Sherlock has a new girlfriend (so unlike him!). Valentine's day is coming and he wants to gift her some jewelry.

He bought n pieces of jewelry. The i-th piece has price equal to i + 1, that is, the prices of the jewelry are 2, 3, 4, ... n + 1.

Watson gave Sherlock a challenge to color these jewelry pieces such that two pieces don't have the same color if the price of one piece is a prime divisor of the price of the other piece. Also, Watson asked him to minimize the number of different colors used.

Help Sherlock complete this trivial task.


-----Input-----

The only line contains single integer n (1 ≤ n ≤ 100000) — the number of jewelry pieces.


-----Output-----

The first line of output should contain a single integer k, the minimum number of colors that can be used to color the pieces of jewelry with the given constraints.

The next line should consist of n space-separated integers (between 1 and k) that specify the color of each piece in the order of increasing price.

If there are multiple ways to color the pieces using k colors, you can output any of them.


-----Examples-----
Input
3

Output
2
1 1 2 
Input
4

Output
2
2 1 1 2



-----Note-----

In the first input, the colors for first, second and third pieces of jewelry having respective prices 2, 3 and 4 are 1, 1 and 2 respectively.

In this case, as 2 is a prime divisor of 4, colors of jewelry having prices 2 and 4 must be distinct.

Difficulty: EASY
Tags: Number theory

Constructive algorithms

Starter code:

Solutions:
n = int(input())
primes = [2]
primes_bool = [2 for _ in range(10 ** 5 + 4)]
primes_bool[2] = 1
for i in range(3, 10 ** 5 + 4, 2):
	isPrime = True
	for j in range(len(primes)):
		if primes[j] ** 2 > i:
			break
		if i % primes[j] == 0:
			isPrime = False
			break
	if isPrime:
		primes.append(i)
		primes_bool[i] = 1
if n <= 2:
	print(1)
else:
	print(2)
print(*primes_bool[2:n + 2])


import math
import bisect

def sieve(n):
	primes = [-1] * n
	primes[0] = -1
	primes[1] = -1
	i = 2
	has_comp = False
	sqrt_n = int(n ** 0.5 + 1)
	while i <= sqrt_n:
		if primes[i] == -1:
			primes[i] = 1
			for j in range(i * i, n, i):
				has_comp = True
				primes[j] = 2
		i += 1
	for i in range(sqrt_n, n):
		if primes[i] == -1:
			primes[i] = 1
	return (has_comp, primes)
n = int(input())
(has_comp, res) = sieve(n + 2)
if has_comp:
	print(2)
else:
	print(1)
res_r = ''
for i in res[2:]:
	res_r = res_r + str(i) + ' '
print(res_r)


def SieveOfEratosthenes(n):
	all_prime = []
	prime = [True for i in range(n + 1)]
	p = 2
	while p * p <= n:
		if prime[p]:
			for i in range(p * p, n + 1, p):
				prime[i] = False
		p += 1
	for p in range(2, n):
		if prime[p]:
			all_prime.append(p)
	return all_prime
c = 1
n = int(input())
r = SieveOfEratosthenes(n + 2)
l = [0] * (n + 2)
if n > 2:
	c = 2
for i in r:
	l[i] = 1
for j in range(n + 2):
	if l[j] == 0:
		l[j] = 2
print(c)
print(*l[2:])


n = int(input())
prime = [True for i in range(n + 3)]

def SieveOfEratosthenes(n):
	p = 2
	while p * p <= n:
		if prime[p] == True:
			for i in range(p * 2, n + 1, p):
				prime[i] = False
		p += 1
SieveOfEratosthenes(n + 2)
p = []
for i in range(2, n + 2):
	if prime[i]:
		p.append(1)
	else:
		p.append(2)
s = set(p)
print(len(s))
for i in range(0, len(p)):
	print(p[i], end=' ')


mod = 10 ** 9 + 7
ii = lambda : int(input())
si = lambda : input()
dgl = lambda : list(map(int, input()))
f = lambda : map(int, input().split())
il = lambda : list(map(int, input().split()))
ls = lambda : list(input())

