#include #include using namespace std; #define rep(i,n) for(long long i = 0; i < (long long)(n); i++) #define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++) #define pb push_back #define all(x) (x).begin(), (x).end() #define fi first #define se second #define mt make_tuple #define mp make_pair template bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); } template bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } #define exists find_if #define forall all_of using ll = long long; using vll = vector; using vvll = vector; using P = pair; using ld = long double; using vld = vector; using vi = vector; using vvi = vector; vll conv(vi& v) { vll r(v.size()); rep(i, v.size()) r[i] = v[i]; return r; } using Pos = complex; template ostream &operator<<(ostream &o, const pair &v) { o << "(" << v.first << ", " << v.second << ")"; return o; } template struct seq{}; template struct gen_seq : gen_seq{}; template struct gen_seq<0, Is...> : seq{}; template void print_tuple(basic_ostream& os, Tuple const& t, seq){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get(t)), 0)...}; } template auto operator<<(basic_ostream& os, tuple const& t) -> basic_ostream& { os << "("; print_tuple(os, t, gen_seq()); return os << ")"; } ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; o << endl; } return o; } template ostream &operator<<(ostream &o, const vector &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const set &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const map &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const unordered_map &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]"; return o; } vector range(const int x, const int y) { vector v(y - x + 1); iota(v.begin(), v.end(), x); return v; } template istream& operator>>(istream& i, vector& o) { rep(j, o.size()) i >> o[j]; return i;} string bits_to_string(ll input, ll n=64) { string s; rep(i, n) s += '0' + !!(input & (1ll << i)); reverse(all(s)); return s; } template unordered_map counter(vector vec){unordered_map ret; for (auto&& x : vec) ret[x]++; return ret;}; string substr(string s, P x) {return s.substr(x.fi, x.se - x.fi); } struct ci : public iterator { ll n; ci(const ll n) : n(n) { } bool operator==(const ci& x) { return n == x.n; } bool operator!=(const ci& x) { return !(*this == x); } ci &operator++() { n++; return *this; } ll operator*() const { return n; } }; size_t random_seed; namespace std { using argument_type = P; template<> struct hash { size_t operator()(argument_type const& x) const { size_t seed = random_seed; seed ^= hash{}(x.fi); seed ^= (hash{}(x.se) << 1); return seed; } }; }; // hash for various class namespace myhash{ const int Bsizes[]={3,9,13,17,21,25,29,33,37,41,45,49,53,57,61,65,69,73,77,81}; const int xor_nums[]={0x100007d1,0x5ff049c9,0x14560859,0x07087fef,0x3e277d49,0x4dba1f17,0x709c5988,0x05904258,0x1aa71872,0x238819b3,0x7b002bb7,0x1cf91302,0x0012290a,0x1083576b,0x76473e49,0x3d86295b,0x20536814,0x08634f4d,0x115405e8,0x0e6359f2}; const int hash_key=xor_nums[rand()%20]; const