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.io.*;
import java.util.*;

public class Stack3 {

    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }
            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

    static Reader sc = new Reader();
    static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
    static int team1 = 0;
    static int team2 = 0;
    static int minkicks = 10;

    public static void main(String[] args) throws IOException {
        //subsequence("abcdefghij");

        /*
         * For integer input: int n=inputInt();
         * For long input: long n=inputLong();
         * For double input: double n=inputDouble();
         * For String input: String s=inputString();
         * Logic goes here
         * For printing without space: print(a+""); where a is a variable of any datatype
         * For printing with space: printSp(a+""); where a is a variable of any datatype
         * For printing with new line: println(a+""); where a is a variable of any datatype
         */

        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int c = 1;
        int[] ar = new int[n + 1];
        for (int i = 2; i <= n; i++) {
            boolean flag = false;
            if (ar[i] == 0) {
                ar[i] = c;
                flag=true;
            }

            for (long j = (long)i * i; j <= n; j += i) {
                if (ar[(int) j] == 0) {
                    flag = true;
                    ar[(int) j] = c;
                }
            }
            if (flag) {
                c++;
            }
        }
        StringBuilder ans = new StringBuilder();
        for (int i = 2; i <= n; i++) {
            ans.append(ar[i]).append(" ");
        }
        System.out.println(ans.toString());


        bw.flush();
        bw.close();


    }

    public static class Ath {
        int r1, r2, r3, r4, r5, index;

        public Ath(int r1, int r2, int r3, int r4, int r5, int index) {
            this.r1 = r1;
            this.r2 = r2;
            this.r3 = r3;

            this.r4 = r4;

            this.r5 = r5;
            this.index = index;

        }
    }

    public static class Score {
        int l;
        String s;

        public Score(int l, String s) {
            this.l = l;
            this.s = s;
        }
    }


    public static int checker(int a) {


        if (a % 2 == 0) {
            return 1;
        } else {
            while (true) {
                int b = 2;
                if ((a + b) == (a ^ b)) {
                    return b;
                }
            }
        }
    }

    public static boolean checkPrime(int n) {
        if (n == 0 || n == 1) {
            return false;
        }
        for (int j = 2; j * j <= n; j++) {
            if (n % j == 0) {
                return false;
            }
        }
        return true;
    }


    public static void dfs1(List<List<Integer>> g, boolean[] visited, Stack<Integer> stack, int num) {
        visited[num] = true;
        for (Integer integer : g.get(num)) {
            if (!visited[integer]) {
                dfs1(g, visited, stack, integer);
            }
        }
        stack.push(num);
    }

    public static void dfs2(List<List<Integer>> g, boolean[] visited, List<Integer> list, int num, int c,
                            int[] raj) {
        visited[num] = true;

        for (Integer integer : g.get(num)) {
            if (!visited[integer]) {
                dfs2(g, visited, list, integer, c, raj);
            }
        }
        raj[num] = c;
        list.add(num);

    }

    public static int inputInt() throws IOException {
        return sc.nextInt();
    }

    public static long inputLong() throws IOException {
        return sc.nextLong();
    }

    public static double inputDouble() throws IOException {
        return sc.nextDouble();
    }

    public static String inputString() throws IOException {
        return sc.readLine();
    }

    public static void print(String a) throws IOException {
        bw.write(a);
    }

    public static void printSp(String a) throws IOException {
        bw.write(a + " ");
    }

    public static void println(String a) throws IOException {
        bw.write(a + "\n");
    }


    public static long getAns(int[] ar, int c, long[][] dp, int i, int sign) {
        if (i < 0) {
            return 1;
        }

        if (c <= 0) {
            return 1;
        }

        dp[i][c] = Math.max(dp[i][c], Math.max(ar[i] * getAns(ar, c - 1, dp, i - 1, sign), getAns(ar, c, dp, i - 1, 1)));
        return dp[i][c];
    }


    public static long power(long a, long b, long c) {
        long ans = 1;
        while (b != 0) {
            if (b % 2 == 1) {
                ans = ans * a;
                ans %= c;
            }
            a = a * a;
            a %= c;
            b /= 2;
        }
        return ans;
    }

    public static long power1(long a, long b, long c) {
        long ans = 1;
        while (b != 0) {
            if (b % 2 == 1) {
                ans = multiply(ans, a, c);
            }
            a = multiply(a, a, c);
            b /= 2;

        }
        return ans;

    }

    public static long multiply(long a, long b, long c) {
        long res = 0;
        a %= c;
        while (b > 0) {
            if (b % 2 == 1) {
                res = (res + a) % c;
            }
            a = (a + a) % c;
            b /= 2;
        }

        return res % c;

    }

    public static long totient(long n) {
        long result = n;
        for (long i = 2; i * i <= n; i++) {
            if (n % i == 0) {
                //sum=sum+2*i;
                while (n % i == 0) {
                    n /= i;
                    // sum=sum+n;
                }
                result -= result / i;

            }
        }
        if (n > 1) {
            result -= result / n;

        }
        return result;
    }


    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        } else {
            return gcd(b, a % b);
        }
    }


    public static boolean[] primes(int n) {
        boolean[] p = new boolean[n + 1];
        p[0] = false;
        p[1] = false;
        for (int i = 2; i <= n; i++) {
            p[i] = true;
        }

        for (int i = 2; i * i <= n; i++) {
            if (p[i]) {
                for (int j = i * i; j <= n; j += i) {
                    p[j] = false;
                }
            }

        }
        return p;
    }

    public String LargestEven(String S) {
        //  char[] ar=S.toCharArray();
        int[] count = new int[10];
        for (int i = 0; i < S.length(); i++) {
            count[S.charAt(i) - '0']++;
        }
        int num = -1;
        for (int i = 0; i <= 8; i += 2) {
            if (count[i] > 0) {
                num = i;
                break;
            }
        }
        StringBuilder ans = new StringBuilder();
        for (int i = 9; i >= 0; i--) {
            if (i != num) {
                for (int j = 1; j <= count[i]; j++) {
                    ans.append(i);
                }
            } else {
                for (int j = 1; j <= count[num] - 1; j++) {
                    ans.append(num);
                }

            }
        }
        if (num != -1 && count[num] > 0) {
            ans.append(num);
        }
        return ans.toString();
    }

}