結果
| 問題 | No.1593 Perfect Distance |
| ユーザー |
 maspy
|
| 提出日時 | 2022-05-05 17:50:59 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 2,000 ms |
| コード長 | 20,566 bytes |
| コンパイル時間 | 2,523 ms |
| コンパイル使用メモリ | 226,692 KB |
| 実行使用メモリ | 5,376 KB |
| 最終ジャッジ日時 | 2024-07-04 19:21:20 |
| 合計ジャッジ時間 | 3,224 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 2 ms
5,248 KB |
| testcase_02 | AC | 2 ms
5,248 KB |
| testcase_03 | AC | 2 ms
5,376 KB |
| testcase_04 | AC | 1 ms
5,376 KB |
| testcase_05 | AC | 2 ms
5,376 KB |
| testcase_06 | AC | 2 ms
5,376 KB |
| testcase_07 | AC | 2 ms
5,376 KB |
| testcase_08 | AC | 2 ms
5,376 KB |
| testcase_09 | AC | 2 ms
5,376 KB |
| testcase_10 | AC | 2 ms
5,376 KB |
| testcase_11 | AC | 1 ms
5,376 KB |
| testcase_12 | AC | 1 ms
5,376 KB |
| testcase_13 | AC | 2 ms
5,376 KB |
| testcase_14 | AC | 1 ms
5,376 KB |
| testcase_15 | AC | 2 ms
5,376 KB |
| testcase_16 | AC | 2 ms
5,376 KB |
| testcase_17 | AC | 2 ms
5,376 KB |
| testcase_18 | AC | 2 ms
5,376 KB |
| testcase_19 | AC | 2 ms
5,376 KB |
ソースコード
#line 1 "main.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1593"
#line 1 "/home/maspy/compro/library/my_template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pi = pair<ll, ll>;
using vi = vector<ll>;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
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 vec(type, name, ...) vector<type> name(__VA_ARGS__)
#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__))))
#define FOR_(n) for (ll _ = 0; (_) < (ll)(n); ++(_))
#define FOR(i, n) for (ll i = 0; (i) < (ll)(n); ++(i))
#define FOR3(i, m, n) for (ll i = (m); (i) < (ll)(n); ++(i))
#define FOR_R(i, n) for (ll i = (ll)(n)-1; (i) >= 0; --(i))
#define FOR3_R(i, m, n) for (ll i = (ll)(n)-1; (i) >= (ll)(m); --(i))
#define FOR_subset(t, s) for (ll t = s; t >= 0; t = (t == 0 ? -1 : (t - 1) & s))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
template <typename T>
T SUM(vector<T> &A) {
T sum = T(0);
for (auto &&a: A) sum += a;
return sum;
}
#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())
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); }
// (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, typename U>
T ceil(T x, U y) {
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
T q = floor(x, y);
return {q, x - q * y};
}
ll binary_search(function<bool(ll)> check, ll ok, ll ng) {
assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
if (check(x))
ok = x;
else
ng = x;
}
return ok;
}
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);
}
vi s_to_vi(const string& S, char first_char) {
vi A(S.size());
FOR(i, S.size()) { A[i] = S[i] - first_char; }
return A;
}
template <typename T>
vector<T> cumsum(vector<T> &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;
}
template <typename CNT, typename T>
vc<CNT> bincount(const vc<T> &A, int size) {
vc<CNT> C(size);
for (auto &&x: A) { ++C[x]; }
return C;
}
template <typename T>
vector<int> argsort(const vector<T> &A) {
// stable
vector<int> ids(A.size());
iota(all(ids), 0);
sort(all(ids),
[&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
int n = len(A);
assert(len(I) == n);
vc<T> B(n);
FOR(i, n) B[i] = A[I[i]];
return B;
}
#line 1 "/home/maspy/compro/library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>
namespace detail {
template <typename T, decltype(&T::is_modint) = &T::is_modint>
std::true_type check_value(int);
template <typename T>
std::false_type check_value(long);
} // namespace detail
template <typename T>
struct is_modint : decltype(detail::check_value<T>(0)) {};
template <typename T>
using is_modint_t = enable_if_t<is_modint<T>::value>;
template <typename T>
using is_not_modint_t = enable_if_t<!is_modint<T>::value>;
