test/1_mytest/palindrome_decomposition_dp.test.cpp

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• Last update: 2024-12-26 06:32:57+09:00
• Problem: https://judge.yosupo.jp/problem/aplusb

Depends on

• my_template.hpp
• other/io.hpp
• random/base.hpp
• string/palindrome_decomposition_dp.hpp
• string/palindromic_tree.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "my_template.hpp"
#include "other/io.hpp"

#include "random/base.hpp"
#include "string/palindrome_decomposition_dp.hpp"

void test_min_palindrome_decomposition() {
  FOR(N, 30) {
    FOR(K, 1, 5) {
      FOR(10) {
        string S;
        FOR(N) {
          char c = 'a' + RNG(0, K);
          S += c;
        }
        vv(int, is_pal, N + 1, N + 1);
        FOR_R(L, N + 1) {
          FOR(R, N + 1) {
            if (R - L <= 1) {
              is_pal[L][R] = 1;
              continue;
            }
            is_pal[L][R] = (S[L] == S[R - 1]) && is_pal[L + 1][R - 1];
          }
        }
        vc<int> DP(N + 1, infty<int>);
        DP[0] = 0;
        FOR(R, 1, N + 1) {
          FOR(L, R) {
            if (is_pal[L][R]) chmin(DP[R], DP[L] + 1);
          }
        }
        vc<int> dp_init(N + 1, infty<int>);
        dp_init[0] = 0;
        auto F = [&](int i, int a, int g) -> int { return min(a, g + 1); };
        auto G = [&](int i, int g, int a) -> int { return min(g, a); };

        vc<int> dp = palindrome_decomposition_dp<int, int>(S, dp_init,
                                                           infty<int>, F, G);
        assert(dp == DP);
      }
    }
  }
}

void test_cnt_palindrome_decomposition() {
  FOR(N, 30) {
    FOR(K, 1, 5) {
      FOR(10) {
        string S;
        FOR(N) {
          char c = 'a' + RNG(0, K);
          S += c;
        }
        vv(int, is_pal, N + 1, N + 1);
        FOR_R(L, N + 1) {
          FOR(R, N + 1) {
            if (R - L <= 1) {
              is_pal[L][R] = 1;
              continue;
            }
            is_pal[L][R] = (S[L] == S[R - 1]) && is_pal[L + 1][R - 1];
          }
        }
        vc<int> DP(N + 1, 0);
        DP[0] = 1;
        FOR(R, 1, N + 1) {
          FOR(L, R) {
            if (is_pal[L][R]) DP[R] += DP[L];
          }
        }
        vc<int> dp_init(N + 1);
        dp_init[0] = 1;
        auto F = [&](int i, int a, int g) -> int { return a + g; };
        auto G = [&](int i, int g, int a) -> int { return g + a; };

        vc<int> dp = palindrome_decomposition_dp<int, int>(S, dp_init, 0, F, G);
        assert(dp == DP);
      }
    }
  }
}

void solve() {
  int a, b;
  cin >> a >> b;
  cout << a + b << "\n";
}

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

#line 1 "test/1_mytest/palindrome_decomposition_dp.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

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

#include <bits/stdc++.h>

using namespace std;

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

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

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

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

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

#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

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

#define stoi stoll

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

template <typename T>
T kth_bit(int k) {
  return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
  return x >> k & 1;
}

template <typename UINT>
struct all_bit {
  struct iter {
    UINT s;
    iter(UINT s) : s(s) {}
    int operator*() const { return lowbit(s); }
    iter &operator++() {
      s &= s - 1;
      return *this;
    }
    bool operator!=(const iter) const { return s != 0; }
  };
  UINT s;
  all_bit(UINT s) : s(s) {}
  iter begin() const { return iter(s); }
  iter end() const { return iter(0); }
};

template <typename UINT>
struct all_subset {
  static_assert(is_unsigned<UINT>::value);
  struct iter {
    UINT s, t;
    bool ed;
    iter(UINT s) : s(s), t(s), ed(0) {}
    int operator*() const { return s ^ t; }
    iter &operator++() {
      (t == 0 ? ed = 1 : t = (t - 1) & s);
      return *this;
    }
    bool operator!=(const iter) const { return !ed; }
  };
  UINT s;
  all_subset(UINT s) : s(s) {}
  iter begin() const { return iter(s); }
  iter end() const { return iter(0); }
};

