#define YRSD
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,popcnt")

#include <iostream>
#include <algorithm>
#include <array>
#include <bitset>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <tuple>
#include <bit>
#include <chrono>
#include <functional>
#include <iomanip>
#include <utility>
#include <type_traits>
#include <cassert>
#include <cctype>
#include <cmath>
#include <cstring>
#include <ctime>
#include <limits>
#include <ranges>
#include <concepts>

#define TE template <typename T>
#define TES template <typename T, typename ...S>
#define Z auto
#define ep emplace_back
#define eb emplace
#define fi first
#define se second
#define bg begin
#define ed end
#define all(x) bg(x), ed(x)

#define ov(a, b, c, d, e, ...) e
#define FO1(a) for (int _ = 0; _ < (a); ++_)
#define FO2(i, a) for (int i = 0; i < (a); ++i)
#define FO3(i, a, b) for (int i = (a); i < (b); ++i)
#define FO4(i, a, b, c) for (int i = (a); i < (b); i += (c))
#define FOR(...) ov(__VA_ARGS__, FO4, FO3, FO2, FO1)(__VA_ARGS__)
#define FF1(a) for (int _ = (a) - 1; _ >= 0; --_)
#define FF2(i, a) for (int i = (a) - 1; i >= 0; --i)
#define FF3(i, a, b) for (int i = (b) - 1; i >= (a); --i)
#define FF4(i, a, b, c) for (int i = (b) - 1; i >= (a); i -= (c))
#define FOR_R(...) ov(__VA_ARGS__, FF4, FF3, FF2, FF1)(__VA_ARGS__)
#define FOR_subset(t, s) for (int t = (s); t > -1; t = (t == 0 ? -1 : (t - 1) & s))

#define sort ranges::sort

using namespace std;

TE using vc = vector<T>;
TE using vvc = vc<vc<T>>;
TE using T1 = tuple<T>;
TE using T2 = tuple<T, T>;
TE using T3 = tuple<T, T, T>;
TE using T4 = tuple<T, T, T, T>;
TE using max_heap = priority_queue<T>;
TE using min_heap = priority_queue<T, vc<T>, greater<T>>;
using u8 = unsigned char; using uint = unsigned int; using ll = long long;      using ull = unsigned long long;
using ld = long double;   using i128 = __int128;     using u128 = __uint128_t;  using f128 = __float128;
using u16 = uint16_t;
using PII = pair<int, int>;   using PLL = pair<ll, ll>;

#ifdef YRSD
constexpr bool dbg = 1;
#else
constexpr bool dbg = 0;
#endif

istream &operator>>(istream &I, i128 &x) {
  static string s;
  I >> s;
  int f = s[0] == '-';
  x = 0;
  const int N = (int)s.size();
  FOR(i, f, N) x = x * 10 + s[i] - '0';
  if (f) x = -x;
  return I;
}
ostream &operator<<(ostream &O, i128 x) {
  static string s;
  s.clear();
  bool f = x < 0;
  if (f) x = -x;
  while (x) s += '0' + x % 10, x /= 10;
  if (s.empty()) s += '0';
  if (f) s += '-';
  reverse(all(s));
  return O << s;
}
istream &operator>>(istream &I, f128 &x) {
  static string s;
  I >> s, x = stold(s);
  return I;
}
ostream &operator<<(ostream &O, const f128 x) { return O << ld(x); }
template <typename... S>
istream &operator>>(istream &I, tuple<S...> &t) {
  return apply([&I](Z &...s) { ((I >> s), ...); }, t), I;
}
template <typename T, typename U>
istream &operator>>(istream &I, pair<T, U> &x) {
  return I >> x.fi >> x.se;
}
template <typename T, typename U>
ostream &operator<<(ostream &O, const pair<T, U> &x) {
  return O << x.fi << ' ' << x.se;
}
TE requires requires(T &c) { begin(c); end(c); } and 
                          (not is_same_v<decay_t<T>, string>)
istream &operator>>(istream &I, T &c) {
  for (Z &e : c) I >> e;
  return I;
}
TE requires requires(const T &c) { begin(c); end(c); } and 
  (not is_same_v<decay_t<T>, const char*>) and 
  (not is_same_v<decay_t<T>, string>) and 
  (not is_array_v<remove_reference_t<T>> or 
   not is_same_v<remove_extent_t<remove_reference_t<T>>, char>)
ostream &operator<<(ostream &O, const T &a) {
  if (a.empty()) return O;
  Z i = a.begin();
  O << *i++;
  for (; i != a.end(); ++i) O << ' ' << *i;
  return O;
}
void IN() {}
TE void IN(T &x, Z &...s) { cin >> x, IN(s...); }
void print() { cout << '\n'; }
TES void print(T &&x, S &&...y) {
  cout << x;
  if constexpr (sizeof...(S)) cout << ' ';
  print(forward<S>(y)...);
}
void put() {}
TES void put(T &&x, S &&...y) {
  cout << x;
  put(forward<S>(y)...);
}