struct Scanner {
FILE *fp;
char line[(1 << 15) + 1];
size_t st = 0, ed = 0;
void reread() {
memmove(line, line + st, ed - st);
ed -= st;
st = 0;
ed += fread(line + ed, 1, (1 << 15) - ed, fp);
line[ed] = '\0';
}
bool succ() {
while (true) {
if (st == ed) {
reread();
if (st == ed) return false;
}
while (st != ed && isspace(line[st])) st++;
if (st != ed) break;
}
if (ed - st <= 50) {
bool sep = false;
for (size_t i = st; i < ed; i++) {
if (isspace(line[i])) {
sep = true;
break;
}
}
if (!sep) reread();
}
return true;
}
template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
bool read_single(T &ref) {
if (!succ()) return false;
while (true) {
size_t sz = 0;
while (st + sz < ed && !isspace(line[st + sz])) sz++;
ref.append(line + st, sz);
st += sz;
if (!sz || st != ed) break;
reread();
}
return true;
}
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
bool read_single(T &ref) {
if (!succ()) return false;
bool neg = false;
if (line[st] == '-') {
neg = true;
st++;
}
ref = T(0);
while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
if (neg) ref = -ref;
return true;
}
template <class T, is_modint_t<T> * = nullptr>
bool read_single(T &ref) {
long long val = 0;
bool f = read_single(val);
ref = T(val);
return f;
}
bool read_single(double &ref) {
string s;
if (!read_single(s)) return false;
ref = std::stod(s);
return true;
}
bool read_single(char &ref) {
string s;
if (!read_single(s) || s.size() != 1) return false;
ref = s[0];
return true;
}
template <class T>
bool read_single(vector<T> &ref) {
for (auto &d: ref) {
if (!read_single(d)) return false;
}
return true;
}
template <class T, class U>
bool read_single(pair<T, U> &p) {
return (read_single(p.first) && read_single(p.second));
}
template <class A, class B, class C>
bool read_single(tuple<A, B, C> &p) {
return (read_single(get<0>(p)) && read_single(get<1>(p))
&& read_single(get<2>(p)));
}
template <class A, class B, class C, class D>
bool read_single(tuple<A, B, C, D> &p) {
return (read_single(get<0>(p)) && read_single(get<1>(p))
&& read_single(get<2>(p)) && read_single(get<3>(p)));
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
bool f = read_single(h);
assert(f);
read(t...);
}
Scanner(FILE *fp) : fp(fp) {}
};
struct Printer {
Printer(FILE *_fp) : fp(_fp) {}
~Printer() { flush(); }
static constexpr size_t SIZE = 1 << 15;
FILE *fp;
char line[SIZE], small[50];
size_t pos = 0;
void flush() {
fwrite(line, 1, pos, fp);
pos = 0;
}
void write(const char &val) {
if (pos == SIZE) flush();
line[pos++] = val;
}
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
void write(T val) {
if (pos > (1 << 15) - 50) flush();
if (val == 0) {
write('0');
return;
}
if (val < 0) {
write('-');
val = -val; // todo min
}
size_t len = 0;
while (val) {
small[len++] = char(0x30 | (val % 10));
val /= 10;
}
for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
pos += len;
}
void write(const string &s) {
for (char c: s) write(c);
}
void write(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) write(s[i]);
}
void write(const double &x) {
ostringstream oss;
oss << setprecision(15) << x;
string s = oss.str();
write(s);
}
void write(const long double &x) {
ostringstream oss;
oss << setprecision(15) << x;
string s = oss.str();
write(s);
}
template <class T, is_modint_t<T> * = nullptr>
void write(T &ref) {
write(ref.val);
}
template <class T>
void write(const vector<T> &val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) write(' ');
write(val[i]);
}
}
template <class T, class U>
void write(const pair<T, U> &val) {
write(val.first);
write(' ');
write(val.second);
}
template <class A, class B, class C>
void write(const tuple<A, B, C> &val) {
auto &[a, b, c] = val;
write(a), write(' '), write(b), write(' '), write(c);