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

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

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

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

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

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

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

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

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

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

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


// https://judge.yosupo.jp/submission/21623

namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf

uint32_t pil = 0, pir = 0, por = 0;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

// gcc expansion. called automaticall after main.

void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio

using fastio::read;
using fastio::print;
using fastio::flush;

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

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

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

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
void YA(bool t = 1) { print(t ? "YA" : "TIDAK"); }
void TIDAK(bool t = 1) { YES(!t); }
#line 4 "test/1_mytest/palindrome_decomposition_dp.test.cpp"

#line 2 "random/base.hpp"

u64 RNG_64() {
  static u64 x_ = u64(chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count()) * 10150724397891781847ULL;
  x_ ^= x_ << 7;
  return x_ ^= x_ >> 9;
}

u64 RNG(u64 lim) { return RNG_64() % lim; }

ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 1 "string/palindromic_tree.hpp"
// palindromic tree を作る
template <int sigma>
struct Palindromic_Tree {
  struct Node {
    array<int, sigma> TO;
    int link;
    int length;
    pair<int, int> pos; // position of first ocurrence
    Node(int link, int length, int l, int r)
        : link(link), length(length), pos({l, r}) {
      fill(all(TO), -1);
    }
  };

  vc<Node> nodes;
  vc<int> path;

  template <typename STRING>
  Palindromic_Tree(const STRING& S, char off) {
    nodes.eb(Node(-1, -1, 0, -1));
    nodes.eb(Node(0, 0, 0, 0));
    int p = 0;
    FOR(i, len(S)) {
      path.eb(p);
      int x = S[i] - off;
      while (p) {
        int j = i - 1 - nodes[p].length;
        bool can = (j >= 0 && S[j] - off == x);
        if (!can) {
          p = nodes[p].link;
          continue;
        }
        break;
      }
      if (nodes[p].TO[x] != -1) {
        p = nodes[p].TO[x];
        continue;
      }
      int to = len(nodes);
      int l = i - 1 - nodes[p].length;
      int r = i + 1;
      nodes[p].TO[x] = to;

      int link;
      if (p == 0) link = 1;
      if (p != 0) {
        while (1) {
          p = nodes[p].link;
          int j = i - 1 - nodes[p].length;
          bool can = (j >= 0 && S[j] - off == x);
          if (can) break;
        }
        assert(nodes[p].TO[x] != -1);
        link = nodes[p].TO[x];
      }
      nodes.eb(Node(link, r - l, l, r));
      p = to;
    }
    path.eb(p);
  }

  // node ごとの出現回数
  vc<int> count() {
    vc<int> res(len(nodes));
    for (auto&& p: path) res[p]++;
    FOR_R(k, 1, len(nodes)) {
      int link = nodes[k].link;
      res[link] += res[k];
    }
    return res;
  }
};
#line 2 "string/palindrome_decomposition_dp.hpp"

/*
https://arxiv.org/pdf/1403.2431.pdf
回文に分割する dp は O(nlog n) time, O(n) space になる
同じところに遷移するものをまとめたもの gdp
・dp[i] := dp_init[i]
・F(i, dp[i], gdp[j]): dp[i] に gdp[j] からの遷移を追加
・gdp[i] := gdp_unit
・G(i, gdp[j], dp[i]): gdp[j] に dp[i] からの遷移をまとめる
偶数長のものに制限してやることもある
この場合 i が奇数のときの F は何もしなければよい
https://codeforces.com/contest/932/problem/G
https://codeforces.com/problemset/problem/906/E
*/
template <typename DP, typename GDP, typename F1, typename F2>
vc<DP> palindrome_decomposition_dp(string S, vc<DP> dp_init, GDP gdp_unit, F1 F,
                                   F2 G) {
  int N = len(S);
  Palindromic_Tree<26> X(S, 'a');
  int n = len(X.nodes);
  /*
  各ノードに対して
  suffix との長さの差分
  同じ差分で何ステップ遡れるか？
  遡った先の node
  */
  vc<int> diff(n, infty<int>);
  vc<int> step(n);
  vc<int> up(n);
  FOR(v, 2, n) {
    int w = X.nodes[v].link;
    int d = X.nodes[v].length - X.nodes[w].length;
    diff[v] = d;
    step[v] = (diff[v] == diff[w] ? step[w] : 0) + 1;
    up[v] = (diff[v] == diff[w] ? up[w] : w);
  }

