結果
| 問題 | No.2620 Sieve of Coins |
| ユーザー |
 hitonanode
|
| 提出日時 | 2024-01-26 23:02:10 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 1,972 ms / 2,000 ms |
| コード長 | 18,587 bytes |
| コンパイル時間 | 2,557 ms |
| コンパイル使用メモリ | 204,612 KB |
| 実行使用メモリ | 82,100 KB |
| 最終ジャッジ日時 | 2024-09-28 08:53:11 |
| 合計ジャッジ時間 | 75,422 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / 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 | 31 ms
28,336 KB |
| testcase_01 | AC | 32 ms
28,336 KB |
| testcase_02 | AC | 32 ms
28,356 KB |
| testcase_03 | AC | 1,894 ms
81,120 KB |
| testcase_04 | AC | 1,889 ms
81,688 KB |
| testcase_05 | AC | 32 ms
28,336 KB |
| testcase_06 | AC | 32 ms
28,336 KB |
| testcase_07 | AC | 31 ms
28,252 KB |
| testcase_08 | AC | 32 ms
28,456 KB |
| testcase_09 | AC | 31 ms
28,356 KB |
| testcase_10 | AC | 32 ms
28,484 KB |
| testcase_11 | AC | 32 ms
28,236 KB |
| testcase_12 | AC | 32 ms
28,232 KB |
| testcase_13 | AC | 31 ms
28,224 KB |
| testcase_14 | AC | 32 ms
28,360 KB |
| testcase_15 | AC | 31 ms
28,256 KB |
| testcase_16 | AC | 32 ms
28,484 KB |
| testcase_17 | AC | 56 ms
29,624 KB |
| testcase_18 | AC | 1,866 ms
81,696 KB |
| testcase_19 | AC | 1,888 ms
80,276 KB |
| testcase_20 | AC | 31 ms
28,356 KB |
| testcase_21 | AC | 1,928 ms
80,376 KB |
| testcase_22 | AC | 1,890 ms
80,036 KB |
| testcase_23 | AC | 1,918 ms
81,972 KB |
| testcase_24 | AC | 1,913 ms
81,532 KB |
| testcase_25 | AC | 1,897 ms
81,016 KB |
| testcase_26 | AC | 1,972 ms
80,032 KB |
| testcase_27 | AC | 1,869 ms
80,324 KB |
| testcase_28 | AC | 31 ms
28,212 KB |
| testcase_29 | AC | 32 ms
28,212 KB |
| testcase_30 | AC | 32 ms
28,484 KB |
| testcase_31 | AC | 1,894 ms
81,564 KB |
| testcase_32 | AC | 1,898 ms
80,964 KB |
| testcase_33 | AC | 1,916 ms
81,680 KB |
| testcase_34 | AC | 1,899 ms
82,004 KB |
| testcase_35 | AC | 1,912 ms
81,172 KB |
| testcase_36 | AC | 1,934 ms
81,388 KB |
| testcase_37 | AC | 1,925 ms
79,952 KB |
| testcase_38 | AC | 1,916 ms
80,020 KB |
| testcase_39 | AC | 1,916 ms
80,260 KB |
| testcase_40 | AC | 1,916 ms
82,100 KB |
| testcase_41 | AC | 1,913 ms
81,248 KB |
| testcase_42 | AC | 1,934 ms
81,908 KB |
| testcase_43 | AC | 1,944 ms
81,668 KB |
| testcase_44 | AC | 1,924 ms
80,284 KB |
| testcase_45 | AC | 32 ms
28,232 KB |
| testcase_46 | AC | 1,941 ms
81,828 KB |
| testcase_47 | AC | 1,939 ms
81,624 KB |
| testcase_48 | AC | 1,913 ms
81,956 KB |
| testcase_49 | AC | 1,903 ms
80,264 KB |
| testcase_50 | AC | 1,929 ms
81,932 KB |
| testcase_51 | AC | 1,950 ms
80,308 KB |
| testcase_52 | AC | 1,901 ms
81,084 KB |
| testcase_53 | AC | 1,910 ms
79,960 KB |
| testcase_54 | AC | 1,925 ms
81,260 KB |
| testcase_55 | AC | 1,924 ms
81,488 KB |
| testcase_56 | AC | 1,913 ms
81,336 KB |
| testcase_57 | AC | 1,899 ms
80,456 KB |
ソースコード
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif
#include <cassert>
#include <map>
#include <vector>
// Linear sieve algorithm for fast prime factorization
// Complexity: O(N) time, O(N) space:
// - MAXN = 10^7: ~44 MB, 80~100 ms (Codeforces / AtCoder GCC, C++17)
// - MAXN = 10^8: ~435 MB, 810~980 ms (Codeforces / AtCoder GCC, C++17)
// Reference:
// [1] D. Gries, J. Misra, "A Linear Sieve Algorithm for Finding Prime Numbers,"
// Communications of the ACM, 21(12), 999-1003, 1978.