#define INT(...)  int    __VA_ARGS__; IN(__VA_ARGS__)
#define UINT(...) uint   __VA_ARGS__; IN(__VA_ARGS__)
#define LL(...)   ll     __VA_ARGS__; IN(__VA_ARGS__)
#define ULL(...)  ull    __VA_ARGS__; IN(__VA_ARGS__)
#define I128(...) i128   __VA_ARGS__; IN(__VA_ARGS__)
#define STR(...)  string __VA_ARGS__; IN(__VA_ARGS__)
#define CH(...)   char   __VA_ARGS__; IN(__VA_ARGS__)
#define REAL(...) re     __VA_ARGS__; IN(__VA_ARGS__)
#define VEC(T, a, n) vc<T> a(n); IN(a)

void YES(bool o = 1) { print(o ? "YES" : "NO"); }
void Yes(bool o = 1) { print(o ? "Yes" : "No"); }
void yes(bool o = 1) { print(o ? "yes" : "no"); }
void NO(bool o = 1) { YES(not o); }
void No(bool o = 1) { Yes(not o); }
void no(bool o = 1) { yes(not o); }
void ALICE(bool o = 1) { print(o ? "ALICE" : "BOB"); }
void Alice(bool o = 1) { print(o ? "Alice" : "Bob"); }
void alice(bool o = 1) { print(o ? "alice" : "bob"); }
void BOB(bool o = 1) { ALICE(not o); }
void Bob(bool o = 1) { Alice(not o); }
void bob(bool o = 1) { alice(not o); }
void POSSIBLE(bool o = 1) { print(o ? "POSSIBLE" : "IMPOSSIBLE"); }
void Possible(bool o = 1) { print(o ? "Possible" : "Impossible"); }
void possible(bool o = 1) { print(o ? "possible" : "impossible"); }
void IMPOSSIBLE(bool o = 1) { POSSIBLE(not o); }
void Impossible(bool o = 1) { Possible(not o); }
void impossible(bool o = 1) { possible(not o); }
void TAK(bool o = 1) { print(o ? "TAK" : "NIE"); }
void NIE(bool o = 1) { TAK(not o); }

#if (__cplusplus >= 202002L)
#include <numbers>
constexpr ld pi = numbers::pi_v<ld>;
#endif
TE constexpr T inf = numeric_limits<T>::max();
template <> constexpr i128 inf<i128> = i128(inf<ll>) * 2'000'000'000'000'000'000;
template <typename T, typename U>
constexpr pair<T, U> inf<pair<T, U>> = {inf<T>, inf<U>};

TE constexpr static inline int pc(T x) { return popcount(make_unsigned_t<T>(x)); }
constexpr static inline ll len(const Z &a) { return a.size(); }

void reverse(Z &a) { reverse(all(a)); }

void unique(Z &a) {
  sort(a);
  a.erase(unique(all(a)), a.end());
}
TE vc<int> inverse(const vc<T> &a) {
  int N = len(a);
  vc<int> b(N, -1);
  FOR(i, N) if (a[i] != -1) b[a[i]] = i;
  return b;
}