  vc<DP>& dp = dp_init;
  assert(len(dp) == N + 1);
  vc<GDP> gdp(N + 1);
  auto& path = X.path;
  FOR(j, 1, N + 1) {
    int v = path[j];
    int i = j - X.nodes[v].length;
    while (v >= 2) {
      if (step[v] == 1) {
        // 1 項だけからなる等差数列の集約で初期化
        gdp[i] = gdp_unit;
        gdp[i] = G(i, gdp[i], dp[i]);
      } else {
        // 等差数列の末尾を追加
        int idx = i + diff[v] * (step[v] - 1);
        gdp[i] = G(idx, gdp[i], dp[idx]);
      }
      dp[j] = F(j, dp[j], gdp[i]), i += diff[v] * step[v], v = up[v];
    }
  }
  return dp;
}
#line 7 "test/1_mytest/palindrome_decomposition_dp.test.cpp"

void test_min_palindrome_decomposition() {
  FOR(N, 30) {
    FOR(K, 1, 5) {
      FOR(10) {
        string S;
        FOR(N) {
          char c = 'a' + RNG(0, K);
          S += c;
        }
        vv(int, is_pal, N + 1, N + 1);
        FOR_R(L, N + 1) {
          FOR(R, N + 1) {
            if (R - L <= 1) {
              is_pal[L][R] = 1;
              continue;
            }
            is_pal[L][R] = (S[L] == S[R - 1]) && is_pal[L + 1][R - 1];
          }
        }
        vc<int> DP(N + 1, infty<int>);
        DP[0] = 0;
        FOR(R, 1, N + 1) {
          FOR(L, R) {
            if (is_pal[L][R]) chmin(DP[R], DP[L] + 1);
          }
        }
        vc<int> dp_init(N + 1, infty<int>);
        dp_init[0] = 0;
        auto F = [&](int i, int a, int g) -> int { return min(a, g + 1); };
        auto G = [&](int i, int g, int a) -> int { return min(g, a); };

        vc<int> dp = palindrome_decomposition_dp<int, int>(S, dp_init,
                                                           infty<int>, F, G);
        assert(dp == DP);
      }
    }
  }
}

void test_cnt_palindrome_decomposition() {
  FOR(N, 30) {
    FOR(K, 1, 5) {
      FOR(10) {
        string S;
        FOR(N) {
          char c = 'a' + RNG(0, K);
          S += c;
        }
        vv(int, is_pal, N + 1, N + 1);
        FOR_R(L, N + 1) {
          FOR(R, N + 1) {
            if (R - L <= 1) {
              is_pal[L][R] = 1;
              continue;
            }
            is_pal[L][R] = (S[L] == S[R - 1]) && is_pal[L + 1][R - 1];
          }
        }
        vc<int> DP(N + 1, 0);
        DP[0] = 1;
        FOR(R, 1, N + 1) {
          FOR(L, R) {
            if (is_pal[L][R]) DP[R] += DP[L];
          }
        }
        vc<int> dp_init(N + 1);
        dp_init[0] = 1;
        auto F = [&](int i, int a, int g) -> int { return a + g; };
        auto G = [&](int i, int g, int a) -> int { return g + a; };

        vc<int> dp = palindrome_decomposition_dp<int, int>(S, dp_init, 0, F, G);
        assert(dp == DP);
      }
    }
  }
}

void solve() {
  int a, b;
  cin >> a >> b;
  cout << a + b << "\n";
}

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

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