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:
#!/usr/bin/env python
import os
import operator
import sys
import bisect
import _operator
from _collections import defaultdict
from io import BytesIO, IOBase

def inar():
    return [int(k) for k in input().split()]
def power(x, p,m):
    res = 1
    while p:
        if p & 1:
            res = (res * x) % m
        x = (x * x) % m
        p >>= 1
    return res

def main():
    #mod=1000000007
    # for _ in range(int(input())):
    #     #n=int(input())
    #     st=input()
    #     dic=defaultdict(int)
    #     n=len(st)
    #     for i in range(len(st)):
    #         dic[st[i]]+=1
    #     ans=n-max(dic.values())
    #     for i in range(0,10):
    #         for j in range(0,10):
    #             ok = True
    #             count = 0
    #             for k in range(n):
    #                 if ok:
    #                     if st[k]==str(i):
    #                         count+=1
    #                         ok=False
    #                 else:
    #                     if st[k]==str(j):
    #                         count+=1
    #                         ok=True
    #             if count%2!=0:
    #                 count-=1
    #             #print(count)
    #             ans=min(ans,n-count)
    #     print(ans)
    # n=int(input())
    # arr=inar()
    # sm1=0
    # sm2=0
    # for i in range(n):
    #     sm1+=arr[i]
    # for i in range(n,2*n):
    #     sm2+=arr[i]
    # if sm1!=sm2:
    #     print(*arr)
    # else:
    #     counter=0
    #     for i in range(n):
    #         if arr[i]!=arr[2*n-i-1]:
    #             temp=arr[i]
    #             arr[i]=arr[2*n-i-1]
    #             arr[2*n-i-1]=temp
    #             counter=1
    #             break
    #     if counter:
    #         print(*arr)
    #     else:
    #         print(-1)
    # n=int(input())
    # arr=inar()
    # odd=0
    # even=0
    # for i in range(n):
    #     if arr[i]%2==0:
    #         even+=1
    #     else:
    #         odd+=1
    # if odd>0 and even>0:
    #     arr.sort()
    #     print(*arr)
    # else:
    #     print(*arr)
    #
    n = int(input())
    primes=[1]*(n+1)
    ans=[0]*(n+1)
    for i in range(2,int(n**0.5)+1):
        if primes[i]==1:
            for j in range(i*i,n+1,i):
                if primes[j]==1:
                    primes[j]=0

    k=1

    for i in range(2,int(n**0.5)+1):
        if ans[i]==0:
            ans[i]=k
            k+=1
            for j in range(i*i,n+1,i):
                if ans[j]==0:
                    ans[j]=ans[i]
    for i in range(2,n+1):
        if ans[i]==0:
            ans[i]=k
            k+=1
    print(*ans[2:n+1])









BUFSIZE = 8192

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")

if __name__ == "__main__":
    main()