int mod_key=xor_nums[rand()%20]; template struct myhash{ std::size_t operator()(const T& val) const { return (hash{}(val)%mod_key)^hash_key; } }; }; template class uset:public std::unordered_set> { using SET=std::unordered_set>; public: uset():SET(){SET::rehash(myhash::Bsizes[rand()%20]);} }; template class umap:public std::unordered_map> { public: using MAP=std::unordered_map>; umap():MAP(){MAP::rehash(myhash::Bsizes[rand()%20]);} }; struct timeval start; double sec() { struct timeval tv; gettimeofday(&tv, NULL); return (tv.tv_sec - start.tv_sec) + (tv.tv_usec - start.tv_usec) * 1e-6; } struct init_{init_(){ gettimeofday(&start, NULL); ios::sync_with_stdio(false); cin.tie(0); srand((unsigned int)time(NULL)); random_seed = RAND_MAX / 2 + rand() / 2; }} init__; static const double EPS = 1e-14; static const long long INF = 1e18; static const long long mo = 1e9+7; #define ldout fixed << setprecision(40) ll ume[] = { 48, 48, 64, 64, 64, 64, 64, 72, 64, 72, 64, 64, 72, 80, 72, 72, 96, 72, 72, 64, 96, 64, 96, 80, 72, 72, 72, 80, 72, 96, 80, 72, 96, 96, 96, 96, 64, 72, 96, 80, 96, 96, 72, 80, 72, 96, 96, 80, 72, 96, 96, 72, 72, 96, 96, 96, 80, 96, 96, 80, 96, 96, 96, 96, 96, 96, 80, 96, 96, 96, 96, 96, 80, 96, 80, 96, 96, 96, 96, 64, 128, 96, 96, 96, 72, 72, 96, 96, 80, 96, 96, 96, 96, 96, 80, 96, 80, 96, 96, 96, 96, 96, 128, 80, 96, 96, 96, 96, 96, 96, 80, 96, 80, 128, 96, 80, 96, 96, 128, 96, 96, 96, 108, 80, 96, 96, 96, 96, 96, 96, 96, 128, 80, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 128, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 128, 96, 96, 96, 96, 96, 96, 128, 128, 128, 96, 96, 96, 96, 128, 96, 96, 96, 96, 120, 72, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 128, 96, 128, 96, 96, 96, 96, 96, 128, 96, 96, 128, 96, 96, 64, 144, 96, 96, 96, 96, 96, 96, 96, 128, 96, 96, 96, 96, 96, 96, 96, 96, 96, 128, 96, 128, 96, 96, 96, 96, 128, 120, 96, 96, 128, 96, 96, 128, 96, 96, 80, 108, 128, 128, 96, 96, 128, 72, 96, 128, 96, 96, 96, 96, 96, 96, 96, 96, 96, 128, 96, 96, 144, 96, 128, 96, 96, 96, 96, 144, 96, 96, 96, 128, 96, 96, 128, 96, 96, 96, 96, 96, 128, 80, 128, 96, 96, 96, 96, 128, 96, 144, 96, 96, 96, 128, 96, 96, 128, 96, 96, 96, 96, 120, 96, 96, 96, 128, 96, 128, 96, 96, 96, 96, 96, 128, 96, 128, 96, 128, 128, 96, 96, 128, 96, 96, 96, 128, 96, 96, 96, 96, 128, 96, 128, 96, 128, 96, 96, 96, 96, 128, 112, 96, 144, 128, 128, 96, 96, 96, 128, 96, 108, 96, 128, 96, 120, 96, 96, 128, 128, 96, 96, 128, 96, 72, 128, 96, 96, 96, 128, 96, 128, 96, 96, 128, 96, 144, 96, 96, 96, 96, 144, 128, 96, 96, 96, 128, 96, 80, 96, 96, 80, 128, 96, 96, 96, 160, 96, 96, 128, 96, 96, 128, 96, 128, 128, 96, 128, 128, 96, 96, 96, 144, 96, 96, 128, 96, 96, 96, 96, 96, 128, 96, 128, 96, 96, 96, 96, 96, 128, 96, 96, 96, 96, 144, 128, 96, 96, 96, 96, 96, 128, 96, 96, 96, 128, 96, 96, 96, 144, 96, 96, 128, 128, 96, 96, 96, 128, 128, 96, 144, 96, 128, 128, 96, 120, 96, 128, 96, 96, 128, 128, 80, 128, 96, 128, 128, 96, 96, 128, 96, 96, 128, 96, 108, 96, 96, 128, 128, 128, 96, 