v) {
  map<T, ll> m;
  if (!v.sz)
    return m;
  SORT(v);
  UNIQUE(v);
  REP(i, v.sz) { m[v[i]] = i; }
  return m;
}

template <class T> vll Cmprs(V<T> v) {
  auto m = Dict(v);
  vll ans(v.sz);
  REP(i, v.sz) { ans[i] = m[v[i]]; }
  return ans;
}

template <class T> vll PCmprs(V<T> v) {
  if (v.sz == 0)
    return V<T>();
  vll tmp(v.sz);
  vll ans(v.sz);
  IOTA(tmp, 0);
  IOTA(ans, 0);
  sort(tmp.bgn, tmp.en, clam(v[l] < v[r]));
  sort(ans.bgn, ans.en, clam(tmp[l] < tmp[r]));
  return ans;
}

ll BblCnt(vll rv) {
  vll v = PCmprs(rv);
  SegT<ll> b(v.sz, 0);
  ll ans = 0;
  REP(i, v.sz) {
    ans += (i - b.que(0, v[i]));
    b.add(v[i], 1);
  }
  return ans;
}

pl NGrid(pl p, ll i, ll H, ll W) {
  p = mp(p.fi + DX[i], p.se + DY[i]);
  if (p.fi < 0 || p.fi >= H || p.se < 0 || p.se >= W)
    return mp(INF, INF);
  return p;
}

vvll llGrid(vs v) {
  vvll r(v.sz, vll(v.sz ? v[0].sz : 0, 0));
  REP(h, v.sz) REP(w, v.sz ? v[0].sz : 0) r[h][w] = (v[h][w] == '#');
  return r;
}

template <class T> auto ven(T val) { return val; }
template <> auto ven<int>(int val) { return (ll)val; }
template <class T, class... Args> auto ven(T val, Args... args) {
  auto tmp = ven(args...);
  return V<decltype(tmp)>(val, tmp);
}

template <class T> void zind(T &v) { v--; }
template <class T> void zind(V<T> &v) { ROR(v, i) zind(i); }
template <class T, class... Args> void zind(T &v, Args &...args) {
  zind(v);
  zind(args...);
}

void Solve();

signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << setprecision(20) << fixed;
  Solve();
}

ll N;
vll a;
vll b;
vvll dp;

ll rec(ll x, ll y) {
  if (x == y)
    return dp[x][y] = 0;
  ll tmp = INF;
  FOR(i, x, y - 1) { emin(tmp, rec(x, i) + rec(i + 1, y) + b[y + 1] - b[x]); }
  return dp[x][y] = tmp;
}

void Solve() {

  cin >> N;
  a = ven(N, 0);
  b = ven(N + 1, 0);
  dp = ven(N, N, -1);
  vInput(N, a);
  REP1(i, N) b[i] = b[i - 1] + a[i - 1];
  sal(rec(0, N - 1));
}

Fixed submission:
#include <bits/stdc++.h>
using namespace std;

template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;
template <class T> using VVV = V<VV<T>>;
template <class S, class T> using P = pair<S, T>;
template <class... T> using TP = tuple<T...>;

using ll = long long;
using ull = unsigned long long;
using dbl = double;
using str = string;
using vll = V<ll>;
using vvll = V<vll>;
using vvvll = V<vvll>;
using pl = P<ll, ll>;
using tl = TP<ll, ll, ll>;
using vpl = V<pl>;
using vvpl = V<vpl>;
using vtl = V<tl>;
using vvtl = V<vtl>;
using vs = V<str>;
using vvs = V<vs>;
using vd = V<dbl>;
using vvd = V<vd>;
using vvvd = V<vvd>;
using qll = queue<ll>;
using qpl = queue<pl>;
using stll = stack<ll>;
using stpl = stack<pl>;
using mapll = map<ll, ll>;
using setll = set<ll>;
using pqll = priority_queue<ll>;

// #define int ll
#define fi first
#define se second
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define pob pop_back()
#define pf push_front
#define pof pop_front()
#define sz size()
#define bgn begin()
#define en end()
#define asn assign
#define emp empty()
#define fr front()
#define bk back()
#define clr clear()
#define ins insert
#define ers erase
#define res resize
#define tp top()
#define p_q priority_queue
#define inv inverse()