def ispr(n):
	for i in range(2, int(n ** 0.5) + 1):
		if n % i == 0:
			return False
	return True
n = ii()
l = []
for i in range(2, n + 2):
	if ispr(i):
		l.append(1)
	else:
		l.append(2)
print(max(l))
print(*l)


from sys import stdin, stdout
import bisect
import math

def st():
	return list(stdin.readline().strip())

def inp():
	return int(stdin.readline())

def li():
	return list(map(int, stdin.readline().split()))

def mp():
	return map(int, stdin.readline().split())

def pr(n):
	stdout.write(str(n) + '\n')

def soe(limit):
	l = [1] * (limit + 1)
	l[0] = 0
	l[1] = 0
	prime = [2]
	for i in range(2, limit + 1):
		if l[i]:
			for j in range(i * i, limit + 1, i):
				l[j] = 0
	for i in range(3, limit + 1, 2):
		if l[i]:
			prime.append(i)
	return l

def segsoe(low, high):
	limit = int(high ** 0.5) + 1
	prime = soe(limit)
	n = high - low + 1
	l = [0] * (n + 1)
	for i in range(len(prime)):
		lowlimit = low // prime[i] * prime[i]
		if lowlimit < low:
			lowlimit += prime[i]
		if lowlimit == prime[i]:
			lowlimit += prime[i]
		for j in range(lowlimit, high + 1, prime[i]):
			l[j - low] = 1
	for i in range(low, high + 1):
		if not l[i - low]:
			if i != 1:
				print(i)

def gcd(a, b):
	while b:
		a = a % b
		(b, a) = (a, b)
	return a

def power(a, n):
	r = 1
	while n:
		if n & 1:
			r = r * a
		a *= a
		n = n >> 1
	return r

def solve():
	n = inp()
	if n > 2:
		print(2)
	else:
		print(1)
	x = soe(n + 100)
	for i in range(2, n + 2):
		if x[i]:
			print(1, end=' ')
		else:
			print(2, end=' ')
for _ in range(1):
	solve()


n = int(input()) + 1
ans = [1] * (n + 1)
prime = [True] * (n + 1)
for i in range(2, n + 1):
	if prime[i]:
		for j in range(i * i, n + 1, i):
			prime[j] = False
if n == 2:
	print(1)
	print(1)
elif n == 3:
	print(1)
	print(1, 1)
else:
	print(2)
	for i in range(2, n + 1):
		if prime[i]:
			print(1, end=' ')
		else:
			print(2, end=' ')


def isPrime(n):
	if n == 1:
		return False
	i = 2
	while i * i <= n:
		if n % i == 0:
			return False
		i += 1
	return True
n = int(input())
c = []
for i in range(2, n + 2):
	c.append(i)
l = []
for i in range(len(c)):
	if isPrime(c[i]) == True:
		l.append(1)
	else:
		l.append(2)
if l.count(2) == 0:
	print(1)
	print(*l)
else:
	print(2)
	print(*l)


def primesFunction(n):
	primes = []
	for i in range(n + 2):
		primes.append(1)
	n = n + 1
	if n > 1:
		primes[0] = 2
		primes[1] = 2
	for i in range(2, int(n ** 0.5) + 1):
		if primes[i] == 1:
			x = i ** 2
			j = i
			while i * j <= n:
				primes[i * j] = 2
				j += 1
	return primes
n = int(input())
primesList = primesFunction(n)
if n == 1:
	print(n)
	print(n)
elif n == 2:
	print(1)
	print(1, end=' ')
	print(1)
else:
	print(2)
	for i in range(2, len(primesList)):
		print(primesList[i], end=' ')


n = int(input())
if n <= 2:
	print(1)
	if n == 1:
		print(1)
	else:
		print(1, 1)
else:
	arr = [1] * (n + 2)
	i = 2
	while i * i <= n + 1:
		if arr[i] == 1:
			j = i
			while j <= (n + 1) // i:
				arr[i * j] = 2
				j += 1
		i += 1
	print(2)
	for i in arr[2:]:
		print(i, end=' ')


