結果
| 問題 | No.736 約比 |
| コンテスト | |
| ユーザー |
 OnjoujiToki
|
| 提出日時 | 2026-01-09 14:29:55 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 2,000 ms |
| コード長 | 25,728 bytes |
| 記録 | |
| コンパイル時間 | 2,869 ms |
| コンパイル使用メモリ | 286,336 KB |
| 実行使用メモリ | 7,852 KB |
| 最終ジャッジ日時 | 2026-01-09 14:30:02 |
| 合計ジャッジ時間 | 5,436 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 65 |
ソースコード
#include <algorithm>
#include <bit>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <cstdint>
#include <functional>
#include <iostream>
#include <iterator>
#include <limits>
#include <map>
#include <numeric>
#include <optional>
#include <queue>
#include <ranges>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#include <iomanip>
#include <random>
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m < 2^31`
explicit barrett(unsigned int m)
: _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) <
// 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m>
constexpr int primitive_root = primitive_root_constexpr(m);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
unsigned long long m,
unsigned long long a,
unsigned long long b) {
unsigned long long ans = 0;
while (true) {
if (a >= m) {
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type, std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t,
unsigned __int128>;
template <class T>
using is_integral =
typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type, std::false_type>::type;
template <class T>
using is_signed_int =
typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type, std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value, make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T>
using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type, std::false_type>::type;
template <class T>
using to_unsigned =
typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T>
using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T>
using is_modint = std::is_base_of<modint_base, T>;
template <class T>
using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id>
struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id>
internal::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class>
struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
// using mint = modint998244353;
/*
g++ -std=c++23 -O2 -Wall -Wextra A.cpp -o A
./A < input.in > output.out
*/
namespace internal {
template <class E>
struct csr {
std::vector<int> start;
std::vector<E> elist;
explicit csr(int n, const std::vector<std::pair<int, E>>& edges)
: start(n + 1), elist(edges.size()) {
for (auto e : edges) {
start[e.first + 1]++;
}
for (int i = 1; i <= n; i++) {
start[i] += start[i - 1];
}
auto counter = start;
for (auto e : edges) {
elist[counter[e.first]++] = e.second;
}
}
};
} // namespace internal
struct scc_graph {
public:
explicit scc_graph(int n) : _n(n) {}
int num_vertices() { return _n; }
void add_edge(int from, int to) { edges.push_back({from, {to}}); }
// @return pair of (# of scc, scc id)
std::pair<int, std::vector<int>> scc_ids() {
auto g = internal::csr<edge>(_n, edges);
int now_ord = 0, group_num = 0;
std::vector<int> visited, low(_n), ord(_n, -1), ids(_n);
visited.reserve(_n);
auto dfs = [&](auto self, int v) -> void {
low[v] = ord[v] = now_ord++;
visited.push_back(v);
for (int i = g.start[v]; i < g.start[v + 1]; i++) {
auto to = g.elist[i].to;
if (ord[to] == -1) {
self(self, to);
low[v] = std::min(low[v], low[to]);
} else {
low[v] = std::min(low[v], ord[to]);
}
}
if (low[v] == ord[v]) {
while (true) {
int u = visited.back();
visited.pop_back();
ord[u] = _n;
ids[u] = group_num;
if (u == v) break;
}
group_num++;
}
};
for (int i = 0; i < _n; i++) {
if (ord[i] == -1) dfs(dfs, i);
}
for (auto& x : ids) {
x = group_num - 1 - x;
}
return {group_num, ids};
}
std::vector<std::vector<int>> scc() {
auto ids = scc_ids();