#define FOR(i, a, b) for (ll i = (a); i <= (ll)(b); i++)
#define rFOR(i, a, b) for (ll i = (b); i >= (ll)(a); i--)
#define REP(i, a) FOR((i), 0, (ll)(a)-1)
#define REP0(i, a) FOR((i), 0, (ll)(a))
#define REP1(i, a) FOR((i), 1, (ll)(a))
#define rREP(i, a) rFOR((i), 0, (ll)(a)-1)
#define rREP0(i, a) rFOR((i), 0, (ll)(a))
#define rREP1(i, a) rFOR((i), 1, (ll)(a))
#define ROR(v, i) for (auto &(i) : (v))
#define IOTA(a, n) iota((a).bgn, (a).en, (n))
#define SORT(a) sort((a).bgn, (a).en)
#define rSORT(a) sort((a).rbegin(), (a).rend())
#define UNIQUE(a) (a).erase(unique((a).bgn, (a).en), (a).en)
#define PREVP(a) prev_permutation((a).bgn, (a).en)
#define NEXTP(a) next_permutation((a).bgn, (a).en)
#define BINS(a, b) binary_search((a).bgn, (a).en, (b))
#define LOWB(a, b) (lower_bound((a).bgn, (a).en, (b)) - (a).bgn)
#define UPB(a, b) (upper_bound((a).bgn, (a).en, (b)) - (a).bgn)
#define CNT(a, b) count((a).bgn, (a).en, b)
#define SUM(a) accumulate((a).bgn, (a).en, 0)
#define REV(a) reverse((a).bgn, (a).en)
#define REGS(a, b) regex_search((a), regex(b))
#define REGM(a, b) regex_match((a), regex(b))
#define yn(a) cout << ((a) ? "yes" : "no") << "\n";
#define Yn(a) cout << ((a) ? "Yes" : "No") << "\n";
#define YN(a) cout << ((a) ? "YES" : "NO") << "\n";
#define imp(a) cout << ((a) ? "possible" : "impossible") << "\n";
#define Imp(a) cout << ((a) ? "Possible" : "Impossible") << "\n";
#define IMP(a) cout << ((a) ? "POSSIBLE" : "IMPOSSIBLE") << "\n";
#define fs(a) cout << ((a) ? "second" : "first") << "\n";
#define Fs(a) cout << ((a) ? "Second" : "First") << "\n";
#define FS(a) cout << ((a) ? "SECOND" : "FIRST") << "\n";
// #define say(a) cout <<(a);
// #define sal(a) cout <<(a)<<"\n";
#define sak cout << "\n";
#define sas cout << " ";
#define sat cout << "\t";
#define dbg(a) cerr << (#a) << ": " << (a) << "\n";
#define dbgs(...)                                                              \
  dal(#__VA_ARGS__);                                                           \
  dal(__VA_ARGS__);
#define c2l(a) ((ll)(a - 48))
#define a2l(a) ((ll)(a - 97))
#define A2l(a) ((ll)(a - 65))
#define l2c(a) ((char)(a + 48))
#define l2a(a) ((char)(a + 97))
#define l2A(a) ((char)(a + 65))
#define DigN2(a) ((llabs(a) == 0) ? (1) : ((ll)(log2(double(llabs(a)))) + 1))
#define DigN10(a) ((llabs(a) == 0) ? (1) : ((ll)(log10(double(llabs(a)))) + 1))
#define Dig2(a, b) (((a) >> (b)) & 1)
#define Dig10(a, b) (ll)(((a) / ((ll)(pow(10.0, (double)(b))))) % 10)
#define Pow2(a) ((ll)(1) << (a))
#define Pow10(a) ((ll)(pow(10.0, double(a))))
#define LSB(a) ((a) & (-(a)))
/*#define llin(a) ll (a);cin >>(a);
#define llin2(a,b) ll (a),(b);cin >>(a)>>(b);
#define llin3(a,b,c) ll (a),(b),(c);cin >>(a)>>(b)>>(c);
#define stin(a) string (a);cin >>(a);*/
#define vin(v)                                                                 \
  ROR((v), (i)) { cin >> (i); };
#define vllin(N, v)                                                            \
  vll(v)((N));                                                                 \
  vin(v);
#define vllin2(N, a, b)                                                        \
  vll(a)(N), (b)(N);                                                           \
  REP(i, N) { cin >> (a)[i] >> (b)[i]; };
#define vsin(N, v)                                                             \
  vs(v)((N));                                                                  \
  vin(v);
#define rdn(a, b) ((a) / (b))
#define rou(a, b)                                                              \
  ((((double(a) / double(b)) - ((a) / (b))) < 0.5) ? ((a) / (b))               \
                                                   : (((a) / (b)) + 1))
#define rup(a, b) ((((a) % (b)) == 0) ? ((a) / (b)) : (((a) / (b)) + 1))
#define powll(a, b) (ll)(pow((double)(a), (double)(b)))
#define Triangle(x1, y1, x2, y2, x3, y3)                                       \
  (((x1) - (x2)) * ((y1) - (y3)) - ((x1) - (x3)) * ((y1) - (y2)))
#define tg(t, i) get<i>(t)

#define Id(x) get<0>(x)
#define Act(x) get<1>(x)
#define InvAct(x) get<2>(x)
#define mg(id, act) mt(id, act, lam(l))
// #define MonoidSet(T) TP<T, function<T(T, T)>>
#define GroupSet(T) TP<T, function<T(T, T)>, function<T(T, T)>>
#define CompareSet(T) TP<T, function<bool(T, T)>>
#define lam(lr) ([](auto l, auto r) { return (lr); })
#define elam(lr) ([=](auto l, auto r) { return (lr); })
#define clam(lr) ([&](auto l, auto r) { return (lr); })
#define lamr(lr) ([](auto l, auto r) { lr })
#define elamr(lr) ([=](auto l, auto r) { lr })
#define clamr(lr) ([&](auto l, auto r) { lr })
#define min(...) Operation(MIN, __VA_ARGS__)
#define max(...) Operation(MAX, __VA_ARGS__)
#define gcd(...) Operation(GCD, __VA_ARGS__)
#define lcm(...) Operation(LCM, __VA_ARGS__)
#define vmin(...) VOperation(MIN, __VA_ARGS__)
#define vmax(...) VOperation(MAX, __VA_ARGS__)
#define vgcd(...) VOperation(GCD, __VA_ARGS__)
#define vlcm(...) VOperation(LCM, __VA_ARGS__)
#define vsum(...) VOperation(ADD, __VA_ARGS__)
#define vpro(...) VOperation(MUL, __VA_ARGS__)
#define emin(a, ...) ((a) = min((a), __VA_ARGS__))
#define emax(a, ...) ((a) = max((a), __VA_ARGS__))
#define egcd(a, ...) ((a) = gcd((a), __VA_ARGS__))
#define elcm(a, ...) ((a) = lcm((a), __VA_ARGS__))
#define ope Operation
#define vope VOperation

#define svll SumV<ll>
#define svvll SumV2<ll>

#define li(...)                                                                \
  ll __VA_ARGS__;                                                              \
  Input(__VA_ARGS__);
#define si(...)                                                                \
  str __VA_ARGS__;                                                             \
  Input(__VA_ARGS__);
// #define vli(size, ...) vll __VA_ARGS__;vInitInput(size,__VA_ARGS__);
#define vlr(size, ...)                                                         \
  vll __VA_ARGS__;                                                             \
  vInitInputR(size, __VA_ARGS__);
#define vlc(size, ...)                                                         \
  vll __VA_ARGS__;                                                             \
  vInitInputC(size, __VA_ARGS__);
#define vli(size, ...)                                                         \
  vll __VA_ARGS__;                                                             \
  vInitInputR(size, __VA_ARGS__);
#define vsr(size, ...)                                                         \
  vs __VA_ARGS__;                                                              \
  vInitInputR(size, __VA_ARGS__);
#define vsc(size, ...)                                                         \
  vs __VA_ARGS__;                                                              \
  vInitInputC(size, __VA_ARGS__);
#define vsi(size, ...)                                                         \
  vs __VA_ARGS__;                                                              \
  vInitInputR(size, __VA_ARGS__);
#define vli2(rowSize, columnSize, ...)                                         \
  vvll __VA_ARGS__;                                                            \
  vInitInput2(rowSize, columnSize, __VA_ARGS__);
#define vplr(size, ...)                                                        \
  vpl __VA_ARGS__;                                                             \
  vInitInputR(size, __VA_ARGS__);
#define vplc(size, ...)                                                        \
  vpl __VA_ARGS__;                                                             \
  vInitInputC(size, __VA_ARGS__);
#define vpli(size, ...)                                                        \
  vpl __VA_ARGS__;                                                             \
  vInitInputR(size, __VA_ARGS__);