def isprime(n):
	n = abs(int(n))
	if n < 2:
		return False
	if n == 2:
		return True
	if not n & 1:
		return False
	for x in range(3, int(n ** 0.5) + 1, 2):
		if n % x == 0:
			return False
	return True

def main():
	n = int(input())
	if n == 1:
		print('1\n1')
	elif n == 2:
		print('1\n1 1')
	else:
		cnt = 1
		ans = []
		for i in range(1, n + 1):
			if isprime(i + 1):
				ans.append(1)
			else:
				ans.append(2)
				cnt = 2
		print(cnt)
		for i in ans:
			print(i, end=' ')
		print('\n')
main()


n = int(input())
if n == 1:
	print(1)
	print(1)
elif n == 2:
	print(1)
	print('1', '1')
else:
	checkPrime = []
	for i in range(0, 100000 + 2):
		checkPrime.append(1)
	checkPrime[0] = 0
	checkPrime[1] = 0
	for i in range(2, int(100000 ** 0.5) + 2):
		if checkPrime[i] == 1:
			for j in range(i + i, 100000 + 2, i):
				checkPrime[j] = 0
	print(2)
	for i in range(2, n + 2):
		if checkPrime[i] == 1:
			print('1', end=' ')
		else:
			print('2', end=' ')


def primes_upto(limit):
	num_list = [1 for i in range(0, limit + 1)]
	ctr = 2
	is_prime = [True] * (limit + 1)
	for n in range(2, int(limit ** 0.5) + 1):
		if is_prime[n]:
			for i in range(n * n, limit + 1, n):
				is_prime[i] = False
				num_list[i] = ctr
	del num_list[0]
	del num_list[1]
	return num_list

def main():
	jewels = int(input())
	result = primes_upto(jewels + 1)
	print(len(set(result)))
	for i in result:
		print(i, end=' ')
main()


import math

def cx(y):
	t = []
	for i in range(8):
		if y % 2 == 0:
			t.append(1)
		else:
			t.append(2)
		y = y // 2
	return t