96, 96, 144, 128, 128, 128, 96, 144, 128, 96, 128, 96, 96, 96, 128, 96, 160, 96, 128, 96, 96, 96, 96, 96, 96, 96, 128, 128, 120, 144, 128, 96, 96, 96, 96, 96, 144, 128, 128, 96, 128, 96, 96, 96, 96, 96, 128, 96, 96, 144, 96, 96, 96, 128, 128, 96, 96, 128, 96, 128, 96, 128, 96, 128, 120, 128, 96, 96, 96, 128, 96, 160, 96, 128, 96, 128, 128, 144, 128, 128, 96, 96, 96, 108, 96, 128, 96, 96, 128, 96, 128, 96, 96, 144, 112, 96, 128, 192, 96, 96, 96, 128, 128, 96, 128, 96, 128, 128, 96, 96, 96, 96, 128, 96, 128, 144, 96, 120, 96, 96, 96, 128, 96, 128, 96, 128, 128, 128, 96, 128, 96, 96, 96, 128, 96, 96, 128, 128, 96, 96, 96, 128, 128, 128, 144, 144, 128, 96, 128, 128, 128, 128, 128, 96, 144, 96, 96, 96, 128, 96, 128, 192, 96, 96, 96, 96, 128, 96, 96, 96, 128, 96, 96, 120, 96, 128, 128, 128, 96, 128, 128, 128, 96, 96, 128, 128, 96, 96, 128, 96, 144, 96, 128, 128, 96, 128, 96, 96, 96, 96, 144, 144, 128, 128, 128, 96, 96, 128, 96, 128, 96, 128, 128, 144, 128, 128, 128, 96, 96, 128, 96, 96, 128, 120, 128, 96, 128, 96, 128, 128, 144, 128, 128, 96, 128, 96, 96, 160, 128, 128, 96, 96, 128, 96, 128, 128, 96, 96, 128, 96, 96, 128, 144, 96, 128, 96, 128, 128, 96, 96, 96, 144, 96, 96, 96, 128, 144, 128, 96, 96, 128, 128, 96, 96, 96, 144, 120, 128, 96, 96, 144, 128, 128, 96, 96, 128, 128, 144, 128, 96, 96, 128, 128, 128, 128, 96, 96, 96, 128, 128, 96, 128, 96, 128, 96, 96, 160, 128, 96, 96, 128, 128, 96, 96, 128, 96, 144, 128, 96, 128, 128, 96, 128, 128, 128, 128, 96, 128, 128, 96, 128, 96, 96, 144, 96, 96, 96, 112, 144, 96, 144, 96, 96, 192, 128, 96, 96, 160, 96, 128, 128, 96, 96, 96, 192, 128, 96, 128, 96, 96, 128, 96, 128, 96, 144, 96, 128, 128, 96, 128, 96, 128, 128, 96, 128, 96, 160, 128, 128, 128, 128, 144, 128, 128, 128, 96, 96, 128, 96, 128, 96, 96, 128, 128, 128, 96, 128, 128, 120, 144, 128, 96, 144, 96, 128, 128, 96, 96, 144, 96, 96, 144, 96, 96, 128, 96, 144, 128, 96, 128, 128, 96, 96, 144, 128, 96, 128, 96, 128, 128, 96, 128, 80, 144, 144, 128, 96, 96, 128, 96, 128, 128, 96, 128, 120, 120, 128, 128, 128, 96, 96, 128, 96, 144, 128, 96, 128, 128, 144, 128, 128, 128, 120, 96, 128, 128, 128, 96, 96, 128, 96, 160, 128, 96, 128, 96, 96, 128, 128, 96, 128, 108, 192, 96, 128, 128, 96, 112, 128, 144, 128, 128, 128, 96, 128, 96, 96, 128, 128, 128, 144, 96, 128, 96, 128, }; vector memo(10048901); ll solve(ll x, ll y) { if (x > y) return 0; ll ret = 0; repi(i, x, y+1) { ll tmp = 0; for (ll j = 1; j * j <= i; j++) { if (memo[i-j*j]) tmp++; } chmax(ret, tmp); } return ret * 4ll; } int main(void) { ll x, y; cin >> x >> y; rep(i, 3170) { memo[i*i] = 1; } // 12345, 52346 // を // 12345-20000, 20001-30000, ..., 40001-50000, 50001-52346とする if (y - x < 50000) { cout << solve(x, y) << endl; } else { ll l = (x + 9999) / 10000 * 10000; // x,l ll lp1 = l+1; ll r = y / 10000 * 10000 + 1; // r,y ll rm1 = r-1; // cout << l << " " << r << endl; ll ret = 0; chmax(ret, solve(x, l)); repi(i, l/10000, (r-2)/10000) { cout << i << endl; chmax(ret, ume[i]); } chmax(ret, solve(r, y)); cout << ret << endl; } return 0; }