using System; using System.Collections.Generic; using System.Linq; using System.IO; using System.Runtime.CompilerServices; using System.Text; using static Template; namespace SolveSpace { using static System.Console; using static System.Convert; using static System.Math; using Pi = Pair; using Number = System.Int64; class Solver { public void Solve() { var num = Input.num; var ar = Input.ar; var dic = new Dictionary>(); for(var i = 0; i < num; i++) { var f = Factorize(ar[i]); foreach(var d in f.Keys) { if (!dic.ContainsKey(d)) dic[d] = new List(); dic[d].Add(i); } } var uf = new UnionFind(num); var res = (long)ar.Count(a => a != 1); foreach (var d in dic.Values) { var ct = new int[num]; for (var i = 0; i < d.Count; i++) ct[uf.Parent(d[i])]++; var r = 1L;var q = 0L; for (var i = 0; i < num; i++) if (ct[i] != 0) { r *= 1L << ct[i]; q += (1L << ct[i])-1; } res += r - q-1; for (var i = 1; i < d.Count; i++) uf.Union(d[i - 1], d[i]); } WriteLine((1L << num) - res - 1); } public static Dictionary Factorize(long num) { var dic = new Dictionary(); for (var i = 2L; i * i <= num; i++) { var ct = 0; while (num % i == 0) { ct++; num /= i; } if (ct != 0) dic[i] = ct; } if (num != 1) dic[num] = 1; return dic; } } public class UnionFind { protected int[] parent, size, rank; public UnionFind(int num) { parent = new int[num]; size = new int[num]; rank = new int[num]; for (var i = 0; i < num; i++) { parent[i] = i; size[i] = 1; } } protected int Find(int i) => i == parent[i] ? i : (parent[i] = Find(parent[i])); public int Parent(int i) => Find(i); public int Size(int i) => size[Find(i)]; public virtual bool Union(int v1, int v2) { v1 = Find(v1); v2 = Find(v2); if (v1 == v2) return false; if (rank[v1] < rank[v2]) swap(ref v1, ref v2); parent[v2] = v1; size[v1] += size[v2]; if (rank[v1] == rank[v2]) rank[v1]++; return true; } public bool IsSame(int v1, int v2) => Find(v1) == Find(v2); } } #region Template public class Template { [MethodImpl(MethodImplOptions.AggressiveInlining)] public static bool chmin(ref T num, T val) where T : IComparable { if (num.CompareTo(val) == 1) { num = val; return true; } return false; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static bool chmax(ref T num, T val) where T : IComparable { if (num.CompareTo(val) == -1) { num = val; return true; } return false; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void swap(ref T v1, ref T v2) { var t = v2; v2 = v1; v1 = t; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static T[] Create(int n, Func f) => Enumerable.Repeat(0, n).Select(_ => f()).ToArray(); public static void Fail() => Fail("No"); public static void Fail(T s) { Console.WriteLine(s); Console.Out.Close(); Environment.Exit(0); } static void Main(string[] args) { var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; Console.SetOut(sw); var p = new SolveSpace.Solver(); for (var i = 1; i > 0; --i) p.Solve(); Console.Out.Flush(); } } public class Input { public static string read => Console.ReadLine().Trim(); public static int[] ar => read.Split(' ').Select(int.Parse).ToArray(); public static int num => Convert.ToInt32(read); public static long[] arL => read.Split(' ').Select(long.Parse).ToArray(); public static long numL => Convert.ToInt64(read); public static char[][] grid(int h) => Create(h, () => read.ToCharArray()); public static int[] ar1D(int n) => Create(n, () => num); public static long[] arL1D(int n) => Create(n, () => numL); public static string[] strs(int n) => Create(n, () => read); public static int[][] ar2D(int n) => Create(n, () => ar); public static long[][] arL2D(int n) => Create(n, () => arL); public static List[] edge(int n) => Create(n, () => new List()); public static void Make(out T1 v1, out T2 v2) { v1 = Next(); v2 = Next(); } public static void Make(out T1 v1, out T2 v2, out T3 v3) { Make(out v1, out v2); v3 = Next(); } public static void Make(out T1 v1, out T2 v2, out T3 v3, out T4 v4) { Make(out v1, out v2, out v3); v4 = Next(); } public static void Make(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5) { Make(out v1, out v2, out v3, out v4); v5 = Next(); } public static void Make(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6) { Make(out v1, out v2, out v3, out v4, out v5); v6 = Next(); } static Input() { sc = new Queue(); dic = new Dictionary>(); dic[typeof(int)] = s => int.Parse(s); dic[typeof(long)] = s => long.Parse(s); dic[typeof(char)] = s => char.Parse(s); dic[typeof(double)] = s => double.Parse(s); dic[typeof(uint)] = s => uint.Parse(s); dic[typeof(ulong)] = s => ulong.Parse(s); dic[typeof(string)] = s => s; } private static Dictionary> dic; private static Queue sc; [MethodImpl(MethodImplOptions.AggressiveInlining)] public static T Next() { if (sc.Count == 0) foreach (var item in read.Split(' ')) sc.Enqueue(item); return (T)dic[typeof(T)](sc.Dequeue()); } public const int MOD = 1000000007; } public class Pair : IComparable> { public T1 v1; public T2 v2; public Pair() { v1 = Input.Next(); v2 = Input.Next(); } public Pair(T1 v1, T2 v2) { this.v1 = v1; this.v2 = v2; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public int CompareTo(Pair p) { var c = Comparer.Default.Compare(v1, p.v1); if (c == 0) c = Comparer.Default.Compare(v2, p.v2); return c; } public override string ToString() => $"{v1.ToString()} {v2.ToString()}"; } public class Pair : Pair, IComparable> { public T3 v3; public Pair() : base() { v3 = Input.Next(); } public Pair(T1 v1, T2 v2, T3 v3) : base(v1, v2) { this.v3 = v3; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public int CompareTo(Pair p) { var c = base.CompareTo(p); if (c == 0) c = Comparer.Default.Compare(v3, p.v3); return c; } public override string ToString() => $"{base.ToString()} {v3.ToString()}"; } #endregion