def cz(t):
	c = 0
	for i in reversed(range(8)):
		c = c * 2 + t[i] - 1
	return c
mmm = [80, 215, 117, 95, 223, 117, 223, 215, 119, 125, 247, 253, 93, 215, 253, 127, 247, 245, 95, 223, 119, 223, 215, 127, 93, 255, 247, 127, 215, 125, 253, 247, 125, 95, 223, 245, 223, 255, 119, 221, 255, 247, 253, 215, 125, 127, 223, 119, 223, 223, 253, 253, 215, 127, 125, 247, 253, 93, 247, 127, 127, 247, 119, 223, 255, 245, 255, 223, 247, 223, 247, 245, 253, 247, 125, 125, 223, 245, 127, 255, 117, 223, 215, 255, 221, 247, 247, 223, 223, 127, 127, 223, 119, 127, 223, 253, 221, 255, 247, 223, 255, 245, 95, 215, 127, 255, 223, 117, 255, 223, 117, 255, 255, 119, 127, 255, 253, 221, 247, 253, 127, 247, 125, 127, 223, 255, 221, 215, 127, 125, 255, 245, 95, 223, 255, 127, 215, 125, 223, 223, 247, 253, 255, 127, 253, 247, 247, 223, 247, 253, 253, 223, 125, 95, 223, 255, 253, 247, 255, 95, 247, 245, 93, 247, 127, 125, 255, 255, 255, 255, 125, 223, 223, 255, 127, 255, 253, 127, 215, 125, 127, 215, 247, 127, 255, 117, 221, 247, 127, 255, 247, 247, 127, 223, 125, 127, 247, 119, 255, 223, 125, 221, 215, 247, 223, 255, 255, 125, 215, 255, 255, 223, 245, 223, 255, 245, 223, 223, 247, 125, 255, 255, 125, 215, 255, 253, 247, 127, 127, 255, 127, 255, 223, 119, 93, 255, 253, 223, 247, 253, 255, 215, 255, 95, 255, 255, 223, 247, 247, 93, 247, 247, 253, 215, 127, 255, 223, 127, 223, 255, 117, 253, 247, 127, 253, 255, 245, 93, 255, 253, 253, 255, 247, 255, 255, 119, 223, 223, 255, 95, 247, 247, 255, 215, 253, 125, 223, 253, 95, 255, 255, 223, 215, 119, 223, 255, 247, 93, 223, 125, 255, 247, 125, 255, 223, 125, 255, 247, 247, 221, 255, 255, 127, 255, 255, 253, 247, 119, 95, 223, 255, 255, 247, 127, 253, 255, 253, 221, 255, 253, 127, 255, 117, 127, 223, 119, 221, 247, 119, 125, 255, 245, 223, 223, 253, 127, 255, 253, 95, 223, 245, 255, 247, 255, 221, 247, 247, 221, 255, 127, 127, 255, 125, 223, 223, 127, 255, 247, 255, 221, 247, 245, 255, 255, 127, 253, 247, 119, 255, 223, 253, 253, 223, 247, 127, 247, 253, 255, 223, 127, 253, 255, 253, 255, 255, 119, 253, 223, 119, 255, 247, 253, 221, 223, 255, 255, 215, 245, 127, 255, 255, 255, 215, 247, 125, 247, 245, 127, 247, 127, 253, 215, 255, 95, 255, 127, 223, 255, 255, 253, 255, 253, 93, 215, 255, 255, 247, 247, 127, 223, 127, 221, 215, 247, 95, 255, 247, 95, 255, 253, 127, 223, 125, 127, 223, 247, 255, 247, 127, 221, 255, 247, 221, 223, 127, 127, 223, 247, 255, 255, 125, 253, 247, 255, 221, 247, 255, 95, 255, 253, 127, 215, 127, 255, 223, 253, 253, 255, 119, 95, 247, 245, 127, 247, 255, 127, 255, 255, 223, 255, 117, 223, 215, 247, 255, 255, 245, 253, 255, 125, 255, 215, 247, 127, 255, 127, 221, 247, 255, 93, 255, 255, 253, 255, 255, 253, 247, 245, 95, 255, 245, 223, 215, 127, 253, 247, 253, 253, 255, 255, 127, 255, 245, 223, 223, 247, 223, 255, 127, 223, 255, 253, 95, 255, 255, 125, 247, 125, 255, 255, 245, 223, 255, 247, 93, 247, 255, 255, 215, 255, 125, 255, 127, 127, 223, 247, 255, 223, 255, 95, 247, 245, 125, 255, 