}
template <class A, class B, class C, class D>
void write(const tuple<A, B, C, D> &val) {
auto &[a, b, c, d] = val;
write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d);
}
template <class A, class B, class C, class D, class E>
void write(const tuple<A, B, C, D, E> &val) {
auto &[a, b, c, d, e] = val;
write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e);
}
template <class A, class B, class C, class D, class E, class F>
void write(const tuple<A, B, C, D, E, F> &val) {
auto &[a, b, c, d, e, f] = val;
write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e), write(' '), write(f);
}
template <class T, size_t S>
void write(const array<T, S> &val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) write(' ');
write(val[i]);
}
}
void write(i128 val) {
string s;
bool negative = 0;
if(val < 0){
negative = 1;
val = -val;
}
while (val) {
s += '0' + int(val % 10);
val /= 10;
}
if(negative) s += "-";
reverse(all(s));
if (len(s) == 0) s = "0";
write(s);
}
};
Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);
void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
printer.write(head);
if (sizeof...(Tail)) printer.write(' ');
print(forward<Tail>(tail)...);
}
void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
scanner.read(head);
read(tail...);
}
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 2 "/home/maspy/compro/library/nt/primetest.hpp"
struct m64 {
using i64 = int64_t;
using u64 = uint64_t;
using u128 = __uint128_t;
inline static u64 m, r, n2; // r * m = -1 (mod 1<<64), n2 = 1<<128 (mod m)
static void set_mod(u64 m) {
assert(m < (1ull << 62));
assert((m & 1) == 1);
m64::m = m;
n2 = -u128(m) % m;
r = m;
FOR(_, 5) r *= 2 - m * r;
r = -r;
assert(r * m == -1ull);
}
static u64 reduce(u128 b) { return (b + u128(u64(b) * r) * m) >> 64; }
u64 x;
m64() : x(0) {}
m64(u64 x) : x(reduce(u128(x) * n2)){};
u64 val() const {
u64 y = reduce(x);
return y >= m ? y - m : y;
}
m64 &operator+=(m64 y) {
x += y.x - (m << 1);
x = (i64(x) < 0 ? x + (m << 1) : x);
return *this;
}
m64 &operator-=(m64 y) {
x -= y.x;
x = (i64(x) < 0 ? x + (m << 1) : x);
return *this;
}
m64 &operator*=(m64 y) {
x = reduce(u128(x) * y.x);
return *this;
}
m64 operator+(m64 y) const { return m64(*this) += y; }
m64 operator-(m64 y) const { return m64(*this) -= y; }
m64 operator*(m64 y) const { return m64(*this) *= y; }
bool operator==(m64 y) const {
return (x >= m ? x - m : x) == (y.x >= m ? y.x - m : y.x);
}
bool operator!=(m64 y) const { return not operator==(y); }
m64 pow(u64 n) const {
m64 y = 1, z = *this;
for (; n; n >>= 1, z *= z)
if (n & 1) y *= z;
return y;
}
};
bool primetest(const uint64_t x) {
using u64 = uint64_t;
if (x == 2 or x == 3 or x == 5 or x == 7) return true;
if (x % 2 == 0 or x % 3 == 0 or x % 5 == 0 or x % 7 == 0) return false;
if (x < 121) return x > 1;
const u64 d = (x - 1) >> __builtin_ctzll(x - 1);
m64::set_mod(x);
const m64 one(1), minus_one(x - 1);
auto ok = [&](u64 a) {
auto y = m64(a).pow(d);
u64 t = d;
while (y != one and y != minus_one and t != x - 1) y *= y, t <<= 1;
if (y != minus_one and t % 2 == 0) return false;
return true;
};
if (x < (1ull << 32)) {
for (u64 a: {2, 7, 61})
if (not ok(a)) return false;
} else {
for (u64 a: {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
if (x <= a) return true;
if (not ok(a)) return false;
}
}
return true;
}
#line 3 "/home/maspy/compro/library/nt/factor.hpp"
mt19937_64 rng_mt{random_device{}()};
ll rnd(ll n) { return uniform_int_distribution<ll>(0, n - 1)(rng_mt); }
ll rho(ll n, ll c) {
m64::set_mod(n);
assert(n > 1);
const m64 cc(c);
auto f = [&](m64 x) { return x * x + cc; };
m64 x = 1, y = 2, z = 1, q = 1;
ll g = 1;
const ll m = 1LL << (__lg(n) / 5); // ?