const ll MOD = 1e9 + 7;
// const ll MOD = 998244353;
// const ll MOD = 924844033;
// const ll MOD = 9007199254740881;
const ll INF = 1LL << 60; // 1.15e18
const double PI = acos(-1.0);
const vll DX = {0, -1, 0, 1, 0, -1, 1, 1, -1};
const vll DY = {0, 0, -1, 0, 1, -1, -1, 1, 1};
const str alp = "abcdefghijklmnopqrstuvwxyz";
const str ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";

template <class T> auto GetVectorValueType(T v) { return v; }
template <class T> auto GetVectorValueType(V<T> v) {
  return GetVectorValueType(T());
}

template <class S, class T> istream &operator>>(istream &in, P<S, T> &p) {
  return in >> p.fi >> p.se;
}
template <class T> istream &operator>>(istream &in, V<T> &v) {
  REP(i, v.sz) in >> v[i];
  return in;
}

void Input() {}
template <class Var, class... Args> void Input(Var &var, Args &...args) {
  cin >> var;
  Input(args...);
}

void vInit(ll size) {}
template <class T, class... Args> void vInit(ll size, V<T> &v, Args &...args) {
  v.res(size);
  vInit(size, args...);
}
void vInput(ll size) {}
template <class T, class... Args> void vInput(ll size, V<T> &v, Args &...args) {
  REP(i, size) cin >> v[i];
  vInput(size, args...);
}
void vInputR(ll size) {}
template <class T, class... Args>
void vInputR(ll size, V<T> &v, Args &...args) {
  REP(i, size) cin >> v[i];
  vInputR(size, args...);
}
void vInputNumC(ll num) {}
template <class T, class... Args>
void vInputNumC(ll num, V<T> &v, Args &...args) {
  cin >> v[num];
  vInputNumC(num, args...);
}
void vInputC(ll size) {}
template <class... Args> void vInputC(ll size, Args &...args) {
  REP(i, size) vInputNumC(i, args...);
}
void vInitInputR(ll size) {}
template <class... Args> void vInitInputR(ll size, Args &...args) {
  vInit(size, args...);
  vInputR(size, args...);
}
void vInitInputC(ll size) {}
template <class... Args> void vInitInputC(ll size, Args &...args) {
  vInit(size, args...);
  vInputC(size, args...);
}
void vInit2(ll rowSize, ll columnSize) {}
template <class T, class... Args>
void vInit2(ll rowSize, ll columnSize, VV<T> &v, Args &...args) {
  v.asn(rowSize, V<T>(columnSize));
  vInit2(rowSize, columnSize, args...);
}
void vInput2(ll rowSize, ll columnSize) {}
template <class T, class... Args>
void vInput2(ll rowSize, ll columnSize, VV<T> &v, Args &...args) {
  REP(r, rowSize) {
    REP(c, columnSize) { cin >> v[r][c]; }
  }
  vInput2(rowSize, columnSize, args...);
}
void vInitInput2(ll rowSize, ll columnSize) {}
template <class... Args>
void vInitInput2(ll rowSize, ll columnSize, Args &...args) {
  vInit2(rowSize, columnSize, args...);
  vInput2(rowSize, columnSize, args...);
}

template <class S, class T>
ostream &operator<<(ostream &out, const P<S, T> &p) {
  return out << "[" << p.fi << ", " << p.se << "]";
}
template <class T> ostream &operator<<(ostream &out, V<T> &v) {
  if (v.emp)
    return out << "{}";
  else {
    auto itr = v.bgn;
    out << "{" << *itr;
    itr++;
    while (itr != v.en) {
      out << ", " << *itr;
      itr++;
    }
    out << "}";
    return out;
  }
}
template <class S, class T>
ostream &operator<<(ostream &out, const map<S, T> &m) {
  if (m.emp)
    return out << "<[]>";
  else {
    auto itr = m.bgn;
    out << "< [" << (itr->fi) << ": " << (itr->se);
    itr++;
    while (itr != m.en) {
      out << "], [" << (itr->fi) << ": " << (itr->se);
      itr++;
    }
    out << "] >";
    return out;
  }
}
template <class T> ostream &operator<<(ostream &out, const set<T> &s) {
  if (s.emp)
    return out << "<>";
  else {
    auto itr = s.bgn;
    out << "<" << *itr;
    itr++;
    while (itr != s.en) {
      out << ", " << *itr;
      itr++;
    }
    out << ">";
    return out;
  }
}

void say() {}
template <class T> void say(T t) { cout << t; }
template <class Head, class... Body> void say(Head head, Body... body) {
  cout << head << " ";
  say(body...);
}
void sal() { cout << "\n"; }
template <class... Args> void sal(Args... args) {
  say(args...);
  cout << "\n";
}

void day() {}
template <class T> void day(T t) { cerr << t; }
template <class Head, class... Body> void day(Head head, Body... body) {
  cerr << head << " ";
  day(body...);
}
void dal() { cerr << "\n"; }
template <class... Args> void dal(Args... args) {
  day(args...);
  cerr << "\n";
}

void salv() {}
template <class T> void salv(V<T> v) {
  if (v.emp)
    sal();
  else {
    auto itr = v.bgn;
    say(*itr);
    itr++;
    while (itr != v.en) {
      sas;
      say(*itr);
      itr++;
    }
    sak;
  }
}
template <class T> void salv(VV<T> v) {
  if (v.emp)
    sal();
  else {
    ROR(v, i) salv(i);
  }
}
template <class T, class... Args> void salv(T v, Args... args) {
  salv(v);
  salv(args...);
}

template <class L, class R> auto Gcd(L l, R r) -> decltype(l + r) {
  if (l < r)
    swap(l, r);
  return r ? Gcd(r, l % r) : l;
}
template <class L, class R> auto Lcm(L l, R r) {
  if (!l || !r)
    return 0;
  return l / Gcd(l, r) * r;
}

