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:
n=int(input())
s=[0]*(n)
j=1
while(j<n):
    s[j]=1
    j+=2
prime=[True]*n
#print(s)
p = 3
k = 2
while (p * p <= n): 
    if (prime[p-1] == True):
        if s[p-1]!=1:
            s[p-1]=k
            k+=1
        for i in range(p*2,n+1,p):
                prime[i-1] = False
                if s[i-1]!=1:
                    s[i-1]=k-1
    #print(prime)
    p += 1
#print(prime)
#print(s)
for i in range(1,n):
    if s[i]==0:
        print(k,end=" ")
        k+=1
    else:
        print(s[i],end=" ")