#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;
}