/*
auto LES = mp(INF, lam(return l < r;));
auto GRT = mp(-INF, lam(return l > r;));
auto EQ = mp(0, lam(return l == r;));

auto ADD = mp(0, lam(return l + r;));
auto SUB = mp(0, lam(return l - r;));
auto MUL = mp(1, lam(return l * r;));
auto DIV = mp(1, lam(return l / r;));
auto MDL = mp(1, lam(return l % r;));
auto XOR = mp(0, lam(return l ^ r;));
auto OR = mp(0, lam(return l | r;));
auto AND = mp(((ll)(1) << 63) - 1, lam(return l & r;));
auto MIN = mp(INF, lam(return (l < r) ? l : r;));
auto MAX = mp(-INF, lam(return (l > r) ? l : r;));
auto GCD = mp(0, lam(return Gcd(l, r);));
auto LCM = mp(1, lam(return Lcm(l, r);));
*/

auto LES = mp(INF, lam(l < r));
auto GRT = mp(-INF, lam(l > r));
auto EQ = mp(0, lam(l == r));

auto ADD = mt(0, lam(l + r), lam(l - r));
auto MUL = mt(1, lam(l *r), lam(l / r));
auto XOR = mt(0, lam(l ^ r), lam(l ^ r));
auto OR = mg(0, lam(l | r));
auto AND = mg(((ll)(1) << 63) - 1, lam(l &r));
auto MIN = mg(0, lam((l < r) ? l : r));
auto MAX = mg(0, lam((l > r) ? l : r));
auto GCD = mg(0, lam(Gcd(l, r)));
auto LCM = mg(0, lam(Lcm(l, r)));

template <class OperationType> auto Operation(OperationType A) { return Id(A); }
template <class OperationType, class T> auto Operation(OperationType A, T x) {
  return x;
}
template <class OperationType, class T, class... Args>
auto Operation(OperationType A, T x, Args... args) {
  auto tmp = Operation(A, args...);
  return Act(A)(x, tmp);
}

template <class OperationType> auto VOperation(OperationType A) {
  return Id(A);
}
template <class OperationType, class T> auto VOperation(OperationType A, T x) {
  return x;
}
template <class OperationType, class T>
auto VOperation(OperationType A, V<T> v) {
  if (v.emp) {
    decltype(GetVectorValueType(T())) tmp = Id(A);
    return tmp;
  }
  auto tmp = VOperation(A, v[0]);
  FOR(i, 1, v.sz - 1) tmp = Act(A)(tmp, VOperation(A, v[i]));
  return tmp;
}
template <class OperationType, class T, class... Args>
auto VOperation(OperationType A, T x, Args... args) {
  auto xResult = VOperation(A, x);
  auto tmp = VOperation(A, args...);
  return Act(A)(xResult, tmp);
}

ll Bset(ll a, ll b, ll c) {
  if (c)
    a |= b;
  else
    a &= ~b;
  return a;
}

struct UFT {

public:
  ll tsize;
  ll mode;
  vll par;
  vll rank;
  UFT(ll tsizeget, ll modeget = 0) {
    tsize = tsizeget;
    mode = modeget;
    par.asn(tsize, -1);
    if (!mode)
      rank.res(tsize, 0);
  }
  ll root(ll x) { return par[x] < 0 ? x : par[x] = root(par[x]); }
  bool isRoot(ll x) { return x == root(x); }
  bool same(ll x, ll y) { return root(x) == root(y); }
  void merge(ll x, ll y) {
    x = root(x);
    y = root(y);
    if (x == y)
      return;
    if (mode) {
      par[x] += par[y];
      par[y] = x;
    } else {
      if (rank[x] < rank[y]) {
        par[y] += par[x];
        par[x] = y;
      } else {
        par[x] += par[y];
        par[y] = x;
        if (rank[x] == rank[y])
          rank[x]++;
      }
    }
  }
  ll size(ll x) { return -par[root(x)]; }
};

template <class T> struct pUFT {

public:
  ll tsize;
  ll now;
  vll par;
  vll rank;
  vll mtime;
  vvll sizepi;
  VV<T> sizepv;
  V<T> elm;
  GroupSet(T) Add;

  pUFT(ll tsize, GroupSet(T) Add = ADD) : tsize(tsize), Add(Add) { init(); }
  void init() {
    now = 0;
    par.asn(tsize, -1);
    rank.asn(tsize, 0);
    mtime.asn(tsize, INF);
    sizepi.asn(tsize, {0});
    sizepv.asn(tsize, {});
  }
  void set(ll x, T s) {
    elm[x] = s;
    sizepv[x] = {s};
  }
  ll root(ll x, ll t) { return (mtime[x] > t) ? x : root(par[x], t); }
  bool same(ll x, ll y, ll t) { return root(x, t) == root(y, t); }
  ll merge(ll x, ll y) {
    now++;
    x = root(x, now);
    y = root(y, now);
    if (x != y) {
      if (rank[x] < rank[y]) {
        elm[y] = Act(Add)(elm[x], elm[y]);
        sizepi[y].pb(now);
        sizepv[y].pb(elm[y]);
        par[x] = y;
        mtime[x] = now;
      } else {
        elm[x] = Act(Add)(elm[x], elm[y]);
        sizepi[x].pb(now);
        sizepv[x].pb(elm[x]);
        par[y] = x;
        mtime[y] = now;
        if (rank[x] == rank[y])
          rank[x]++;
      }
    }
    return now;
  }
  T size(ll x, ll t) {
    x = root(x, t);
    return sizepv[x][UPB(sizepi[x], t) - 1];
  }
};

struct wUFT {
public:
  ll tsize;
  ll mode;
  vll par;
  vll rank;
  vll dweight;
  wUFT(ll tsizeget, ll modeget = 0) {
    tsize = tsizeget;
    mode = modeget;
    par.asn(tsize, -1);
    if (!mode)
      rank.res(tsize, 0);
    dweight.asn(tsize, 0);
  }
  ll root(ll x) {
    if (par[x] < 0)
      return x;
    else {
      ll r = root(par[x]);
      dweight[x] += dweight[par[x]];
      return par[x] = r;
    }
  }
  ll weight(ll x) {
    root(x);
    return dweight[x];
  }
  ll diff(ll x, ll y) { return weight(y) - weight(x); }
  bool isRoot(ll x) { return x == root(x); }
  bool same(ll x, ll y) { return root(x) == root(y); }
  void merge(ll x, ll y, ll w) {
    w += weight(x);
    w -= weight(y);
    x = root(x);
    y = root(y);
    if (x == y)
      return;
    if (mode) {
      par[x] += par[y];
      par[y] = x;
    } else {
      if (rank[x] < rank[y]) {
        par[y] += par[x];
        par[x] = y;
        dweight[x] = -w;
      } else {
        par[x] += par[y];
        par[y] = x;
        if (rank[x] == rank[y])
          rank[x]++;
        dweight[y] = w;
      }
    }
  }
  ll size(ll x) { return -par[root(x)]; }
};

