using System;
using System.Buffers;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Runtime.Intrinsics.X86;
using System.Text;
using YukicoderContest305.Problems;
namespace YukicoderContest305.Problems
{
public class ProblemB : ProblemBase
{
public ProblemB() : base(true) { }
Eratosthenes eratosthenes = new Eratosthenes(1000000);
[MethodImpl(MethodImplOptions.AggressiveOptimization)]
protected override void SolveEach(IOManager io)
{
var x = io.ReadLong();
var i = 2;
while (true)
{
var current = x;
var div = i;
while (div > 1)
{
if (current % eratosthenes._spf[div] != 0)
{
if (eratosthenes._spf[div] == div)
{
io.WriteLine(x * i);
return;
}
else
{
break;
}
}
current /= eratosthenes._spf[div];
div /= eratosthenes._spf[div];
}
i++;
}
}
public class Eratosthenes
{
///
/// Smallest Prime Factorを保存した配列
///
public readonly int[] _spf;
public Eratosthenes(int max)
{
_spf = Enumerable.Range(0, max + 1).ToArray();
for (int i = 2; i * i <= max; i++)
{
if (_spf[i] == i)
{
for (int mul = i << 1; mul <= max; mul += i)
{
if (_spf[mul] == mul)
{
_spf[mul] = i;
}
}
}
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public bool IsPrime(int n) => n >= 2 && _spf[n] == n;
public IEnumerable<(int prime, int count)> PrimeFactorize(int n)
{
if (n <= 0 || _spf.Length <= n)
{
throw new ArgumentOutOfRangeException(nameof(n), $"{nameof(n)}は[0, {_spf.Length})の間でなければなりません");
}
else if (n == 1)
{
yield break;
}
else
{
var last = _spf[n];
var streak = 0;
while (n > 1)
{
if (_spf[n] == last)
{
streak++;
}
else
{
yield return (last, streak);
last = _spf[n];
streak = 1;
}
n /= last;
}
yield return (last, streak);
}
}
public IEnumerable GetDivisiors(int n)
{
if (n <= 0 || _spf.Length <= n)
{
throw new ArgumentOutOfRangeException(nameof(n), $"{nameof(n)}は[0, {_spf.Length})の間でなければなりません");
}
else
{
var primes = PrimeFactorize(n).ToArray();
return GetDivisiors(primes, 0);
}
}
IEnumerable GetDivisiors((int prime, int count)[] primes, int depth)
{
if (depth == primes.Length)
{
yield return 1;
}
else
{
var current = 1;
var children = GetDivisiors(primes, depth + 1).ToArray();
foreach (var child in children)
{
yield return child;
}
for (int i = 0; i < primes[depth].count; i++)
{
current *= primes[depth].prime;
foreach (var child in children)
{
yield return current * child;
}
}
}
}
}
}
}
namespace YukicoderContest305
{
class Program
{
static void Main(string[] args)
{
IProblem question = new ProblemB();
using var io = new IOManager(Console.OpenStandardInput(), Console.OpenStandardOutput());
question.Solve(io);
}
}
}
#region Base Class
namespace YukicoderContest305.Problems
{
public interface IProblem
{
string Solve(string input);
void Solve(IOManager io);
}
public abstract class ProblemBase : IProblem
{
protected bool HasMultiTestCases { get; }
protected ProblemBase(bool hasMultiTestCases) => HasMultiTestCases = hasMultiTestCases;
public string Solve(string input)
{
var inputStream = new MemoryStream(Encoding.UTF8.GetBytes(input));
var outputStream = new MemoryStream();
using var manager = new IOManager(inputStream, outputStream);
Solve(manager);
manager.Flush();
outputStream.Seek(0, SeekOrigin.Begin);
var reader = new StreamReader(outputStream);
return reader.ReadToEnd();
}
public void Solve(IOManager io)
{
var tests = HasMultiTestCases ? io.ReadInt() : 1;
for (var t = 0; t < tests; t++)
{
SolveEach(io);
}
}
protected abstract void SolveEach(IOManager io);
}
}
#endregion
#region Utils
namespace YukicoderContest305
{
public class IOManager : IDisposable
{
private readonly BinaryReader _reader;
private readonly StreamWriter _writer;
private bool _disposedValue;
private byte[] _buffer = new byte[1024];
private int _length;
private int _cursor;
private bool _eof;
const char ValidFirstChar = '!';
const char ValidLastChar = '~';
public IOManager(Stream input, Stream output)
{
_reader = new BinaryReader(input);
_writer = new StreamWriter(output) { AutoFlush = false };
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private char ReadAscii()
{
if (_cursor == _length)
{
_cursor = 0;
_length = _reader.Read(_buffer);
if (_length == 0)
{
if (!_eof)
{
_eof = true;
return char.MinValue;
}
else
{
ThrowEndOfStreamException();
}
}
}
return (char)_buffer[_cursor++];