Z QMAX(const Z &a) { return *max_element(all(a)); }
Z QMIN(const Z &a) { return *min_element(all(a)); }
TE Z QMAX(T l, T r) { return *max_element(l, r); }
TE Z QMIN(T l, T r) { return *min_element(l, r); }
constexpr bool chmax(Z &a, const Z &b) { return (a < b ? a = b, 1 : 0); }
constexpr bool chmin(Z &a, const Z &b) { return (a > b ? a = b, 1 : 0); }

vc<int> argsort(const Z &a) {
  vc<int> I(len(a));
  iota(all(I), 0);
  sort(I, [&](int i, int k) { return a[i] < a[k] or (a[i] == a[k] and i < k); });
  return I;
}
TE vc<T> rearrange(const vc<T> &a, const vc<int> &I) {
  int N = len(I);
  vc<T> b(N);
  FOR(i, N) b[i] = a[I[i]];
  return b;
}
template <int of = 1, typename T> 
vc<T> pre_sum(const vc<T> &a) {
  int N = len(a);
  vc<T> c(N + 1);
  FOR(i, N) c[i + 1] = c[i] + a[i];
  if (of == 0) c.erase(c.begin());
  return c;
}

TE constexpr static int topbit(T x) {
  if (x == 0) return - 1;
  if constexpr (sizeof(T) <= 4) return 31 - __builtin_clz(x);
  else return 63 - __builtin_clzll(x);
}
TE constexpr static int lowbit(T x) {
  if (x == 0) return -1;
  if constexpr (sizeof(T) <= 4) return __builtin_ctz(x);
  else return __builtin_ctzll(x);
}

TE constexpr T floor(T x, T y) { return x / y - (x % y and (x ^ y) < 0); }
TE constexpr T ceil(T x, T y) { return floor(x + y - 1, y); }
TE constexpr T bmod(T x, T y) { return x - floor(x, y) * y; }
TE constexpr pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return pair{q, x - q * y};
}
template <typename T = ll>
T SUM(const Z &v) {
  return accumulate(all(v), T(0));
}
int lb(const Z &a, Z x) { return lower_bound(all(a), x) - a.begin(); }
TE int lb(T l, T r, Z x) { return lower_bound(l, r, x) - l; }
int ub(const Z &a, Z x) { return upper_bound(all(a), x) - a.begin(); }
TE int ub(T l, T r, Z x) { return upper_bound(l, r, x) - l; }

template <bool ck = 1>
ll bina(Z f, ll l, ll r) {
  if constexpr (ck) assert(f(l));
  while (abs(l - r) > 1) {
    ll x = (r + l) >> 1;
    (f(x) ? l : r) = x;
  }
  return l;
}
TE T bina_real(Z f, T l, T r, int c = 100) {
  while (c--) {
    T x = (l + r) / 2;
    (f(x) ? l : r) = x;
  }
  return (l + r) / 2;
}

Z pop(Z &s) {
  if constexpr (requires { s.pop_back(); }) {
    Z x = s.back();
    return s.pop_back(), x;
  } else if constexpr (requires { s.top(); }) {
    Z x = s.top();
    return s.pop(), x;
  } else {
    Z x = s.front();
    return s.pop(), x;
  }
}
void setp(int x) { cout << fixed << setprecision(x); }

TE inline void sh(vc<T> &a, int N, T b = {}) {
  a.resize(N, b);
}

#define FIO

static constexpr uint SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];

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

inline 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));
}

TE inline void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}

TE inline 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;
  }
}

inline void rd(int16_t &x) { rd_integer(x); }
inline void rd(uint16_t &x) { rd_integer(x); }
inline void rd(int &x) { rd_integer(x); }
inline void rd(long &x) { rd_integer(x); }
inline void rd(ll &x) { rd_integer(x); }
inline void rd(i128 &x) { rd_integer(x); }
inline void rd(uint &x) { rd_integer(x); }
inline void rd(ull &x) { rd_integer(x); }
inline void rd(u128 &x) { rd_integer(x); }
inline void rd(double &x) { rd_real(x); }
inline void rd(long double &x) { rd_real(x); }
inline void rd(f128 &x) { rd_real(x); }