125, 255, 247, 127, 255, 255, 245, 221, 255, 127, 127, 255, 255, 127, 215, 125, 253, 223, 253, 127, 255, 255, 255, 223, 127, 223, 255, 253, 127, 223, 127, 255, 215, 125, 127, 223, 127, 221, 255, 247, 125, 247, 245, 95, 255, 127, 255, 247, 247, 255, 223, 125, 255, 215, 247, 125, 255, 255, 255, 247, 253, 127, 247, 247, 223, 223, 255, 253, 255, 119, 221, 255, 255, 223, 255, 125, 253, 255, 125, 223, 255, 247, 223, 255, 119, 255, 255, 255, 223, 247, 125, 127, 223, 245, 127, 223, 245, 253, 255, 127, 95, 247, 255, 95, 247, 127, 125, 247, 255, 255, 223, 247, 221, 223, 127, 255, 255, 255, 127, 255, 127, 125, 215, 245, 223, 255, 247, 221, 223, 127, 223, 255, 255, 93, 223, 255, 255, 255, 119, 127, 255, 125, 223, 223, 247, 127, 247, 245, 221, 215, 127, 253, 255, 125, 255, 255, 119, 255, 247, 255, 253, 255, 255, 223, 247, 255, 127, 247, 255, 223, 223, 119, 223, 255, 247, 125, 255, 245, 223, 255, 253, 253, 215, 127, 127, 255, 247, 223, 255, 255, 95, 247, 247, 221, 223, 255, 127, 255, 125, 95, 223, 127, 255, 215, 127, 223, 247, 253, 125, 255, 125, 125, 223, 247, 223, 223, 255, 255, 223, 247, 255, 255, 245, 255, 223, 253, 253, 247, 255, 255, 255, 253, 253, 255, 119, 253, 247, 245, 221, 255, 127, 127, 255, 247, 255, 223, 255, 223, 215, 255, 125, 255, 245, 95, 223, 127, 255, 223, 253, 255, 255, 245, 255, 215, 127, 253, 247, 255, 127, 215, 253, 253, 255, 125, 95, 255, 247, 255, 247, 119, 223, 255, 255, 255, 215, 127, 125, 247, 125, 127, 223, 253, 223, 247, 247, 127, 247, 255, 253, 223, 127, 255, 255, 127, 223, 255, 125, 253, 255, 127, 127, 255, 255, 253, 247, 253, 127, 215, 247, 223, 223, 119, 223, 255, 255, 255, 247, 255, 253, 215, 255, 253, 215, 255, 95, 255, 255, 253, 255, 255, 253, 255, 247, 253, 255, 253, 255, 247, 245, 255, 223, 125, 253, 247, 247, 223, 247, 253, 221, 215, 127, 253, 223, 125, 95, 255, 119, 255, 223, 255, 127, 247, 253, 255, 223, 253, 125, 247, 119, 255, 223, 119, 255, 223, 255, 93, 255, 255, 255, 223, 253, 255, 255, 125, 223, 255, 253, 223, 255, 247, 93, 247, 255, 223, 247, 127, 127, 223, 253, 95, 255, 247, 255, 255, 255, 253, 255, 245, 253, 255, 127, 255, 223, 247, 223, 255, 125, 221, 223, 127, 223, 247, 255, 255, 247, 255, 125, 247, 247, 127, 255, 255, 253, 215, 127, 221, 247, 255, 127, 223, 253, 127, 215, 253, 127, 223, 255, 253, 255, 255, 253, 247, 253, 253, 215, 255, 255, 255, 119, 95, 255, 119, 255, 223, 247, 255, 255, 255, 223, 255, 253, 125, 255, 117, 255, 255, 247, 223, 223, 255, 95, 255, 253, 127, 215, 255, 125, 255, 127, 223, 223, 253, 221, 247, 247, 125, 255, 247, 221, 247, 253, 253, 255, 119, 255, 255, 119, 255, 215, 127, 95, 255, 253, 95, 247, 255, 127, 223, 255, 255, 255, 247, 221, 223, 127, 255, 247, 245, 255, 255, 127, 125, 215, 255, 223, 255, 245, 253, 247, 247, 255, 255, 247, 127, 223, 255, 127, 223, 253, 127, 223, 253, 223, 223, 247, 127, 247, 253, 223, 247, 127, 253, 255, 253, 255, 223, 245, 223, 255, 127, 127, 247, 255, 93, 223, 255, 255, 247, 253, 127, 223, 247, 223, 215, 127, 93, 255, 255, 95, 