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public char ReadChar()
{
char c;
while (!IsValidChar(c = ReadAscii())) { }
return c;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public string ReadString()
{
var builder = new StringBuilder();
char c;
while (!IsValidChar(c = ReadAscii())) { }
do
{
builder.Append(c);
} while (IsValidChar(c = ReadAscii()));
return builder.ToString();
}
public int ReadInt() => (int)ReadLong();
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public long ReadLong()
{
long result = 0;
bool isPositive = true;
char c;
while (!IsNumericChar(c = ReadAscii())) { }
if (c == '-')
{
isPositive = false;
c = ReadAscii();
}
do
{
result *= 10;
result += c - '0';
} while (IsNumericChar(c = ReadAscii()));
return isPositive ? result : -result;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private Span ReadChunk(Span span)
{
var i = 0;
char c;
while (!IsValidChar(c = ReadAscii())) { }
do
{
span[i++] = c;
} while (IsValidChar(c = ReadAscii()));
return span.Slice(0, i);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public double ReadDouble() => double.Parse(ReadChunk(stackalloc char[32]));
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public decimal ReadDecimal() => decimal.Parse(ReadChunk(stackalloc char[32]));
public int[] ReadIntArray(int n)
{
var a = new int[n];
for (int i = 0; i < a.Length; i++)
{
a[i] = ReadInt();
}
return a;
}
public long[] ReadLongArray(int n)
{
var a = new long[n];
for (int i = 0; i < a.Length; i++)
{
a[i] = ReadLong();
}
return a;
}
public double[] ReadDoubleArray(int n)
{
var a = new double[n];
for (int i = 0; i < a.Length; i++)
{
a[i] = ReadDouble();
}
return a;
}
public decimal[] ReadDecimalArray(int n)
{
var a = new decimal[n];
for (int i = 0; i < a.Length; i++)
{
a[i] = ReadDecimal();
}
return a;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Write(T value) => _writer.Write(value.ToString());
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void WriteLine(T value) => _writer.WriteLine(value.ToString());
public void WriteLine(IEnumerable values, char separator)
{
var e = values.GetEnumerator();
if (e.MoveNext())
{
_writer.Write(e.Current.ToString());
while (e.MoveNext())
{
_writer.Write(separator);
_writer.Write(e.Current.ToString());
}
}
_writer.WriteLine();
}
public void WriteLine(T[] values, char separator) => WriteLine((ReadOnlySpan)values, separator);
public void WriteLine(Span values, char separator) => WriteLine((ReadOnlySpan)values, separator);
public void WriteLine(ReadOnlySpan values, char separator)
{
for (int i = 0; i < values.Length - 1; i++)
{
_writer.Write(values[i]);
_writer.Write(separator);
}
if (values.Length > 0)
{
_writer.Write(values[^1]);
}
_writer.WriteLine();
}
public void Flush() => _writer.Flush();
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static bool IsValidChar(char c) => ValidFirstChar <= c && c <= ValidLastChar;
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static bool IsNumericChar(char c) => ('0' <= c && c <= '9') || c == '-';
private void ThrowEndOfStreamException() => throw new EndOfStreamException();
protected virtual void Dispose(bool disposing)
{
if (!_disposedValue)
{
if (disposing)
{
_reader.Dispose();
_writer.Flush();
_writer.Dispose();
}
_disposedValue = true;
}
}
public void Dispose()
{
Dispose(disposing: true);
GC.SuppressFinalize(this);
}
}
public static class UtilExtensions
{
public static bool ChangeMax(ref this T value, T other) where T : struct, IComparable
{
if (value.CompareTo(other) < 0)
{
value = other;
return true;
}
return false;
}
public static bool ChangeMin(ref this T value, T other) where T : struct, IComparable
{
if (value.CompareTo(other) > 0)
{
value = other;
return true;
}
return false;
}
public static void SwapIfLargerThan(ref this T a, ref T b) where T : struct, IComparable
{
if (a.CompareTo(b) > 0)
{
(a, b) = (b, a);
}
}
public static void SwapIfSmallerThan(ref this T a, ref T b) where T : struct, IComparable
{
if (a.CompareTo(b) < 0)
{
(a, b) = (b, a);
}
}
public static void Sort(this T[] array) where T : IComparable => Array.Sort(array);
public static void Sort(this T[] array, Comparison comparison) => Array.Sort(array, comparison);
}
public static class CollectionExtensions
{