// - https://cp-algorithms.com/algebra/prime-sieve-linear.html
// - https://37zigen.com/linear-sieve/
struct Sieve {
std::vector<int> min_factor;
std::vector<int> primes;
Sieve(int MAXN) : min_factor(MAXN + 1) {
for (int d = 2; d <= MAXN; d++) {
if (!min_factor[d]) {
min_factor[d] = d;
primes.emplace_back(d);
}
for (const auto &p : primes) {
if (p > min_factor[d] or d * p > MAXN) break;
min_factor[d * p] = p;
}
}
}
// Prime factorization for 1 <= x <= MAXN^2
// Complexity: O(log x) (x <= MAXN)
// O(MAXN / log MAXN) (MAXN < x <= MAXN^2)
template <class T> std::map<T, int> factorize(T x) const {
std::map<T, int> ret;
assert(x > 0 and
x <= ((long long)min_factor.size() - 1) * ((long long)min_factor.size() - 1));
for (const auto &p : primes) {
if (x < T(min_factor.size())) break;
while (!(x % p)) x /= p, ret[p]++;
}
if (x >= T(min_factor.size())) ret[x]++, x = 1;
while (x > 1) ret[min_factor[x]]++, x /= min_factor[x];
return ret;
}
// Enumerate divisors of 1 <= x <= MAXN^2
// Be careful of highly composite numbers https://oeis.org/A002182/list
// https://gist.github.com/dario2994/fb4713f252ca86c1254d#file-list-txt (n, (# of div. of n)):
// 45360->100, 735134400(<1e9)->1344, 963761198400(<1e12)->6720
template <class T> std::vector<T> divisors(T x) const {
std::vector<T> ret{1};
for (const auto p : factorize(x)) {
int n = ret.size();
for (int i = 0; i < n; i++) {
for (T a = 1, d = 1; d <= p.second; d++) {
a *= p.first;
ret.push_back(ret[i] * a);
}
}
}
return ret; // NOT sorted
}
// Euler phi functions of divisors of given x
// Verified: ABC212 G https://atcoder.jp/contests/abc212/tasks/abc212_g
// Complexity: O(sqrt(x) + d(x))
template <class T> std::map<T, T> euler_of_divisors(T x) const {
assert(x >= 1);
std::map<T, T> ret;
ret[1] = 1;
std::vector<T> divs{1};
for (auto p : factorize(x)) {
int n = ret.size();
for (int i = 0; i < n; i++) {
ret[divs[i] * p.first] = ret[divs[i]] * (p.first - 1);
divs.push_back(divs[i] * p.first);
for (T a = divs[i] * p.first, d = 1; d < p.second; a *= p.first, d++) {
ret[a * p.first] = ret[a] * p.first;
divs.push_back(a * p.first);
}
}
}
return ret;
}
// Moebius function Table, (-1)^{# of different prime factors} for square-free x
// return: [0=>0, 1=>1, 2=>-1, 3=>-1, 4=>0, 5=>-1, 6=>1, 7=>-1, 8=>0, ...] https://oeis.org/A008683
std::vector<int> GenerateMoebiusFunctionTable() const {
std::vector<int> ret(min_factor.size());
for (unsigned i = 1; i < min_factor.size(); i++) {
if (i == 1) {
ret[i] = 1;
} else if ((i / min_factor[i]) % min_factor[i] == 0) {
ret[i] = 0;
} else {
ret[i] = -ret[i / min_factor[i]];
}
}
return ret;
}
// Calculate [0^K, 1^K, ..., nmax^K] in O(nmax)
// Note: **0^0 == 1**
template <class MODINT> std::vector<MODINT> enumerate_kth_pows(long long K, int nmax) const {
assert(nmax < int(min_factor.size()));
assert(K >= 0);
if (K == 0) return std::vector<MODINT>(nmax + 1, 1);
std::vector<MODINT> ret(nmax + 1);
ret[0] = 0, ret[1] = 1;
for (int n = 2; n <= nmax; n++) {
if (min_factor[n] == n) {
ret[n] = MODINT(n).pow(K);
} else {
ret[n] = ret[n / min_factor[n]] * ret[min_factor[n]];
}
}
return ret;
}
};
Sieve sieve((1 << 20));
struct CountPrimes {
// Count Primes less than or equal to x (\pi(x)) for each x = N / i (i = 1, ..., N) in O(N^(2/3)) time
// Learned this algorihtm from https://old.yosupo.jp/submission/14650
// Reference: https://min-25.hatenablog.com/entry/2018/11/11/172216
using Int = long long;
Int n, n2, n3, n6;
std::vector<int> is_prime; // [0, 0, 1, 1, 0, 1, 0, 1, ...]