int group_num = ids.first;
std::vector<int> counts(group_num);
for (auto x : ids.second) counts[x]++;
std::vector<std::vector<int>> groups(ids.first);
for (int i = 0; i < group_num; i++) {
groups[i].reserve(counts[i]);
}
for (int i = 0; i < _n; i++) {
groups[ids.second[i]].push_back(i);
}
return groups;
}
private:
int _n;
struct edge {
int to;
};
std::vector<std::pair<int, edge>> edges;
};
class Solution {
public:
int minRunesToAdd(int n, std::vector<int>& crystals, std::vector<int>& from,
std::vector<int>& to) {
scc_graph g(n);
for (size_t i = 0; i < from.size(); i++) {
g.add_edge(from[i], to[i]);
}
auto [scc_num, scc_id] = g.scc_ids();
std::vector<std::vector<int>> dag(scc_num);
std::vector<std::vector<int>> tmp(scc_num);
for (size_t i = 0; i < from.size(); i++) {
int u = from[i], v = to[i];
int cu = scc_id[u], cv = scc_id[v];
if (cu == cv) continue;
tmp[cu].push_back(cv);
}
for (int c = 0; c < scc_num; c++) {
auto& t = tmp[c];
std::sort(t.begin(), t.end());
t.erase(std::unique(t.begin(), t.end()), t.end());
dag[c] = std::move(t);
}
std::queue<int> q;
std::vector<bool> reachable(scc_num, false);
for (int node : crystals) {
int c = scc_id[node];
if (!reachable[c]) {
reachable[c] = true;
q.push(c);
}
}
while (!q.empty()) {
int u = q.front();
q.pop();
for (int v : dag[u]) {
if (!reachable[v]) {
reachable[v] = 1;
q.push(v);
}
}
}
int ans = 0;
for (int c = 0; c < scc_num; c++) {
if (!reachable[c]) ans++;
}
return ans;
}
};
// wavelet matrix topK sum 付き
// Wavelet matrix + range topK sum (small)
// https://kopricky.github.io/code/DataStructure_Advanced/wavelet_matrix.html
#include <algorithm>
#include <vector>
struct BitRank {
// block: bit 列を管理, count: block ごとに立っている 1 の数を管理
std::vector<unsigned long long> block;
std::vector<unsigned int> count;
BitRank() {}
void resize(const unsigned int num) {
block.resize(((num + 1) >> 6) + 1, 0);
count.resize(block.size(), 0);
}
// i ビット目を val(0,1) にセット
void set(const unsigned int i, const unsigned long long val) {
block[i >> 6] |= (val << (i & 63));
}
void build() {
for (unsigned int i = 1; i < block.size(); i++) {
count[i] = count[i - 1] + __builtin_popcountll(block[i - 1]);
}
}
// [0, i) ビットの 1 の数
unsigned int rank1(const unsigned int i) const {
return count[i >> 6] +
__builtin_popcountll(block[i >> 6] & ((1ULL << (i & 63)) - 1ULL));
}
// [i, j) ビットの 1 の数
unsigned int rank1(const unsigned int i, const unsigned int j) const {
return rank1(j) - rank1(i);
}
// [0, i) ビットの 0 の数
unsigned int rank0(const unsigned int i) const { return i - rank1(i); }
// [i, j) ビットの 0 の数
unsigned int rank0(const unsigned int i, const unsigned int j) const {
return rank0(j) - rank0(i);
}
};
class WaveletMatrix {
private:
unsigned int height;
std::vector<BitRank> B;
std::vector<int> pos;
std::vector<std::vector<long long>> rui;
public:
WaveletMatrix() {}
WaveletMatrix(std::vector<int> vec)
: WaveletMatrix(vec, *std::max_element(vec.begin(), vec.end()) + 1) {}
// sigma:文字の種類数
WaveletMatrix(std::vector<int> vec, const unsigned int sigma) {
init(vec, sigma);
}
void init(std::vector<int>& vec, const unsigned int sigma) {
height = (sigma == 1) ? 1 : (64 - __builtin_clzll(sigma - 1));
B.resize(height), pos.resize(height);
std::vector<int> A = vec;
rui.resize(height + 1);
for (unsigned int i = 0; i < height; ++i) {
B[i].resize(vec.size());
for (unsigned int j = 0; j < vec.size(); ++j) {
B[i].set(j, get(vec[j], height - i - 1));
}
B[i].build();
auto it = stable_partition(vec.begin(), vec.end(), [&](int c) {
return !get(c, height - i - 1);
});
pos[i] = it - vec.begin();
}
for (unsigned int i = 0; i <= height; ++i) {
rui[i].resize(A.size() + 1);
for (int j = 1; j <= A.size(); j++) {
rui[i][j] = rui[i][j - 1] + A[j - 1];
}
if (i == height) break;
std::stable_partition(A.begin(), A.end(),
[&](int c) { return !get(c, height - i - 1); });
}
}
// val の i ビット目の値を返す(0,1)