private class ArrayWrapper
{
#pragma warning disable CS0649
public T[] Array;
#pragma warning restore CS0649
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Span AsSpan(this List list)
{
return Unsafe.As>(list).Array.AsSpan(0, list.Count);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Span GetRowSpan(this T[,] array, int i)
{
var width = array.GetLength(1);
return MemoryMarshal.CreateSpan(ref array[i, 0], width);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Span GetRowSpan(this T[,,] array, int i, int j)
{
var width = array.GetLength(2);
return MemoryMarshal.CreateSpan(ref array[i, j, 0], width);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Span GetRowSpan(this T[,,,] array, int i, int j, int k)
{
var width = array.GetLength(3);
return MemoryMarshal.CreateSpan(ref array[i, j, k, 0], width);
}
public static void Fill(this T[] array, T value) => array.AsSpan().Fill(value);
public static void Fill(this T[,] array, T value) => MemoryMarshal.CreateSpan(ref array[0, 0], array.Length).Fill(value);
public static void Fill(this T[,,] array, T value) => MemoryMarshal.CreateSpan(ref array[0, 0, 0], array.Length).Fill(value);
public static void Fill(this T[,,,] array, T value) => MemoryMarshal.CreateSpan(ref array[0, 0, 0, 0], array.Length).Fill(value);
}
public static class SearchExtensions
{
struct LowerBoundComparer : IComparer where T : IComparable
{
public int Compare(T x, T y) => 0 <= x.CompareTo(y) ? 1 : -1;
}
struct UpperBoundComparer : IComparer where T : IComparable
{
public int Compare(T x, T y) => 0 < x.CompareTo(y) ? 1 : -1;
}
// https://trsing.hatenablog.com/entry/2019/08/27/211038
public static int GetGreaterEqualIndex(this ReadOnlySpan span, T inclusiveMin) where T : IComparable => ~span.BinarySearch(inclusiveMin, new UpperBoundComparer());
public static int GetGreaterThanIndex(this ReadOnlySpan span, T exclusiveMin) where T : IComparable => ~span.BinarySearch(exclusiveMin, new LowerBoundComparer());
public static int GetLessEqualIndex(this ReadOnlySpan span, T inclusiveMax) where T : IComparable => ~span.BinarySearch(inclusiveMax, new LowerBoundComparer()) - 1;
public static int GetLessThanIndex(this ReadOnlySpan span, T exclusiveMax) where T : IComparable => ~span.BinarySearch(exclusiveMax, new UpperBoundComparer()) - 1;
public static int GetGreaterEqualIndex(this Span span, T inclusiveMin) where T : IComparable => ((ReadOnlySpan)span).GetGreaterEqualIndex(inclusiveMin);
public static int GetGreaterThanIndex(this Span span, T exclusiveMin) where T : IComparable => ((ReadOnlySpan)span).GetGreaterThanIndex(exclusiveMin);
public static int GetLessEqualIndex(this Span span, T inclusiveMax) where T : IComparable => ((ReadOnlySpan)span).GetLessEqualIndex(inclusiveMax);
public static int GetLessThanIndex(this Span span, T exclusiveMax) where T : IComparable => ((ReadOnlySpan)span).GetLessThanIndex(exclusiveMax);
public static int BoundaryBinarySearch(Predicate predicate, int ok, int ng)
{
while (Math.Abs(ok - ng) > 1)
{
var mid = (ok + ng) / 2;
if (predicate(mid))
{
ok = mid;
}
else
{
ng = mid;
}
}
return ok;
}
public static long BoundaryBinarySearch(Predicate predicate, long ok, long ng)
{
while (Math.Abs(ok - ng) > 1)
{
var mid = (ok + ng) / 2;
if (predicate(mid))
{
ok = mid;
}
else
{
ng = mid;
}
}
return ok;
}
public static BigInteger BoundaryBinarySearch(Predicate predicate, BigInteger ok, BigInteger ng)
{
while (BigInteger.Abs(ok - ng) > 1)
{
var mid = (ok + ng) / 2;
if (predicate(mid))
{
ok = mid;
}
else
{
ng = mid;
}
}
return ok;
}
public static double BoundaryBinarySearch(Predicate predicate, double ok, double ng, double eps = 1e-9, int loopLimit = 1000)
{
var count = 0;
while (Math.Abs(ok - ng) > eps && count++ < loopLimit)
{
var mid = (ok + ng) * 0.5;
if (predicate(mid))
{
ok = mid;
}
else
{
ng = mid;
}
}
return (ok + ng) * 0.5;
}
public static double Bisection(Func f, double a, double b, double eps = 1e-9)
{
if (f(a) * f(b) >= 0)
{
throw new ArgumentException("f(a)とf(b)は異符号である必要があります。");
}
const int maxLoop = 100;
double mid = (a + b) / 2;
for (int i = 0; i < maxLoop; i++)
{
if (f(a) * f(mid) < 0)
{
b = mid;
}
else
{
a = mid;
}
mid = (a + b) / 2;
if (Math.Abs(b - a) < eps)
{
break;
}
}
return mid;
}
}
}
#endregion