template <class T> struct sUFT {

public:
  ll tsize;
  ll mode;
  vll par;
  vll rank;
  GroupSet(T) Add;
  V<T> elm;
  sUFT(ll tsize, GroupSet(T) Add = ADD, ll mode = 0)
      : tsize(tsize), Add(Add), mode(mode) {
    init();
  }
  void init() {
    par.asn(tsize, -1);
    if (!mode)
      rank.res(tsize, 0);
    elm.asn(tsize, Id(Add));
  }
  ll root(ll x) { return par[x] < 0 ? x : par[x] = root(par[x]); }
  bool isRoot(ll x) { return x == root(x); }
  bool same(ll x, ll y) { return root(x) == root(y); }
  void merge(ll x, ll y) {
    x = root(x);
    y = root(y);
    if (x == y)
      return;
    if (mode) {
      elm[x] = Act(Add)(elm[x], elm[y]);
      par[y] = x;
    } else {
      if (rank[x] < rank[y]) {
        elm[y] = Act(Add)(elm[x], elm[y]);
        par[x] = y;
      } else {
        elm[x] = Act(Add)(elm[x], elm[y]);
        par[y] = x;
        if (rank[x] == rank[y])
          rank[x]++;
      }
    }
  }
  T size(ll x) { return elm[root(x)]; }
  T &operator[](ll x) { return elm[x]; }
};

template <typename valtype> class SegT {

public:
  ll size;
  vector<valtype> v;

  valtype initv;
  function<valtype(valtype x, valtype y)> calc;

  SegT() {}
  SegT(const SegT &segt) {}

  SegT(ll sizeget, ll modeget = 0) {
    sizeset(sizeget);
    modeset(modeget);
    init();
  }
  SegT(vector<valtype> cpyvec, ll modeget = 0) {
    sizeset(cpyvec.sz);
    modeset(modeget);
    init();
    copy(cpyvec);
  }
  SegT(ll sizeget, valtype initvget,
       function<valtype(valtype x, valtype y)> calcget) {
    sizeset(sizeget);
    initv = initvget;
    calc = calcget;
    init();
  }
  SegT(vector<valtype> cpyvec, valtype initvget,
       function<valtype(valtype x, valtype y)> calcget) {
    sizeset(cpyvec.sz);
    initv = initvget;
    calc = calcget;
    init();
    copy(cpyvec);
  }
  void sizeset(ll rsize) {
    size = DigN2(rsize);
    if (rsize == Pow2(size - 1))
      size--;
    return;
  }
  void modeset(ll mode) {
    switch (mode) {
    case 0:
      initv = 0;
      calc = [](valtype x, valtype y) { return x + y; };
      break;
    case 1:
      initv = INF;
      calc = [](valtype x, valtype y) { return min(x, y); };
      break;
    case 2:
      initv = -INF;
      calc = [](valtype x, valtype y) { return max(x, y); };
      break;
    }
    return;
  }
  void init() { v.asn(Pow2(size + 1) - 1, initv); }
  void copy(vector<valtype> cpyvec) {
    REP(i, min(cpyvec.sz, Pow2(size))) set(i, cpyvec[i]);
  }
  ll i2v(ll i) const {
    if (i < 0 || i >= Pow2(size))
      return -1;
    return Pow2(size) + i - 1;
  }
  ll top(ll i) const {
    if (i == 0)
      return -1;
    return (i - 1) / 2;
  }
  pl bot(ll i) const {
    if (i + 1 >= Pow2(size))
      return mp(-1, -1);
    return mp(2 * i + 1, 2 * i + 2);
  }
  void set(ll i, valtype x) {
    i = i2v(i);
    v[i] = x;
    while (i > 0) {
      i = top(i);
      v[i] = calc(v[bot(i).fi], v[bot(i).se]);
    }
    return;
  }
  void add(ll i, valtype x) {
    set(i, v[i2v(i)] + x);
    return;
  }
  valtype operator[](const ll &i) const { return v[i2v(i)]; }
  //	valtype que(ll a = 0, ll b = Pow2(size) - 1) {
  valtype que(ll a, ll b) {
    if (a == b)
      return v[i2v(a)];
    if (a > b)
      return initv; // swap(a, b);
    valtype ans = initv;
    ll ai = i2v(a);
    ll bi = i2v(b);
    FOR(i, 1, size + 1) {
      if (a > b)
        break;
      if (a % Pow2(i)) {
        ans = calc(ans, v[ai]);
        a += Pow2(i - 1);
        ai = top(ai) + 1;
      } else {
        ai = top(ai);
      }
      if (a > b)
        break;
      if ((b + 1) % Pow2(i)) {
        ans = calc(ans, v[bi]);
        b -= Pow2(i - 1);
        bi = top(bi) - 1;
      } else {
        bi = top(bi);
      }
      if (a > b)
        break;
    }
    return ans;
  }
  valtype que(ll b) { return que(0, b); }
  valtype que() { return que(0, Pow2(size) - 1); }
};

/*template <class Type> class DP {

public:

        vector<Type> v;
        Type initv;
        vll size, block;

        DP() {}
        DP(const DP &dp) {}

        template<class... Args> DP(Args... args) {
                block.asn(1, 1);
                Initialize(args...);
        }

        void Initialize(Type initv_) {
                initv = initv_;
                v.asn(block.bk, initv);
        }
        template<class... Args> void Initialize(ll val, Args... args) {
                size.pb(val);
                block.pb(block.bk*val);
                Initialize(args...);
        }



