using System; using System.IO; using System.Collections.Generic; using System.Linq; using System.Text; using System.Threading.Tasks; namespace AtCoder.Contest.A { static class Program { public static List prime; public static SortedDictionary dp; public static void Main(string[] args) { var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; Console.SetOut(sw); var cin = new Scanner(); prime = new List(); dp = new SortedDictionary(); int n = cin.NextInt(); for (int i = 2; i < n; i++) { bool isPrime = true; foreach (var item in prime) { if (item * item > i) break; if (i % item == 0) { isPrime = false; break; } } if (isPrime) { prime.Add(i); } } dp.Add(0, -1); dp.Add(1, -1); dp.Add(2, 1); Console.WriteLine(a(n)); Console.Out.Flush(); } public static int a(int n) { int now = -1; if (dp.ContainsKey(n)) return dp[n]; if (prime.Contains(n)) now = Math.Max(now, 1); for (var i = prime.UpperBound(n) - 1; i >= 0; i--) { if (prime[i] * 2 > n) now = Math.Max(now, a(n - prime[i]) == -1 ? -1 : a(n - prime[i]) + 1); else if (prime[i] * 2 == n) now = Math.Max(now, a(n - prime[i]) <= 1 ? -1 : a(n - prime[i]) + 1); else break; } dp.Add(n, now); return now; } } static class BinarySearch { public static int UpperBound(T[] array, T value) => UpperBound(array, 0, array.Length - 1, value, Comparer.Default); public static int UpperBound(T[] array, T value, Comparer comparer) => UpperBound(array, 0, array.Length - 1, value, comparer); public static int UpperBound(T[] array, int index, int length, T value) => UpperBound(array, index, length, value, Comparer.Default); public static int UpperBound(T[] array, int index, int length, T value, Comparer comparer) { var l = index; var r = l + length - 1; while (l <= r) { var mid = l + (r - l) / 2; var res = comparer.Compare(array[mid], value); if (res <= 0) l = mid + 1; else r = mid - 1; } return l; } public static int UpperBound(this List list, T item) => list.UpperBound(0, list.Count, item, Comparer.Default); public static int UpperBound(this List list, T item, Comparer comparer) => list.UpperBound(0, list.Count, item, comparer); public static int UpperBound(this List list, int index, int count, T item, Comparer comparer) { var l = index; var r = l + count - 1; while (l <= r) { var mid = l + (r - l) / 2; var res = comparer.Compare(list[mid], item); if (res <= 0) l = mid + 1; else r = mid - 1; } return l; } public static int LowerBound(T[] array, T value) => LowerBound(array, 0, array.Length - 1, value, Comparer.Default); public static int LowerBound(T[] array, T value, Comparer comparer) => LowerBound(array, 0, array.Length - 1, value, comparer); public static int LowerBound(T[] array, int index, int length, T value) => LowerBound(array, index, length, value, Comparer.Default); public static int LowerBound(T[] array, int index, int length, T value, Comparer comparer) { var l = index; var r = l + length - 1; while (l <= r) { var mid = l + (r - l) / 2; var res = comparer.Compare(array[mid], value); if (res == -1) l = mid + 1; else r = mid - 1; } return l; } public static int LowerBound(this List list, T item) => list.LowerBound(0, list.Count, item, Comparer.Default); public static int LowerBound(this List list, T item, Comparer comparer) => list.LowerBound(0, list.Count, item, comparer); public static int LowerBound(this List list, int index, int count, T item, Comparer comparer) { var l = index; var r = l + count - 1; while (l <= r) { var mid = l + (r - l) / 2; var res = comparer.Compare(list[mid], item); if (res == -1) l = mid + 1; else r = mid - 1; } return l; } } public class Pair : IComparable, IEquatable> where T : IComparable, IEquatable where U : IComparable, IEquatable { public T First { get; set; } public U Second { get; set; } public Pair(T first, U second) { First = first; Second = second; } public int CompareTo(object obj) { Pair castedObj = (Pair)obj; int x = First.CompareTo(castedObj.First); if (x != 0) return x; else return Second.CompareTo(castedObj.Second); } public static bool operator ==(Pair x, Pair y) => x.CompareTo(y) == 0; public static bool operator !