247, 125, 255, 247, 253, 127, 255, 253, 223, 247, 119, 255, 255, 255, 255, 247, 255, 253, 223, 119, 95, 255, 247, 253, 223, 255, 95, 255, 253, 253, 255, 127, 253, 223, 119, 223, 255, 127, 253, 223, 119, 255, 247, 247, 253, 223, 125, 255, 247, 245, 127, 255, 119, 255, 223, 247, 255, 247, 245, 223, 223, 255, 127, 223, 255, 255, 255, 127, 253, 255, 255, 95, 255, 255, 223, 215, 127, 255, 215, 119, 127, 255, 255, 223, 215, 127, 127, 247, 253, 221, 255, 253, 255, 247, 127, 255, 255, 119, 223, 247, 119, 253, 255, 253, 95, 255, 253, 253, 215, 125, 255, 223, 255, 253, 255, 127, 127, 255, 255, 255, 215, 253, 255, 223, 117, 255, 223, 127, 255, 215, 255, 253, 255, 245, 255, 255, 127, 127, 255, 255, 223, 223, 125, 223, 255, 119, 127, 255, 247, 125, 247, 255, 127, 247, 255, 95, 255, 247, 221, 247, 255, 253, 255, 247, 223, 223, 127, 255, 255, 255, 127, 223, 127, 223, 215, 247, 255, 247, 245, 127, 223, 255, 255, 255, 245, 223, 223, 255, 223, 247, 247, 253, 247, 255, 255, 247, 255, 127, 255, 245, 95, 255, 119, 223, 255, 255, 93, 255, 247, 255, 223, 127, 253, 215, 253, 255, 223, 255, 223, 255, 255, 127, 247, 247, 221, 255, 125, 127, 255, 247, 127, 223, 253, 253, 255, 127, 253, 255, 253, 127, 255, 125, 255, 247, 127, 255, 223, 119, 255, 255, 119, 255, 247, 245, 125, 255, 127, 127, 255, 255, 95, 255, 255, 255, 247, 247, 221, 255, 255, 221, 255, 253, 255, 255, 253, 255, 223, 253, 253, 215, 255, 95, 255, 247, 127, 255, 255, 255, 255, 117, 223, 255, 125, 223, 223, 119, 125, 255, 255, 127, 247, 255, 127, 255, 125, 223, 255, 119, 223, 215, 255, 125, 255, 245, 223, 247, 255, 127, 247, 255, 255, 223, 245, 253, 255, 127, 253, 255, 255, 221, 215, 125, 255, 255, 127, 223, 223, 245, 255, 255, 255, 223, 247, 247, 255, 247, 127, 253, 215, 127, 223, 223, 253, 253, 223, 255, 255, 247, 253, 127, 247, 255, 255, 223, 245, 127, 255, 253, 221, 223, 255, 221, 255, 247, 253, 255, 125, 127, 247, 125, 127, 223, 127, 255, 215, 247, 253, 255, 253, 125, 223, 255, 253, 215, 247, 255, 223, 125, 223, 247, 127, 255, 255, 253, 125, 255, 253, 253, 255, 119, 255, 223, 247, 255, 223, 127, 127, 255, 253, 95, 223, 255, 253, 223, 255, 255, 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255, 253, 247, 255, 255, 255, 119, 127, 255, 253, 223, 255, 255, 127, 255, 255, 221, 247, 255, 127, 247, 255, 127, 223, 255, 223, 215, 255, 255, 255, 247, 127, 223, 127, 125, 255, 253, 223, 223, 245, 253, 247, 127, 255, 255, 255, 253, 255, 127, 127, 223, 253, 127, 223, 247, 255, 255, 255, 221, 247, 255, 93, 255, 255, 255, 215, 247, 255, 255, 253, 221, 255, 127, 255, 255, 253, 255, 215, 255, 125, 247, 255, 127, 255, 125, 223, 255, 247, 223, 255, 245, 127, 255, 255, 255, 223, 255, 255, 255, 127, 255, 247, 247, 93, 255, 245, 255, 247, 127, 253, 247, 247, 255, 223, 255, 255, 223, 119, 255, 247, 255, 221, 223, 253, 127, 247, 125, 255, 255, 247, 221, 223, 255, 127, 255, 255, 255, 255, 255, 255, 215, 253, 223, 223, 253, 255, 255, 255, 127, 247, 255, 255, 223, 255, 255, 223, 255, 223, 255, 125, 