};*/

pl Bezout(ll a, ll b) {
  if (b != 0) {
    pl xy;
    xy = Bezout(b, a % b);
    return mp(xy.se, xy.fi - ((a / b) * xy.se));
  } else {
    return mp(1, 0);
  }
}
pl Bez(ll a, ll b, ll c) {
  pl xy;
  ll x, y, z, gc;
  xy = Bezout(a, b);
  gc = gcd(a, b);
  if (c % gc != 0)
    return mp(-1, -1);
  x = xy.fi * (c / gc);
  y = xy.se * (c / gc);
  if (x < 0)
    z = rup(-x, (b / gc));
  if (x >= 0)
    z = -x / (b / gc);
  x += z * (b / gc);
  y -= z * (a / gc);
  return mp(x, y);
}

ll DigS10(ll n) {
  ll ans = 0;
  while (1) {
    ans += n % 10;
    n /= 10;
    if (!n)
      break;
  }
  return ans;
}

ll isP(ll n) {
  if (n <= 1)
    return 0;
  FOR(i, 2, (ll)sqrt(n) + 1) {
    if (n % i == 0)
      return 0;
  }
  return 1;
}

ll Tot(ll n) {
  if (n <= 0)
    return 0;
  ll ans = n, x = 2;
  while (x * x <= n) {
    if (n % x == 0) {
      ans -= ans / x;
      while (n % x == 0)
        n /= x;
    }
    x++;
  }
  if (n > 1)
    ans -= ans / n;
  return ans;
}

template <class T> struct Graph {
public:
  ll vSize;
  ll eMode;
  ll mapMode;
  GroupSet(T) Add;
  CompareSet(T) Less;
  CompareSet(T) Equal;
  VV<P<T, ll>> adj;
  map<pl, T> len;
  Graph(ll vSize, ll eMode = 0, ll mapMode = 0, GroupSet(T) Add = ADD,
        CompareSet(T) Less = LES, CompareSet(T) Equal = EQ)
      : vSize(vSize), eMode(eMode), mapMode(mapMode), Add(Add), Less(Less),
        Equal(Equal) {}
  void Init() { adj.asn(vSize, V<P<T, ll>>()); }
  void AddE(ll x, ll y, T cost) {
    iAddE(x, y, cost);
    if (!eMode)
      iAddE(y, x, cost);
  }
  void iAddE(ll x, ll y, T cost) {
    adj[x].pb(mp(cost, y));
    if (mapMode)
      len[mp(x, y)] = cost;
  }
  P<bool, T> getE(ll x, ll y) {
    if (!len.count(mp(x, y)))
      return mp(false, Id(Less));
    return mp(true, len[mp(x, y)]);
  }
  V<T> Dijk(ll x) {
    V<T> ans(vSize, Id(Less));
    if (x < 0 || x >= vSize)
      return ans;
    SegT<P<T, ll>> segt(vSize, mp(Id(Less), -1),
                        clamr(if (l.se < 0) return r; if (r.se < 0) return l;
                              return Act(Less)(l.fi, r.fi) ? l : r;));
    segt.set(x, mp(Id(Add), x));
    P<T, ll> now;
    while ((now = segt.que(0, vSize - 1)).se >= 0) {
      ans[now.se] = segt[now.se].fi;
      segt.set(now.se, mp(Id(Less), -2));
      ROR(adj[now.se], i) {
        if (segt[i.se].se == -2)
          continue;
        if (segt[i.se].se == -1) {
          segt.set(i.se, mp(Act(Add)(ans[now.se], i.fi), i.se));
          continue;
        }
        if (Act(Less)(Act(Add)(ans[now.se], i.fi), segt[i.se].fi)) {
          segt.set(i.se, mp(Act(Add)(ans[now.se], i.fi), i.se));
          continue;
        }
      }
    }
    return ans;
  }
  V<P<T, vll>> rDijk(ll x) {
    V<P<T, vll>> ans(vSize, mp(Id(Less), vll()));
    if (x < 0 || x >= vSize)
      return ans;
    SegT<P<T, ll>> segt(vSize, mp(Id(Less), -1),
                        clamr(if (l.se < 0) return r; if (r.se < 0) return l;
                              return Act(Less)(l.fi, r.fi) ? l : r;));
    segt.set(x, mp(Id(Add), x));
    P<T, ll> now;
    while ((now = segt.que(0, vSize - 1)).se >= 0) {
      ans[now.se].fi = segt[now.se].fi;
      segt.set(now.se, mp(Id(Less), -2));
      ROR(adj[now.se], i) {
        if (segt[i.se].se == -2)
          continue;
        if (segt[i.se].se == -1) {
          segt.set(i.se, mp(Act(Add)(ans[now.se].fi, i.fi), i.se));
          ans[i.se].se = {now.se};
          continue;
        }
        if (Act(Less)(Act(Add)(ans[now.se].fi, i.fi), segt[i.se].fi)) {
          segt.set(i.se, mp(Act(Add)(ans[now.se].fi, i.fi), i.se));
          ans[i.se].se = {now.se};
          continue;
        }
        if (Act(Equal)(Act(Add)(ans[now.se].fi, i.fi), segt[i.se].fi)) {
          ans[i.se].se.pb(now.se);
          continue;
        }
      }
    }
    return ans;
  }

  T Prim(ll x = 0) {
    T ans = Id(Add);
    if (x < 0 || x >= vSize)
      return ans;
    SegT<P<T, ll>> segt(vSize, mp(Id(Less), -1),
                        clamr(if (l.se < 0) return r; if (r.se < 0) return l;
                              return Act(Less)(l.fi, r.fi) ? l : r;));
    segt.set(x, mp(Id(Add), x));
    P<T, ll> now;
    while ((now = segt.que(0, vSize - 1)).se >= 0) {
      ans = Act(Add)(ans, segt[now.se].fi);
      segt.set(now.se, mp(Id(Less), -2));
      ROR(adj[now.se], i) {
        if (segt[i.se].se == -2)
          continue;
        if (segt[i.se].se == -1) {
          segt.set(i.se, i);
          continue;
        }
        if (Act(Less)(i.fi, segt[i.se].fi)) {
          segt.set(i.se, i);
          continue;
        }
      }
    }
    return ans;
  }