for (ll r = 1; g == 1; r <<= 1) {
x = y;
FOR(_, r) y = f(y);
for (ll k = 0; k < r and g == 1; k += m) {
z = y;
FOR(_, min(m, r - k)) y = f(y), q *= x - y;
g = gcd(q.val(), n);
}
}
if (g == n)
do {
z = f(z);
g = gcd((x - z).val(), n);
} while (g == 1);
return g;
}
ll find_prime_factor(ll n) {
assert(n > 1);
if (primetest(n))
return n;
FOR(_, 100) {
ll m = rho(n, rnd(n));
if (primetest(m))
return m;
n = m;
}
cerr << "failed" << endl;
assert(false);
return -1;
}
vc<pi> factor(ll n) {
assert(n >= 1);
vc<pi> pf;
FOR3(p, 2, 100) {
if (p * p > n)
break;
if (n % p == 0) {
ll e = 0;
do {
n /= p, e += 1;
} while (n % p == 0);
pf.eb(p, e);
}
}
while (n > 1) {
ll p = find_prime_factor(n);
ll e = 0;
do {
n /= p, e += 1;
} while (n % p == 0);
pf.eb(p, e);
}
sort(all(pf));
return pf;
}
#line 1 "/home/maspy/compro/library/mod/fast_div.hpp"
struct fast_div {
// Min25 https://judge.yosupo.jp/submission/46090
// 同じ定数で何度も除算するときの高速化に使える
using i64 = long long;
using u64 = unsigned long long;
using u128 = __uint128_t;
constexpr fast_div() : m(), s(), x() {}
constexpr fast_div(int n)
: m(n), s(std::__lg(n - 1)), x(((u128(1) << (s + 64)) + n - 1) / n) {}
constexpr friend u64 operator/(u64 n, const fast_div& d) {
return (u128(n) * d.x >> d.s) >> 64;
}
constexpr friend int operator%(u64 n, const fast_div& d) {
return n - n / d * d.m;
}
constexpr std::pair<i64, int> divmod(u64 n) const {
u64 q = n / *this;
return {q, n - q * m};
}
int m;
int s;
u64 x;
};
#line 2 "/home/maspy/compro/library/mod/mod_pow.hpp"
// int
ll mod_pow(ll a, ll n, int mod){
fast_div fd(mod);
a = a % fd;
ll p = a;
ll v = 1;
while(n){
if(n & 1) v = v * p % fd;
p = p * p % fd;
n >>= 1;
}
return v;
}
ll mod_pow_long(ll a, ll n, ll mod){
a %= mod;
ll p = a;
ll v = 1;
while(n){
if(n & 1) v = i128(v) * p % mod;
p = i128(p) * p % mod;
n >>= 1;
}
return v;
}
#line 3 "/home/maspy/compro/library/nt/gaussian_integers.hpp"
template <typename INT>
struct Gaussian_Integer {
INT x, y;
using G = Gaussian_Integer;
Gaussian_Integer(INT x = 0, INT y = 0) : x(x), y(y) {}
Gaussian_Integer(pair<INT, INT> p) : x(p.fi), y(p.se) {}
INT norm() const { return x * x + y * y; }
G conjugate() const { return G(x, -y); }
G &operator+=(const G &g) {
x += g.x, y += g.y;
return *this;
}
G &operator-=(const G &g) {
x -= g.x, y -= g.y;
return *this;
}
G &operator*=(const G &g) {
tie(x, y) = mp(x * g.x - y * g.y, x * g.y + y * g.x);
return *this;
}
G &operator/=(const G &g) {