int get(const int val, const int i) { return val >> i & 1; }
// [l, r) の間に現れる値 val の数
int rank(const int val, const int l, const int r) {
return rank(val, r) - rank(val, l);
}
// [0, i) の間に現れる値 val の数
int rank(int val, int i) {
int p = 0;
for (unsigned int j = 0; j < height; ++j) {
if (get(val, height - j - 1)) {
p = pos[j] + B[j].rank1(p);
i = pos[j] + B[j].rank1(i);
} else {
p = B[j].rank0(p);
i = B[j].rank0(i);
}
}
return i - p;
}
// [l, r) の k(0,1,2...) 番目に小さい値を返す
int quantile(int k, int l, int r) {
int res = 0;
for (unsigned int i = 0; i < height; ++i) {
const int j = B[i].rank0(l, r);
if (j > k) {
l = B[i].rank0(l);
r = B[i].rank0(r);
} else {
l = pos[i] + B[i].rank1(l);
r = pos[i] + B[i].rank1(r);
k -= j;
res |= (1 << (height - i - 1));
}
}
return res;
}
long long topKsum(int k, int l, int r) {
if (l == r) return 0LL;
long long res = 0;
int atai = 0;
for (unsigned int i = 0; i < height; ++i) {
const int j = B[i].rank0(l, r);
if (j > k) {
l = B[i].rank0(l);
r = B[i].rank0(r);
} else {
int l2 = B[i].rank0(l);
int r2 = B[i].rank0(r);
res += rui[i + 1][r2] - rui[i + 1][l2];
l = pos[i] + B[i].rank1(l);
r = pos[i] + B[i].rank1(r);
k -= j;
atai |= (1 << (height - i - 1));
}
}
res += (long long)atai * k;
return res;
}
int rangefreq(const int i, const int j, const int a, const int b, const int l,
const int r, const int x) {
if (i == j || r <= a || b <= l) return 0;
const int mid = (l + r) >> 1;
if (a <= l && r <= b) {
return j - i;
} else {
const int left =
rangefreq(B[x].rank0(i), B[x].rank0(j), a, b, l, mid, x + 1);
const int right = rangefreq(pos[x] + B[x].rank1(i),
pos[x] + B[x].rank1(j), a, b, mid, r, x + 1);
return left + right;
}
}
// [l,r) で値が [a,b) 内に含まれる数を返す
int rangefreq(const int l, const int r, const int a, const int b) {
return rangefreq(l, r, a, b, 0, 1 << height, 0);
}
int rangemin(const int i, const int j, const int a, const int b, const int l,
const int r, const int x, const int val) {
if (i == j || r <= a || b <= l) return -1;
if (r - l == 1) return val;
const int mid = (l + r) >> 1;
const int res =
rangemin(B[x].rank0(i), B[x].rank0(j), a, b, l, mid, x + 1, val);
if (res < 0)
return rangemin(pos[x] + B[x].rank1(i), pos[x] + B[x].rank1(j), a, b, mid,
r, x + 1, val + (1 << (height - x - 1)));
else
return res;
}
// [l,r) で値が [a,b) 内に最小の数を返す(数が存在しない場合は -1 を返す)
int rangemin(int l, int r, int a, int b) {
return rangemin(l, r, a, b, 0, 1 << height, 0, 0);
}
};
template <typename T>
class OrthogonalRangeCount {
private:
using ptt = std::pair<T, T>;
const int sz;
std::vector<T> X, Y;
WaveletMatrix wm;
public:
OrthogonalRangeCount(std::vector<ptt> candidate)
: sz((int)candidate.size()), X(sz), Y(sz) {
sort(candidate.begin(), candidate.end());
std::vector<int> vec(sz);
for (int i = 0; i < sz; ++i) {
X[i] = candidate[i].first, Y[i] = candidate[i].second;
}
sort(Y.begin(), Y.end());
Y.erase(unique(Y.begin(), Y.end()), Y.end());
for (int i = 0; i < sz; ++i) {
vec[i] = lower_bound(Y.begin(), Y.end(), candidate[i].second) - Y.begin();
}
wm.init(vec, Y.size());
}
// [lx,rx) × [ly, ry) の長方形領域に含まれる点の数を答える
int query(const T lx, const T ly, const T rx, const T ry) {
const int lxid = lower_bound(X.begin(), X.end(), lx) - X.begin();
const int rxid = lower_bound(X.begin(), X.end(), rx) - X.begin();
const int lyid = lower_bound(Y.begin(), Y.end(), ly) - Y.begin();
const int ryid = lower_bound(Y.begin(), Y.end(), ry) - Y.begin();
if (lxid >= rxid || lyid >= ryid) return 0;
return wm.rangefreq(lxid, rxid, lyid, ryid);
}
};
int main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
int n;
std::cin >> n;
std::vector<long long> a(n);
for (int i = 0; i < n; ++i) {
std::cin >> a[i];
}
long long gcd = a[0];
for (int i = 1; i < n; ++i) {
gcd = std::gcd(gcd, a[i]);
}
for (int i = 0; i < n; ++i) {
long long x = a[i];
x /= gcd;
std::cout << x << ":\n"[i == n - 1];
}
return 0;
}