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

template <size_t N = 0, typename T>
inline void rd(array<T, N> &x) {
  for (Z &e : x) rd(e);
}
TE inline void rd(vc<T> &x) {
  for (Z &e : x) rd(e);
}

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

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

TE inline 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;
}

TE inline void wt_real(T x) {
  ostringstream oss;
  oss << fixed << setprecision(10) << double(x);
  string s = oss.str();
  wt(s);
}

inline void wt(int x) { wt_integer(x); }
inline void wt(long x) { wt_integer(x); }
inline void wt(ll x) { wt_integer(x); }
inline void wt(i128 x) { wt_integer(x); }
inline void wt(uint x) { wt_integer(x); }
inline void wt(ull x) { wt_integer(x); }
inline void wt(u128 x) { wt_integer(x); }
inline void wt(double x) { wt_real(x); }
inline void wt(long double x) { wt_real(x); }
inline void wt(f128 x) { wt_real(x); }

template <typename T, typename U>
inline void wt(const pair<T, U> &val) {
  wt(val.fi);
  wt(' ');
  wt(val.se);
}
template <size_t N = 0, typename T>
inline void wt_tuple(const T &t) {
  if constexpr (N < tuple_size<T>::value) {
    if constexpr (N > 0) {
      wt(' ');
    }
    const Z x = get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <typename... T>
inline void wt(tuple<T...> &tpl) {
  wt_tuple(tpl);
}
template <typename T, size_t S>
inline void wt(const array<T, S> &val) {
  Z n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
TE inline void wt(const vc<T> &a) {
  int N = len(a);
  FOR(i, N) {
    if (i) wt(' ');
    wt(a[i]);
  }
}
TE inline void wt(const vc<vc<T>> &v) {
  int N = len(v);
  FOR(i, N) {
    wt(v[i]);
    if (i + 1 != N) wt('\n');
  }
}
template <typename T, const size_t s>
inline void wt(const vc<array<T, s>> &v) {
  int N = len(v);
  FOR(i, N) {
    wt(v[i]);
    if (i + 1 != N) wt('\n');
  }
}

inline void __attribute__((destructor)) _d() { flush(); }

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

#define IN(...) read(__VA_ARGS__)
#define print(...) println(__VA_ARGS__)
#define FLUSH() flush()

#include <concepts>

TE concept has_pow = requires(typename T::X x, ll k) {
  { T::pow(x, k) } -> same_as<typename T::X>;
};

TE typename T::X monoid_pow(typename T::X x, ll k) {
  using X = T::X;
  if constexpr (has_pow<T>) {
    return T::pow(x, k);
  } else {
    assert(k >= 0);
    X s = T::unit();
    for (; k; k >>= 1, x = T::op(x, x)) {
      if (k & 1) s = T::op(s, x);
    }
    return s;
  }
}

struct fset {
  int N, n;
  vc<ull> a[6];

  fset(int N = 0) { build(N); }

  fset(const string &s) { build(s); }

  void build(int M) {
    N = M;
    int m = max(N, 1), d = 0;
    do {
      m = (m + 63) >> 6;
      a[d++].assign(m, 0);
    } while (m != 1);
    n = d;
  }
  
  void build(const string &s) {
    N = len(s);
    build(N);
    FOR(i, N) if (s[i] == '1') a[0][i >> 6] |= 1ull << (i & 63);
    FOR(h, n - 1) {
      int sz = len(a[h]);
      FOR(i, sz) if (a[h][i]) a[h + 1][i >> 6] |= 1ull << (i & 63);
    }
  }

  void set() {
    FOR(i, N) a[0][i >> 6] |= 1ull << (i & 63);
    FOR(h, n - 1) {
      int sz = len(a[h]);
      FOR(i, sz) if (a[h][i]) a[h + 1][i >> 6] |= 1ull << (i & 63);
    }
  }

  void clear() { FOR(i, 6) fill(all(a[i]), 0); }

  bool empty() const { return not a[n - 1][0]; }

  bool operator[](int x) const { return a[0][x >> 6] >> (x & 63) & 1; }

  bool contains(int x) const { return a[0][x >> 6] >> (x & 63) & 1; }
  
  void insert(int x) {
    FOR(d, n) {
      int i = x >> 6, k = x & 63;
      a[d][i] |= 1ull << k;
      x = i;
    }
  }