std::vector<Int> primes; // primes up to O(N^(1/2)), [2, 3, 5, 7, ...]
int s; // size of vs
std::vector<Int> vs; // [N, ..., n2, n2 - 1, n2 - 2, ..., 3, 2, 1]
std::vector<Int> pi; // pi[i] = (# of primes s.t. <= vs[i]) is finally obtained
std::vector<int> _fenwick;
int getidx(Int a) const {
return a <= n2 ? s - a : n / a - 1;
} // vs[i] >= a を満たす最大の i を返す
void _fenwick_rec_update(
int i, Int cur,
bool first) { // pi[n3:] に対して cur * (primes[i] 以上の素因数) の数の寄与を減じる
if (!first) {
for (int x = getidx(cur) - n3; x >= 0; x -= (x + 1) & (-x - 1)) _fenwick[x]--;
}
for (int j = i; cur * primes[j] <= vs[n3]; j++)
_fenwick_rec_update(j, cur * primes[j], false);
}
CountPrimes(Int n_) : n(n_), n2((Int)sqrtl(n)), n3((Int)cbrtl(n)), n6((Int)sqrtl(n3)) {
is_prime.assign(n2 + 300, 1),
is_prime[0] = is_prime[1] = 0; // `+ 300`: https://en.wikipedia.org/wiki/Prime_gap
for (size_t p = 2; p < is_prime.size(); p++) {
if (is_prime[p]) {
primes.push_back(p);
for (size_t j = p * 2; j < is_prime.size(); j += p) is_prime[j] = 0;
}
}
for (Int now = n; now; now = n / (n / now + 1))
vs.push_back(
now); // [N, N / 2, ..., 1], Relevant integers (decreasing) length ~= 2sqrt(N)
s = vs.size();
// pi[i] = (# of integers x s.t. x <= vs[i], (x is prime or all factors of x >= p))
// pre = (# of primes less than p)
// 最小の素因数 p = 2, ..., について篩っていく
pi.resize(s);
for (int i = 0; i < s; i++) pi[i] = vs[i] - 1;
int pre = 0;
auto trans = [&](int i, Int p) { pi[i] -= pi[getidx(vs[i] / p)] - pre; };
size_t ip = 0;
// [Sieve Part 1] For each prime p satisfying p <= N^(1/6) (Only O(N^(1/6) / log N) such primes exist),
// O(sqrt(N)) simple operation is conducted.
// - Complexity of this part: O(N^(2/3) / logN)
for (; primes[ip] <= n6; ip++, pre++) {
const auto &p = primes[ip];
for (int i = 0; p * p <= vs[i]; i++) trans(i, p);
}
// [Sieve Part 2] For each prime p satisfying N^(1/6) < p <= N^(1/3),
// point-wise & Fenwick tree-based hybrid update is used
// - first N^(1/3) elements are simply updated by quadratic algorithm.
// - Updates of latter segments are managed by Fenwick tree.
// - Complexity of this part: O(N^(2/3)) (O(N^(2/3)/log N) operations for Fenwick tree (O(logN) per query))
_fenwick.assign(s - n3, 0); // Fenwick tree, inversed order (summation for upper region)
auto trans2 = [&](int i, Int p) {
int j = getidx(vs[i] / p);
auto z = pi[j];
if (j >= n3) {
for (j -= n3; j < int(_fenwick.size()); j += (j + 1) & (-j - 1)) z += _fenwick[j];
}
pi[i] -= z - pre;
};
for (; primes[ip] <= n3; ip++, pre++) {
const auto &p = primes[ip];
for (int i = 0; i < n3 and p * p <= vs[i]; i++)
trans2(i, p); // upto n3, total trans2 times: O(N^(2/3) / logN)
_fenwick_rec_update(ip, primes[ip], true); // total update times: O(N^(2/3) / logN)
}
for (int i = s - n3 - 1; i >= 0; i--) {
int j = i + ((i + 1) & (-i - 1));
if (j < s - n3) _fenwick[i] += _fenwick[j];
}
for (int i = 0; i < s - n3; i++) pi[i + n3] += _fenwick[i];
// [Sieve Part 3] For each prime p satisfying N^(1/3) < p <= N^(1/2), use only simple updates.