253, 223, 255, 253, 255, 245, 125, 247, 127, 255, 223, 255, 223, 223, 255, 253, 255, 247, 255, 247, 253, 253, 247, 253, 127, 255, 253, 95, 255, 117, 255, 255, 127, 223, 255, 255, 255, 255, 127, 255, 255, 127, 127, 255, 125, 223, 215, 255, 221, 255, 247, 125, 255, 255, 255, 247, 245, 223, 255, 253, 223, 247, 255, 127, 247, 253, 127, 215, 255, 253, 247, 127, 255, 255, 127, 223, 223, 247, 221, 255, 255, 223, 255, 253, 255, 223, 255, 223, 255, 247, 255, 255, 255, 253, 255, 247, 221, 255, 255, 127, 255, 119, 95, 223, 245, 255, 255, 127, 127, 255, 255, 255, 255, 127, 253, 247, 119, 255, 255, 247, 253, 255, 247, 95, 247, 255, 255, 255, 255, 127, 223, 255, 127, 255, 247, 221, 215, 255, 255, 247, 253, 127, 255, 255, 255, 223, 127, 255, 255, 127, 253, 247, 247, 255, 247, 255, 95, 255, 255, 253, 255, 127, 127, 255, 125, 223, 255, 119, 127, 255, 255, 93, 255, 255, 253, 255, 247, 255, 223, 119, 255, 255, 127, 255, 255, 245, 255, 247, 125, 255, 255, 253, 255, 223, 255, 223, 255, 255, 221, 255, 247, 221, 255, 255, 253, 255, 247, 95, 223, 127, 255, 255, 127, 253, 247, 255, 255, 247, 125, 255, 255, 127, 223, 255, 245, 255, 255, 127, 255, 247, 255, 125, 223, 255, 125, 255, 255, 223, 255, 253, 223, 223, 255, 255, 255, 255, 221, 255, 253, 127, 247, 255, 127, 255, 253, 223, 255, 255, 95, 247, 253, 95, 215, 127, 255, 247, 255, 255, 223, 247, 255, 247, 119, 127, 255, 253, 125, 255, 255, 255, 255, 245, 127, 255, 127, 255, 255, 127, 95, 255, 245, 255, 223, 253, 125, 255, 127, 95, 223, 247, 221, 255, 119, 255, 255, 247, 221, 255, 255, 125, 255, 247, 255, 255, 125, 253, 247, 127, 125, 247, 247, 127, 247, 255, 253, 223, 127, 255, 223, 253, 223, 255, 255, 127, 255, 253, 127, 247, 255, 255, 223, 247, 255, 255, 255, 221, 255, 127, 255, 255, 253, 125, 255, 127, 127, 255, 253, 127, 255, 253, 253, 247, 255, 127, 255, 255, 223, 255, 255, 253, 255, 245, 255, 223, 119, 223, 247, 127, 253, 247, 255, 255, 223, 253, 253, 255, 247, 255, 223, 247, 255, 223, 119, 223, 255, 255, 223, 247, 255, 127, 255, 255, 255, 255, 253, 255, 255, 247, 95, 255, 255, 255, 247, 127, 127, 255, 253, 95, 223, 255, 255, 215, 255, 253, 255, 245, 125, 255, 253, 127, 255, 127, 255, 255, 247, 221, 255, 255, 255, 255, 247, 253, 247, 253, 253, 255, 253, 255, 255, 255, 255, 215, 119, 223, 247, 253, 127, 255, 127, 255, 223, 253, 255, 223, 127, 221, 223, 255, 127, 255, 253, 223, 255, 255, 255, 255, 245, 223, 255, 255, 255, 255, 127, 127, 247, 255, 127, 255, 255, 127, 255, 127, 127, 255, 255, 223, 247, 119, 125, 255, 255, 223, 247, 253, 253, 255, 255, 95, 255, 253, 255, 247, 255, 125, 247, 255, 223, 223, 127, 255, 223, 253, 223, 223, 127, 255, 247, 255, 93, 255, 247, 127, 247, 253, 255, 247, 255, 255, 255, 253, 223, 255, 255, 255, 255, 247, 253, 223, 127, 253, 255, 247, 223, 255, 253, 221, 223, 119, 253, 255, 255, 253, 223, 255, 127, 215, 245, 255, 255, 255, 255, 255, 255, 223, 255, 253, 253, 255, 255, 253, 215, 125, 223, 255, 117, 255, 223, 247, 253, 255, 253, 95, 247, 255, 255, 255, 119, 255, 