=(Pair x, Pair y) => x.CompareTo(y) != 0; public static bool operator <(Pair x, Pair y) => x.CompareTo(y) == 1; public static bool operator >(Pair x, Pair y) => x.CompareTo(y) == -1; public static bool operator <=(Pair x, Pair y) => x.CompareTo(y) > 0; public static bool operator >=(Pair x, Pair y) => x.CompareTo(y) < 0; public bool Equals(Pair x) => First.Equals(x.First) && Second.Equals(x.Second); public override bool Equals(object obj) { return obj is Pair pair && EqualityComparer.Default.Equals(First, pair.First) && EqualityComparer.Default.Equals(Second, pair.Second); } public override int GetHashCode() { unchecked { var hashCode = 405212230; hashCode = hashCode * -1521134295 + EqualityComparer.Default.GetHashCode(First); hashCode = hashCode * -1521134295 + EqualityComparer.Default.GetHashCode(Second); return hashCode; } } } /// /// Self-Balancing Binary Search Tree /// (using Randamized BST) /// public class SB_BinarySearchTree where T : IComparable { public class Node { public T Value; public Node LChild; public Node RChild; public int Count; //size of the sub tree public Node(T v) { Value = v; Count = 1; } } static Random _rnd = new Random(); public static int Count(Node t) { return t == null ? 0 : t.Count; } static Node Update(Node t) { t.Count = Count(t.LChild) + Count(t.RChild) + 1; return t; } public static Node Merge(Node l, Node r) { if (l == null || r == null) return l == null ? r : l; if ((double)Count(l) / (double)(Count(l) + Count(r)) > _rnd.NextDouble()) { l.RChild = Merge(l.RChild, r); return Update(l); } else { r.LChild = Merge(l, r.LChild); return Update(r); } } /// /// split as [0, k), [k, n) /// public static Tuple Split(Node t, int k) { if (t == null) return new Tuple(null, null); if (k <= Count(t.LChild)) { var s = Split(t.LChild, k); t.LChild = s.Item2; return new Tuple(s.Item1, Update(t)); } else { var s = Split(t.RChild, k - Count(t.LChild) - 1); t.RChild = s.Item1; return new Tuple(Update(t), s.Item2); } } public static Node Remove(Node t, T v) { if (Find(t, v) == null) return t; return RemoveAt(t, LowerBound(t, v)); } public static Node RemoveAt(Node t, int k) { var s = Split(t, k); var s2 = Split(s.Item2, 1); return Merge(s.Item1, s2.Item2); } public static bool Contains(Node t, T v) { return Find(t, v) != null; } public static Node Find(Node t, T v) { while (t != null) { var cmp = t.Value.CompareTo(v); if (cmp > 0) t = t.LChild; else if (cmp < 0) t = t.RChild; else break; } return t; } public static Node FindByIndex(Node t, int idx) { if (t == null) return null; var currentIdx = Count(t) - Count(t.RChild) - 1; while (t != null) { if (currentIdx == idx) return t; if (currentIdx > idx) { t = t.LChild; currentIdx -= (Count(t == null ? null : t.RChild) + 1); } else { t = t.RChild; currentIdx += (Count(t == null ? null : t.LChild) + 1); } } return null; } public static int UpperBound(Node t, T v) { var torg = t; if (t == null) return -1; var ret = Int32.MaxValue; var idx = Count(t) - Count(t.RChild) - 1; while (t != null) { var cmp = t.Value.CompareTo(v); if (cmp > 0) { ret = Math.Min(ret, idx); t = t.LChild; idx -= (Count(t == null ? null : t.RChild) + 1); } else if (cmp <= 0) { t = t.RChild; idx += (Count(t == null ? null : t.LChild) + 1); } } return ret == Int32.MaxValue ? Count(torg) : ret; } public static int LowerBound(Node t, T v) { var torg = t; if (t == null) return -1; var idx = Count(t) - Count(t.RChild) - 1; var ret = Int32.MaxValue; while (t != null) { var cmp = t.Value.CompareTo(v); if (cmp >= 0) { if (cmp == 0) ret = Math.Min(ret, idx); t = t.LChild; if (t == null) ret = Math.Min(ret, idx); idx -= t == null ? 0 : (Count(t.RChild) + 1); } else if (cmp < 0) { t = t.RChild; idx += (Count(t == null ? null : t.LChild) + 1); if (t == null) return idx; } } return ret == Int32.MaxValue ? Count(torg) : ret; } public static Node Insert(Node t, T v) { var ub = LowerBound(t, v); return InsertByIdx(t, ub, v); } static Node InsertByIdx(Node t, int k, T v) { var s = Split(t, k); return Merge(Merge(s.Item1, new Node(v)), s.Item2); } public static IEnumerable Enumerate(Node t) { var ret = new List(); Enumerate(t, ret); return ret; } static void Enumerate(Node t, List ret) { if (t == null) return; Enumerate(t.LChild, ret); ret.Add(t.Value); Enumerate(t.RChild, ret); } } /// /// C-like set /// public class Set where T : IComparable { protected SB_BinarySearchTree.Node _root; public T this[int idx] { get { return ElementAt(idx); } } public int Count() { return SB_BinarySearchTree.Count(_root); } public virtual void Insert(T v) { if (_root == null) _root = new SB_BinarySearchTree.Node(v); else { if (SB_BinarySearchTree.Find(_root, v) != null) return; _root = SB_BinarySearchTree.Insert(_root, v); } } public void Clear() { _root = null; } public void Remove(T v) { _root = SB_BinarySearchTree.Remove(_root, v); } public bool Contains(T v) { return SB_BinarySearchTree.Contains(_root, v); } public T ElementAt(int k) { var node = SB_BinarySearchTree.FindByIndex(_root, k); if (node == null) throw new IndexOutOfRangeException(); return node.Value; } public int Count(T v) { return SB_BinarySearchTree.UpperBound(_root, v) - SB_BinarySearchTree.LowerBound(_root, v); } public int LowerBound(T v) { return SB_BinarySearchTree.LowerBound(_root, v); } public int UpperBound(T v) { return SB_BinarySearchTree.UpperBound(_root, v); } public Tuple EqualRange(T v) { if (!Contains(v)) return new Tuple(-1, -1); return new Tuple(SB_BinarySearchTree.LowerBound(_root, v), SB_BinarySearchTree.UpperBound(_root, v) - 1); } public List ToList() { return new List(SB_BinarySearchTree.Enumerate(_root)); } } class Scanner { string[] s; int i; char[] cs = new char[] { ' ' }; public Scanner() { s = new string[0]; i = 0; } public string Next() { if (i < s.Length) return s[i++]; string st = Console.ReadLine(); while (st == "") st = Console.ReadLine(); s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries); if (s.Length == 0) return Next(); i = 0; return s[i++]; } public int NextInt() { return int.Parse(Next()); } public int[] ArrayInt(int N, int add = 0) { int[] Array = new int[N]; for (int i = 0; i < N; i++) { Array[i] = NextInt() + add; } return Array; } public long NextLong() { return long.Parse(Next()); } public long[] ArrayLong(int N, long add = 0) { long[] Array = new long[N]; for (int i = 0; i < N; i++) { Array[i] = NextLong() + add; } return Array; } public double NextDouble() { return double.Parse(Next()); } public double[] ArrayDouble(int N, double add = 0) { double[] Array = new double[N]; for (int i = 0; i < N; i++) { Array[i] = NextDouble() + add; } return Array; } } }