// - Complexity of this part: O(N^(2/3) / logN)
// \sum_i (# of factors of vs[i] of the form p^2, p >= N^(1/3)) = \sum_{i=1}^{N^(1/3)} \pi(\sqrt(vs[i])))
// = sqrt(N) \sum_i^{N^(1/3)}
// i^{-1/2} / logN = O(N^(2/3) / logN)
// (Note: \sum_{i=1}^{N} i^{-1/2} = O(sqrt N)
// https://math.stackexchange.com/questions/2600796/finding-summation-of-inverse-of-square-roots )
for (; primes[ip] <= n2; ip++, pre++) {
const auto &p = primes[ip];
for (int i = 0; p * p <= vs[i]; i++) trans(i, p);
}
}
};
void expe(int n) {
vector<int> dp(n + 1);
dp.at(1) = 1;
FOR(i, 1, dp.size()) {
if (dp.at(i)) {
dbg(sieve.factorize(i));
for (int j = i * 2; j <= n; j += i) dp.at(j) ^= 1;
}
}
dbg(dp);
}
int main() {
// expe(211);
lint L;
int N;
cin >> L >> N;
CountPrimes cp(L);
dbg(cp.pi.at(0));
auto moebius = sieve.GenerateMoebiusFunctionTable();
vector<plint> nonzeros;
FOR(i, 1, moebius.size()) {
if (moebius.at(i)) nonzeros.emplace_back(i, moebius.at(i));
}
auto f = [&](lint x) {
lint ret = 0;
for (auto [d, m] : nonzeros) {
if (d * d > x) break;
ret += m * (x / (d * d));
}
return ret;
};
vector<lint> A(N);
cin >> A;
int D3 = 2;
{
lint tmp = L;
while (tmp) {
++D3;
tmp /= 3;
}
}
const int D2 = floor_lg(L) + 2;
vector dp(D2, vector<lint>(D3));
IREP(i, D2) IREP(j, D3) {
if (i + 1 < D2) dp.at(i).at(j) -= dp.at(i + 1).at(j);
if (j + 1 < D3) dp.at(i).at(j) -= dp.at(i).at(j + 1);
if (i + 1 < D2 and j + 1 < D3) dp.at(i).at(j) -= dp.at(i + 1).at(j + 1);
lint base = 1LL << i;
REP(_, j) base *= 3;
dp.at(i).at(j) += f(L / base);
dbgif(L <= 100, make_tuple(i, j, L / base, dp.at(i).at(j)));
}
vector acnt(D2, vector<int>(D3));
for (lint a : A) {
int n2 = 0, n3 = 0;
while (a % 2 == 0) a /= 2, n2++;
while (a % 3 == 0) a /= 3, n3++;
REP(d, 2) REP(e, 2) acnt.at(n2 + d).at(n3 + e) ^= 1;
}
lint ret = 0;
REP(n2, D2) REP(n3, D3) {
if (!acnt.at(n2).at(n3)) continue;
ret += dp.at(n2).at(n3);
}
cout << ret << '\n';
// FOR(i, 1, acnt.size()) {
// REP(j, acnt.at(i).size()) acnt.at(i).at(j) ^= acnt.at(i - 1).at(j);
// }
// // dbg(acnt);
// lint ret = 0;
// vector<lint> bads;
// for (lint p : sieve.primes) {
// for (lint n = p * p; n <= L; n *= p) bads.push_back(n);
// }
// sort(ALL(bads));
// dbg(bads.size());
// auto f = [&](lint b) -> lint {
// const lint u = L / b;
// return u;
// // return u - arglb(bads, u);
// };
// REP(n2, D2) REP(n3, D3) {
// if (!acnt.at(n2).at(n3)) continue;
// lint b = 1LL << n2;
// REP(_, n3) b *= 3;
// lint tmp = f(b) - f(b * 2) - f(b * 3) + f(b * 6);
// ret += tmp;
// }
// cout << ret << '\n';
}