Problem: You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:

  * For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j. 
  * The maximal value of all a_i should be minimized (that is, as small as possible). 



A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.

Input

The only line contains the integer n (2 ≤ n ≤ 10^5).

Output

Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n). 

If there are multiple solutions, print any of them.

Examples

Input


4


Output


1 2 1 

Input


3


Output


2 1

Note

In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.BigInteger;
public class cf1 {
    static long mod = (long)1e9 + 7;
    static long mod1 = 998244353;
    static FastScanner f;
    static PrintWriter pw = new PrintWriter(System.out);
    static Scanner S = new Scanner(System.in);
    static long x0; static long y0;
    static int inf = (int)(1e9);
    static long iinf = (long)(1e18);
    static void solve()throws IOException {
        int n = f.ni();
        int lpf[] = new int[n + 1];
        ArrayList<Integer> primes = new ArrayList<>();
        HashMap<Integer , Integer> h = new HashMap<>();
        int last = 0;
        for (int i = 2; i <= n; ++i) {
            if (lpf[i] == 0) {
                lpf[i] = i;
                primes.add(i);
            }
            for (int j = 0; j < primes.size() && primes.get(j) <= lpf[i] && i * primes.get(j) <= n; ++j)
                lpf[i * primes.get(j)] = primes.get(j);
            if (h.containsKey(lpf[i])) continue;
            h.put(lpf[i] , last + 1);
            ++last;
        }
        for (int i = 2; i <= n; ++i) {
            int ans = h.get(lpf[i]);
            p(ans + " ");
        }
    }
    public static void main(String[] args)throws IOException {
        init(); 
        int t = 1;
        while(t --> 0) {solve();}
        pw.flush(); 
        pw.close();  
    }
        
/******************************END OF MAIN PROGRAM*******************************************/
    public static void init()throws IOException{if(System.getProperty("ONLINE_JUDGE")==null){f=new FastScanner("");}else{f=new FastScanner(System.in);}}
    public static class FastScanner {
        BufferedReader br;StringTokenizer st;
        FastScanner(InputStream stream){try{br=new BufferedReader(new InputStreamReader(stream));}catch(Exception e){e.printStackTrace();}}
        FastScanner(String str){try{br=new BufferedReader(new FileReader("!a.txt"));}catch(Exception e){e.printStackTrace();}}
        String next(){while(st==null||!st.hasMoreTokens()){try{st=new StringTokenizer(br.readLine());}catch(IOException e){e.printStackTrace();}}return st.nextToken();}
        String nextLine()throws IOException{return br.readLine();}int ni(){return Integer.parseInt(next());}long nl(){return Long.parseLong(next());}double nd(){return Double.parseDouble(next());}
    }
    public static void pn(Object o){pw.println(o);}
    public static void p(Object o){pw.print(o);}
    public static void pni(Object o){pw.println(o);pw.flush();}
    static int gcd(int a,int b){if(b==0)return a;else{return gcd(b,a%b);}}
    static long gcd(long a,long b){if(b==0l)return a;else{return gcd(b,a%b);}}
    static long lcm(long a,long b){return (a*b/gcd(a,b));}
    static long exgcd(long a,long b){if(b==0){x0=1;y0=0;return a;}long temp=exgcd(b,a%b);long t=x0;x0=y0;y0=t-a/b*y0;return temp;}
    static long pow(long a,long b){long res=1;while(b>0){if((b&1)==1)res=res*a;b>>=1;a=a*a;}return res;}
    static long mpow(long a,long b){long res=1;while(b>0l){if((b&1)==1l)res=((res%mod)*(a%mod))%mod;b>>=1l;a=((a%mod)*(a%mod))%mod;}return res;}
    static long mul(long a , long b){return ((a%mod)*(b%mod)%mod);}
    static long adp(long a , long b){return ((a%mod)+(b%mod)%mod);}
    static int log2(int x){return (int)(Math.log(x)/Math.log(2));}
    static boolean isPrime(long n){if(n<=1)return false;if(n<=3)return true;if(n%2==0||n%3==0)return false;for(long i=5;i*i<=n;i=i+6)if(n%i==0||n%(i+2)==0)return false;return true;}
    static boolean isPrime(int n){if(n<=1)return false;if(n<=3)return true;if(n%2==0||n%3==0)return false;for(int i=5;i*i<=n;i=i+6)if(n%i==0||n%(i+2)==0)return false;return true;}
    static HashSet<Long> factors(long n){HashSet<Long> hs=new HashSet<Long>();for(long i=1;i<=(long)Math.sqrt(n);i++){if(n%i==0){hs.add(i);hs.add(n/i);}}return hs;}
    static HashSet<Integer> factors(int n){HashSet<Integer> hs=new HashSet<Integer>();for(int i=1;i<=(int)Math.sqrt(n);i++){if(n%i==0){hs.add(i);hs.add(n/i);}}return hs;}
    static HashSet<Long> pf(long n){HashSet<Long> ff=factors(n);HashSet<Long> ans=new HashSet<Long>();for(Long i:ff)if(isPrime(i))ans.add(i);return ans;}
    static HashSet<Integer> pf(int n){HashSet<Integer> ff=factors(n);HashSet<Integer> ans=new HashSet<Integer>();for(Integer i:ff)if(isPrime(i))ans.add(i);return ans;}
    static int[] inpint(int n){int arr[]=new int[n];for(int i=0;i<n;i++){arr[i]=f.ni();}return arr;}
    static long[] inplong(int n){long arr[] = new long[n];for(int i=0;i<n;i++){arr[i]=f.nl();}return arr;}
    static boolean ise(int x){return ((x&1)==0);}static boolean ise(long x){return ((x&1)==0);}
    static int gnv(char c){return Character.getNumericValue(c);}//No. of integers less than equal to i in ub
    static int log(long x){return x==1?0:(1+log(x/2));} static int log(int x){return x==1?0:(1+log(x/2));}
    static int upperbound(int a[],int i){int lo=0,hi=a.length-1,mid=0;int count=0;while(lo<=hi){mid=(lo+hi)/2;if(a[mid]<=i){count=mid+1;lo=mid+1;}else hi=mid-1;}return count;}
    static void sort(int[] a){ArrayList<Integer> l=new ArrayList<>();for(int i:a)l.add(i);Collections.sort(l);for(int i=0;i<a.length;++i)a[i]=l.get(i);}
    static void sort(long[] a){ArrayList<Long> l=new ArrayList<>();for(long i:a)l.add(i);Collections.sort(l);for(int i=0;i<a.length;++i)a[i]=l.get(i);}
    static void sort(ArrayList<Integer> a){Collections.sort(a);}//!Precompute fact in ncr()!
    static int nextPowerOf2(int n){int count=0;if(n>0&&(n&(n-1))==0)return n;while(n!=0){n>>=1;count += 1;}return 1<<count;} 
}