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 PYTHON3):

Solution:
# -*- coding: utf-8 -*-
"""
Created on Mon Jun  3 10:01:38 2019

@author: plosi
"""

def compute(n): 
    val=1 
    primes=[True for i in range(n+1)] 
    primes[0]=False
    primes[1]=False  
    fs=[0 for i in range(n+1)]
    p=2
    fs[2]=1
    while p<=int(n**(.5)) :
        cur=p
        cur=cur+p
        while cur<=n: 
            primes[cur]=False
            if fs[cur]==0: 
                fs[cur]=val
            cur=cur+p
        p=p+1
        while not primes[p]: 
            p=p+1
        val=val+1
        fs[p]=val
    
    for i in range(int(n**.5)+1,n+1):
        if primes[i]: 
            fs[i]=val
            val=val+1
        
    return fs 

def main(): 
    n=int(input()) 
    fs=compute(n) 
    st=""
    for i in range(2,n+1):
        st=st+str(fs[i])+" "
    print(st)
main()