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.math.*;

// **** PROBLEM TITLE ****

public class C {
	static char [] in = new char [1000000];
	public static void main (String [] arg) throws Throwable {
		int n = nextInt();
		int [] color = new int [n-1];
		int count = 0;
		for (int i = 2;i-2<color.length; ++i) {
			if (color[i-2] == 0) {
				//System.err.println(i + " is found to be prime");
				count++; 
				color[i-2] = count;
				for (int j = i<<1; j-2<color.length; j+=i) if (color[j-2] == 0) color[j-2] = count;
			}
		}
		System.out.println(stringFromArray(color));
	}

	
	
	
	
	
	
	
	
	
	
	
	
	
	/************** HELPER CLASSES ***************/
    static class HS extends HashSet<Integer>{public HS(){super();}public HS(int a){super(a);}};
	static class AL extends ArrayList<Integer>{public AL(){super();}public AL(int a){super (a);}};
	static class Pair implements Comparable<Pair> {int x,y,L; public Pair(int xx, int yy, int LL){x=xx;y=yy;L=LL;} public int compareTo(Pair p) {return this.L-p.L;}}	
	
	/************** FAST IO CODE FOLLOWS *****************/
	public static long nextLong() throws Throwable {
		long i = System.in.read();boolean neg = false;while (i < 33) i = System.in.read();if (i == 45) {neg=true;i=48;}i = i - 48;
		int j = System.in.read();while (j > 32) {i*=10;i+=j-48;j = System.in.read();}return (neg) ? -i : i;
	}
	public static int nextInt() throws Throwable {return (int)nextLong();}
	public static String next() throws Throwable {
		int i = 0; while (i < 33 && i != -1) i = System.in.read(); int cptr = 0; while (i >= 33) { in[cptr++] = (char)i; i = System.in.read();}
		return new String(in, 0,cptr);
	}
	/**** LIBRARIES ****/
	public static long gcdL(long a, long b) {while (b != 0) {long tmp = b;b = (a % b);a = tmp;}return a;}
	public static int gcd(int a, int b) {while (b != 0) {int tmp = b;b = (a % b);a = tmp;}return a;}
	public static int[] sieve(int LIM) {
		int i,count = 0;
		boolean [] b = new boolean [LIM];
		for (i = 2;i<LIM; ++i) if (!b[i]) {count++; for (int j = i<<1; j<LIM; j+=i) b[j] = true;}
		int [] primes = new int[count];
		for (i = 2,count=0;i<LIM;++i) if (!b[i]) primes[count++] = i;
		return primes;
	}
	public static int[] numPrimeFactors(int LIM) {
		int i,count = 0;
		int [] b = new int [LIM];
		for (i = 2;i<LIM; ++i) if (b[i] == 0) {count++; for (int j = i; j<LIM; j+=i) b[j]++;}
		return b;
	}
	public static String stringFromArray(int [] a) {
		StringBuilder b = new StringBuilder(2*a.length);
		for (int i = 0; i<a.length; ++i) {
			if (i != 0) b = b.append(' ');
			b = b.append(a[i]);
		}
		return b.toString();
	}
}

/* Full Problem Text:
 PROBLEM STATEMENT
 */