  void emplace(int x) { insert(x); }

  void erase(int x) {
    FOR(d, n) {
      int i = x >> 6, k = x & 63;
      if (a[d][i] &= ~(1ull << k)) break;
      x = i;
    }
  }
  
  void extract(int x) { erase(x); }

  
  int prev(int x) const {
    chmin(x, N - 1);
    FOR(d, n) {
      if (x < 0) break;
      int i = x >> 6, k = x & 63;
      ull lw = a[d][i] << (63 - k);
      if (lw) {
        x -= __builtin_clzll(lw);
        for (int i = d; i--; ) x = x << 6 | topbit(a[i][x]);
        return x;
      }
      x = i - 1;
    }
    return -1;
  }
  
  int next(int x) const {
    if (x < 0) x = 0;
    FOR(d, n) {
      int i = x >> 6, k = x & 63;
      if (i >= len(a[d])) break;
      ull r = a[d][i] >> k;
      if (r) {
        x += lowbit(r);
        for (int i = d; i--; ) x = x << 6 | lowbit(a[i][x]);
        return x;
      }
      x = i + 1;
    }
    return N;
  }
  
  bool any(int l, int r) const { return next(l) < r; }

  vc<int> get_all() const { return get_all(0, N); }
  
  vc<int> get_all(int l, int r) const {
    vc<int> s;
    for (int x = next(l); x < r; x = next(x + 1)) s.ep(x);
    return s;
  }

  string to_string() const {
    string s(N, '?');
    FOR(i, N) s[i] = contains(i) + '0';
    return s;
  }
};

TE struct seg_t : T {
  using X = T::X;
  using T::op, T::unit;
  
  vc<X> a;
  int N, n, sz;

  seg_t(int N = 0) { build(N, [](int i) { return unit(); }); }
  seg_t(int N, Z f) { build(N, f); }
  seg_t(const vc<X> &v) { build(v); }

  void build(const vc<X> &v) {
    build(len(v), [&](int i) { return v[i]; });
  }

  void build(int M, Z f) {
    N = M, n = 1;
    while ((1 << n) < N) ++n;
    sz = 1 << n;
    a.assign(sz << 1, unit());
    FOR(i, N) a[sz + i] = f(i);
    FOR_R(i, 1, sz) upd(i);
  }

  void upd(int i) { a[i] = op(a[i << 1], a[i << 1 | 1]); }

  X get(int i) { return a[sz + i]; }
  vc<X> get_all() { return {a.begin() + sz, a.begin() + sz + N}; }

  void set(int i, const X &x) {
    a[i += sz] = x;
    while (i >>= 1) upd(i);
  }
  void multiply(int i, const X &x) {
    i += sz;
    a[i] = op(a[i], x);
    while (i >>= 1) upd(i);
  }
  
  X prod(int l, int r) {
    X x = unit(), y = unit();
    l += sz, r += sz;
    while (l < r) {
      if (l & 1) x = op(x, a[l++]);
      if (r & 1) y = op(a[--r], y);
      l >>= 1, r >>= 1;
    }
    return op(x, y);
  }
  X prod_all() { return a[1]; }

  
  int max_right(Z ck, int l) {
    if (l == N) return N;
    l += sz;
    X s = unit();
    do {
      while (not(l & 1)) l >>= 1;
      if (not ck(op(s, a[l]))) {
        while (l < sz) {
          l <<= 1;
          if (ck(op(s, a[l]))) s = op(s, a[l++]);
        }
        return l - sz;
      }
      s = op(s, a[l++]);
    } while ((l & -l) != l);
    return N;
  }
  
  int min_left(Z ck, int r) {
    if (r == 0) return 0;
    r += sz;
    X s = unit();
    do {
      --r;
      while (r > 1 and (r & 1)) r >>= 1;
      if (not ck(op(a[r], s))) {
        while (r < sz) {
          r = r << 1 | 1;
          if (ck(op(a[r], s))) s = op(a[r--], s);
        }
        return r + 1 - sz;
      }
      s = op(a[r], s);
    } while ((r & -r) != r);
    return 0;
  }
  X xor_prod(int l, int r, int xo) {
    static_assert(T::commute);
    X x = unit();
    for (int k = 0; k < n + 1 and l < r; ++k) {
      if (l & 1) x = op(x, a[(sz >> k) + ((l++) ^ xo)]);
      if (r & 1) x = op(x, a[(sz >> k) + ((--r) ^ xo)]);
      l >>= 1, r >>= 1, xo >>= 1;
    }
    return x;
  }
};