  P<T, V<P<T, vll>>> rPrim(ll x = 0) {
    P<T, V<P<T, vll>>> ans =
        mp(Id(Add), V<P<T, vll>>(vSize, mp(Id(Less), vll())));
    if (x < 0 || x >= vSize)
      return ans;
    SegT<P<T, ll>> segt(vSize, mp(Id(Less), -1),
                        clamr(if (l.se < 0) return r; if (r.se < 0) return l;
                              return Act(Less)(l.fi, r.fi) ? l : r;));
    segt.set(x, mp(Id(Add), x));
    P<T, ll> now;
    while ((now = segt.que(0, vSize - 1)).se >= 0) {
      ans.se[now.se].fi = segt[now.se].fi;
      ans.fi = Act(Add)(ans.fi, ans.se[now.se].fi);
      segt.set(now.se, mp(Id(Less), -2));
      ROR(adj[now.se], i) {
        if (segt[i.se].se == -2)
          continue;
        if (segt[i.se].se == -1) {
          segt.set(i.se, i);
          ans.se[i.se].se = {now.se};
          continue;
        }
        if (Act(Less)(i.fi, segt[i.se].fi)) {
          segt.set(i.se, i);
          ans.se[i.se].se = {now.se};
          continue;
        }
        if (Act(Equal)(i.fi, segt[i.se].fi)) {
          ans.se[i.se].se.pb(now.se);
          continue;
        }
      }
    }
    return ans;
  }
};

template <class T> struct Sum {
public:
  V<T> v, s;
  ll size;
  GroupSet(T) Add;
  Sum(V<T> v, GroupSet(T) Add = ADD) : v(v), size(v.sz), Add(Add) {
    Init();
    Calc();
  }
  void Init() { s.asn(size + 1, Id(Add)); }
  void Calc() { REP(i, size) s[i + 1] = Act(Add)(s[i], v[i]); }
  T operator()(ll x) {
    if (x < -1)
      x = -1;
    if (x > size - 1)
      x = size - 1;
    return s[x + 1];
  }
  T operator()(ll l, ll r) {
    if (l < 0)
      l = 0;
    if (r >= size)
      r = size - 1;
    if (l > r)
      return Id(Add);
    return InvAct(Add)(s[r + 1], s[l]);
  }
};
using sumll = Sum<ll>;

template <class T> struct Sum2 {
public:
  VV<T> v, s;
  ll RowSize, ColumnSize;
  GroupSet(T) Add;
  Sum2(VV<T> v, GroupSet(T) Add = ADD)
      : v(v), RowSize(v.sz), ColumnSize(v.sz ? v[0].sz : 0), Add(Add) {
    Init();
    Calc();
  }
  void Init() { s.asn(RowSize + 1, V<T>(ColumnSize + 1, Id(Add))); }
  void Calc() {
    REP1(r, RowSize) {
      REP1(c, ColumnSize) {
        //				s[r][c] = InvAct(Add)(Act(Add)(Act(Add)(v[r -
        //1][c - 1], operator()(r - 1, c - 2)), operator()(r - 2, c - 1)),
        //operator()(r - 2, c - 2));
        s[r][c] = Act(Add)(s[r][c - 1], v[r - 1][c - 1]);
      }
    }
    REP1(r, RowSize) {
      REP1(c, ColumnSize) { s[r][c] = Act(Add)(s[r - 1][c], s[r][c]); }
    }
  }
  T operator()(ll r, ll c) {
    if (r < -1)
      r = -1;
    if (c < -1)
      c = -1;
    if (r > RowSize - 1)
      r = RowSize - 1;
    if (c > ColumnSize - 1)
      c = ColumnSize - 1;
    return s[r + 1][c + 1];
  }
  T operator()(ll r1, ll c1, ll r2, ll c2) {
    if (r1 < 0)
      r1 = 0;
    if (c1 < 0)
      c1 = 0;
    if (r2 >= RowSize)
      r2 = RowSize - 1;
    if (c2 >= ColumnSize)
      c2 = ColumnSize - 1;
    if (r1 > r2)
      return Id(Add);
    if (c1 > c2)
      return Id(Add);
    return InvAct(Add)(Act(Add)(s[r2 + 1][c2 + 1], s[r1][c1]),
                       Act(Add)(s[r2 + 1][c1], s[r1][c2 + 1]));
  }
};
using sumll2 = Sum2<ll>;

template <class T> struct Point2 {
public:
  VV<T> v;
  ll h, w;
  Point2() : h(0), w(0) {}
  Point2(ll h, ll w) : h(h), w(w) { asn(h, w); }
  Point2(ll h, ll w, T val) : h(h), w(w) { asn(h, w, val); }
  Point2(VV<T> cv) : h(cv.sz), w(cv.sz ? cv[0].sz : 0) {
    asn(h, w);
    copy(cv);
  }
  void assign(ll h, ll w) { v.asn(h, V<T>(w)); }
  void assign(ll h, ll w, ll val) { v.asn(h, V<T>(w, val)); }
  void copy(VV<T> cv) { REP(_h, h) REP(_w, w) v[_h][_w] = cv[_h][_w]; }
  T &operator()(ll h, ll w) { return v[h][w]; }
  T &operator()(pl p) { return v[p.fi][p.se]; }
  T &operator[](pl p) { return v[p.fi][p.se]; }
};
template <class T> using P2 = Point2<T>;

template <ll Mod> struct Modll {
public:
  ll v;
  Modll() : v(0) {}
  Modll(ll _v) { set(_v % Mod + Mod); }
  Modll &set(ll _v) {
    v = (_v < Mod) ? _v : (_v - Mod);
    return *this;
  }
  Modll pow(ll n) const {
    Modll x = *this, ans = 1;
    while (n) {
      if (n & 1)
        ans *= x;
      x *= x;
      n >>= 1;
    }
    return ans;
  }
  Modll inverse() const { return (*this).pow(Mod - 2); }
  Modll operator+(const Modll &m) const { return Modll().set(v + m.v); }
  Modll operator-(const Modll &m) const { return Modll().set(Mod + v - m.v); }
  Modll operator*(const Modll &m) const {
    return Modll().set((ull(v) * m.v) % Mod);
  }
  Modll operator/(const Modll &m) const { return *this * m.inv; }
  Modll &operator+=(const Modll &m) { return *this = *this + m; }
  Modll &operator-=(const Modll &m) { return *this = *this - m; }
  Modll &operator*=(const Modll &m) { return *this = *this * m; }
  Modll &operator/=(const Modll &m) { return *this = *this / m; }
  Modll operator-() const { return Modll(0) - *this; }
  explicit operator bool() const { return v != 0; }
  friend istream &operator>>(istream &in, Modll &m) { return in >> m.v; }
  friend ostream &operator<<(ostream &out, const Modll &m) {
    return out << m.v;
  }
};
using mll = Modll<MOD>;
using vmll = V<mll>;
using vvmll = V<vmll>;
using vvvmll = V<vvmll>;