*this *= g.conjugate();
INT n = g.norm();
x = floor(x + n / 2, n);
y = floor(y + n / 2, n);
return *this;
}
G &operator%=(const G &g) {
auto q = G(*this) / g;
q *= g;
(*this) -= q;
return *this;
}
G operator-() { return G(-x, -y); }
G operator+(const G &g) { return G(*this) += g; }
G operator-(const G &g) { return G(*this) -= g; }
G operator*(const G &g) { return G(*this) *= g; }
G operator/(const G &g) { return G(*this) /= g; }
G operator%(const G &g) { return G(*this) %= g; }
bool operator==(const G &g) { return (x == g.x && y == g.y); }
static G gcd(G a, G b) {
while (b.x != 0 || b.y != 0) {
a %= b;
swap(a, b);
}
return a;
}
};
// ノルムがとれるように、2 乗してもオーバーフローしない型を使おう
// 0 <= arg < 90 となるもののみ返す。
// 単数倍は作らないので、使うときに気を付ける。
template <typename INT>
vc<Gaussian_Integer<INT>> solve_norm_equation(INT N) {
using G = Gaussian_Integer<INT>;
vc<G> res;
if (N < 0) return {};
if (N == 0) {
res.eb(G(0, 0));
return res;
}
auto pfs = factor(N);
for (auto &&[p, e]: pfs) {
if (p % 4 == 3 && e % 2 == 1) return {};
}
auto find = [&](INT p) -> G {
// p は素数. ノルム p のガウス整数をひとつ見つける
if (p == 2) return G(1, 1);
// x^2 = -1 mod p をひとつ見つける
INT x = [&]() -> INT {
INT x = 1;
while (1) {
++x;
INT pow_x = 1;
if (p < (1 << 30)) {
pow_x = mod_pow(x, (p - 1) / 4, p);
if (pow_x * pow_x % p == p - 1) return pow_x;
} else {
pow_x = mod_pow_long(x, (p - 1) / 4, p);
if (i128(pow_x) * pow_x % p == p - 1) return pow_x;
}
}
return -1;
}();
assert(x != -1);
// x は非剰余
G a(p, 0), b(x, 1);
a = G::gcd(a, b);
assert(a.norm() == p);
return a;
};
res.eb(G(1, 0));
for (auto &&[p, e]: pfs) {
if (p % 4 == 3) {
INT pp = 1;
FOR_(e / 2) pp *= p;
for (auto &&g: res) {
g.x *= pp;
g.y *= pp;
}
continue;
}
auto pi = find(p);
vc<G> pows(e + 1);
pows[0] = G(1, 0);
FOR(i, e) pows[i + 1] = pows[i] * pi;
if (p == 2) {
for (auto &&g: res) g *= pows[e];
continue;
}
vc<G> pis(e + 1);
FOR(j, e + 1) { pis[j] = pows[j] * (pows[e - j].conjugate()); }
vc<G> new_res;
new_res.reserve(len(res) * (e + 1));
for (auto &&g: res) {
for (auto &&a: pis) { new_res.eb(g * a); }
}
swap(res, new_res);
}
for (auto &&g: res) {
while (g.x <= 0 || g.y < 0) { g = G(-g.y, g.x); }
}
return res;
}
#line 5 "main.cpp"
void solve() {
LL(N);
ll ANS = 0;
auto res = solve_norm_equation(N * N);
for (auto &&g: res) {
if (g.x > 0 && g.y > 0) ++ANS;
}
print(ANS);
}
signed main() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << setprecision(15);
ll T = 1;
// LL(T);
FOR(_, T) solve();
return 0;
}