TE struct range_assign_seg : T {
  using X = T::X;
  using T::op, T::unit;

  int N;
  seg_t<T> seg;
  fset cut;
  vc<X> dat;

  range_assign_seg() {}
  range_assign_seg(int N) { build(N); }
  range_assign_seg(int N, Z f) { build(N, f); }
  range_assign_seg(const vc<X> &v) { build(v); }

  void build(int m) {
    build(m, [](int i) -> X { return unit(); });
  }
  void build(const vc<X> &v) {
    build(len(v), [&](int i) -> X { return v[i]; });
  }
  void build(int m, Z f) {
    N = m;
    seg.build(m, f);
    cut.build(N);
    cut.set();
    dat = seg.get_all();
  }

  X prod(int l, int r) {
    int a = cut.prev(l), b = cut.next(l), c = cut.prev(r);
    if (a == c) return monoid_pow<T>(dat[a], r - l);
    assert(b <= c);
    X x = monoid_pow<T>(dat[a], b - l);
    X y = seg.prod(b, c);
    X z = monoid_pow<T>(dat[c], r - c);
    return op(op(x, y), z);
  }

  X prod_all() { return seg.prod_all(); }

  void assign(int l, int r, X x) {
    int a = cut.prev(l), b = cut.next(r);
    if (a < l) seg.set(a, monoid_pow<T>(dat[a], l - a));
    if (r < b) {
      X y = dat[cut.prev(r)];
      dat[r] = y;
      cut.eb(r);
      seg.set(r, monoid_pow<T>(y, b - r));
    }
    for (int i : cut.get_all(l + 1, r)) {
      seg.set(i, unit());
      cut.erase(i);
    }
    dat[l] = x;
    cut.eb(l);
    seg.set(l, monoid_pow<T>(x, r - l));
  }

  vc<X> get_all() {
    vc<X> s(N);
    int l = 0;
    while (l < N) {
      int r = cut.next(l + 1);
      FOR(i, l, r) s[i] = dat[l];
      l = r;
    }
    return s;
  }
};

TE struct monoid_add {
  using X = T;
  static constexpr inline X op(const X &x, const X &y) { return x + y; }
  static constexpr inline X inv(const X &x) { return -x; }
  static constexpr inline X pow(const X &x, ll n) { return X(n) * x; }
  static constexpr inline X unit() { return X(0); }
  static constexpr bool commute = 1;
};

void Yorisou() {
  INT(N, Q);
  
  range_assign_seg<monoid_add<uint>> a(N), b(N);
  ull sa = 0, sb = 0;
  FOR(Q) {
    UINT(op, l, r);
    ++r;
    if (op == 0) {
      
      uint sca = a.prod(l, r), scb = b.prod(l, r);
      if (sca > scb) sa += sca;
      if (sca < scb) sb += scb;
    } else if (op == 1) {
      
      
      a.assign(l, r, 1);
      b.assign(l, r, 0);
    } else {
      
      
      a.assign(l, r, 0);
      b.assign(l, r, 1);
    }
  }
  print(sa + a.prod_all(), sb + b.prod_all());
  
}
constexpr int tests = 0, fl = 0, DB = 10;
int main() {
  cin.tie(0)->sync_with_stdio(0);
  int T = 1;
  if (fl) cerr.tie(0);
  if (tests and not fl) IN(T);
  for (int i = 0; i < T or fl; ++i) {
    Yorisou();
    if (fl and i % DB == 0) cerr << "Case: " << i << '\n';
  }
  return 0;
}