vmll MFactMemo(2, 1);
vmll MIFactMemo(2, 1);

mll mFact(ll n) {
  if (MFactMemo.sz <= n) {
    ll oldsize = MFactMemo.sz;
    MFactMemo.res(n + 1, 1);
    FOR(i, oldsize, n) MFactMemo[i] = MFactMemo[i - 1] * i;
  }
  return MFactMemo[n];
}
mll miFact(ll n) {
  if (MIFactMemo.sz <= n) {
    ll oldsize = MIFactMemo.sz;
    MIFactMemo.res(n + 1, 1);
    MIFactMemo.bk = mFact(n).inv;
    rFOR(i, oldsize + 1, n) MIFactMemo[i - 1] = MIFactMemo[i] * i;
  }
  return MIFactMemo[n];
}
mll mComb(ll n, ll k) {
  if (n < 0 || k < 0 || n < k)
    return 0;
  return mFact(n) * miFact(k) * miFact(n - k);
}

ll LIS(vll v, ll m = 0) {

  if (v.sz > 0) {
    ll ans = 0;
    vll dp(v.sz, INF);
    FOR(i, 0, v.sz - 1) { dp[m ? UPB(dp, v[i]) : LOWB(dp, v[i])] = v[i]; }
    FOR(i, 0, v.sz - 1) {
      if (dp[i] == INF)
        break;
      ans++;
    }
    return ans;
  } else {
    return 0;
  }
}

ll Bsrch(function<bool(ll x)> f, ll mi, ll ma) {
  ll ng = mi - 1, ok = ma, mid;
  while (ok - ng > 1) {
    mid = (ng + ok) / 2;
    (f(mid) ? ok : ng) = mid;
  }
  return ok;
}

template <class T, class M = decltype(MUL), class S = decltype(ADD)>
VV<T> MultiMatrix(VV<T> A, VV<T> B, M Mul = MUL, S Add = ADD) {
  VV<T> ans;
  ll ii = A.sz;
  if (!ii)
    return ans;
  ll jj = A[0].sz;
  if (!jj)
    return ans;
  ll jj2 = B.sz;
  if (!jj2)
    return ans;
  if (jj != jj2)
    return ans;
  ll kk = B[0].sz;
  if (!kk)
    return ans;
  ans.asn(ii, V<T>(kk, 0));
  REP(i, ii) {
    REP(k, kk) {
      REP(j, jj) {
        ans[i][k] = Act(Add)(ans[i][k], Act(Mul)(A[i][j], B[j][k]));
      }
    }
  }
  return ans;
}

vvll CombMemo(1000, vll(1000, -1));

ll Comb(ll n, ll k) {
  if ((n < 0) || (k < 0))
    return 0;
  if (CombMemo[n][k] == -1) {
    if (n < k)
      CombMemo[n][k] = 0;
    else {
      if (n == 0)
        CombMemo[n][k] = 1;
      else if (k == 0)
        CombMemo[n][k] = 1;
      else if (n == k)
        CombMemo[n][k] = 1;
      else
        CombMemo[n][k] = Comb(n - 1, k - 1) + Comb(n - 1, k);
    }
  }
  return CombMemo[n][k];
}

template <class T> map<T, ll> Dict(V<T> v) {
  map<T, ll> m;
  if (!v.sz)
    return m;
  SORT(v);
  UNIQUE(v);
  REP(i, v.sz) { m[v[i]] = i; }
  return m;
}

template <class T> vll Cmprs(V<T> v) {
  auto m = Dict(v);
  vll ans(v.sz);
  REP(i, v.sz) { ans[i] = m[v[i]]; }
  return ans;
}

template <class T> vll PCmprs(V<T> v) {
  if (v.sz == 0)
    return V<T>();
  vll tmp(v.sz);
  vll ans(v.sz);
  IOTA(tmp, 0);
  IOTA(ans, 0);
  sort(tmp.bgn, tmp.en, clam(v[l] < v[r]));
  sort(ans.bgn, ans.en, clam(tmp[l] < tmp[r]));
  return ans;
}

ll BblCnt(vll rv) {
  vll v = PCmprs(rv);
  SegT<ll> b(v.sz, 0);
  ll ans = 0;
  REP(i, v.sz) {
    ans += (i - b.que(0, v[i]));
    b.add(v[i], 1);
  }
  return ans;
}

pl NGrid(pl p, ll i, ll H, ll W) {
  p = mp(p.fi + DX[i], p.se + DY[i]);
  if (p.fi < 0 || p.fi >= H || p.se < 0 || p.se >= W)
    return mp(INF, INF);
  return p;
}

vvll llGrid(vs v) {
  vvll r(v.sz, vll(v.sz ? v[0].sz : 0, 0));
  REP(h, v.sz) REP(w, v.sz ? v[0].sz : 0) r[h][w] = (v[h][w] == '#');
  return r;
}

template <class T> auto ven(T val) { return val; }
template <> auto ven<int>(int val) { return (ll)val; }
template <class T, class... Args> auto ven(T val, Args... args) {
  auto tmp = ven(args...);
  return V<decltype(tmp)>(val, tmp);
}

template <class T> void zind(T &v) { v--; }
template <class T> void zind(V<T> &v) { ROR(v, i) zind(i); }
template <class T, class... Args> void zind(T &v, Args &...args) {
  zind(v);
  zind(args...);
}

void Solve();

signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << setprecision(20) << fixed;
  Solve();
}

ll N;
vll a;
vll b;
vvll dp;

ll rec(ll x, ll y) {
  if (dp[x][y] != -1)
    return dp[x][y];
  if (x == y)
    return dp[x][y] = 0;
  ll tmp = INF;
  FOR(i, x, y - 1) { emin(tmp, rec(x, i) + rec(i + 1, y) + b[y + 1] - b[x]); }
  return dp[x][y] = tmp;
}

void Solve() {

  cin >> N;
  a = ven(N, 0);
  b = ven(N + 1, 0);
  dp = ven(N, N, -1);
  vInput(N, a);
  REP1(i, N) b[i] = b[i - 1] + a[i - 1];
  sal(rec(0, N - 1));
}