255, 127, 223, 247, 247, 95, 255, 255, 223, 255, 127, 255, 247, 255, 127, 223, 255, 255, 255, 119, 255, 255, 255, 223, 215, 253, 127, 223, 253, 127, 255, 127, 253, 223, 127, 125, 255, 247, 127, 255, 125, 127, 255, 255, 223, 223, 255, 253, 223, 247, 255, 247, 253, 255, 247, 255, 127, 255, 255, 223, 255, 127, 253, 255, 127, 253, 255, 245, 255, 255, 253, 127, 255, 253, 255, 223, 127, 255, 255, 255, 127, 247, 247, 223, 215, 255, 255, 247, 253, 95, 223, 117, 255, 223, 255, 253, 255, 255, 253, 215, 255, 253, 255, 117, 223, 255, 247, 253, 247, 127, 253, 255, 253, 127, 255, 255, 255, 255, 253, 95, 223, 247, 221, 255, 255, 253, 247, 255, 255, 223, 255, 253, 223, 117, 127, 255, 117, 253, 255, 127, 223, 247, 255, 221, 255, 127, 255, 247, 255, 255, 223, 247, 223, 223, 255, 95, 247, 255, 127, 255, 125, 255, 255, 255, 255, 255, 245, 223, 247, 247, 255, 255, 247, 127, 223, 125, 255, 215, 255, 255, 255, 253, 253, 223, 255, 127, 255, 255, 125, 255, 255, 255, 255, 255, 223, 223, 127, 223, 255, 119, 125, 247, 253, 255, 255, 255, 255, 247, 247, 223, 223, 127, 253, 255, 119, 223, 255, 253, 95, 247, 255, 127, 255, 253, 223, 255, 253, 221, 255, 255, 127, 255, 255, 253, 255, 127, 127, 223, 255, 223, 255, 247, 255, 215, 255, 127, 255, 245, 125, 255, 253, 127, 215, 255, 255, 255, 119, 221, 223, 127, 95, 255, 247, 255, 247, 253, 255, 255, 255, 255, 255, 255, 253, 215, 255, 253, 247, 247, 127, 223, 253, 127, 255, 117, 127, 223, 253, 255, 223, 247, 127, 255, 255, 223, 247, 255, 255, 255, 247, 95, 255, 253, 223, 255, 247, 253, 255, 255, 223, 255, 255, 255, 255, 125, 95, 255, 119, 223, 247, 247, 255, 255, 245, 255, 223, 127, 125, 247, 255, 127, 255, 253, 221, 247, 255, 253, 255, 247, 253, 255, 255, 255, 255, 247, 255, 255, 117, 253, 255, 255, 95, 247, 255, 223, 247, 125, 255, 215, 255, 255, 223, 127, 255, 255, 255, 255, 247, 245, 127, 255, 253, 255, 255, 247, 255, 255, 247, 255, 223, 255, 223, 247, 253, 127, 255, 255, 127, 255, 119, 127, 223, 255, 221, 223, 255, 223, 255, 255, 253, 255, 255, 255, 255, 253, 255, 255, 119, 255, 215, 119, 253, 247, 255, 253, 215, 253, 255, 255, 247, 127, 255, 255, 255, 215, 255, 223, 255, 255, 127, 223, 127, 125, 255, 125, 127, 223, 247, 253, 247, 127, 223, 255, 255, 253, 255, 255, 255, 255, 253, 255, 223, 245, 255, 247, 127, 223, 255, 253, 221, 255, 127, 253, 223, 127, 255, 255, 255, 253, 223, 255, 95, 255, 255, 253, 255, 255, 253, 223, 253, 127, 255, 255, 223, 255, 255, 253, 247, 255, 253, 223, 253, 255, 247, 127, 127, 255, 253, 223, 247, 255, 255, 255, 253, 127, 247, 255, 255, 247, 253, 255, 255, 127, 223, 215, 247, 255, 255, 253, 255, 255, 255, 125, 247, 125, 255, 255, 247, 255, 215, 127, 127, 255, 247, 95, 223, 127, 127, 255, 127, 255, 255, 255, 255, 247, 247, 93, 255, 255, 255, 215, 255, 255, 255, 253, 95, 255, 125, 255, 223, 127, 223, 247, 253, 125, 247, 255, 253, 255, 119, 223, 255, 245, 223, 255, 127, 127, 255, 255, 255, 223, 255, 255, 255, 255, 95, 255, 255, 221, 247, 255, 253, 255, 247, 221, 255, 125, 255, 247, 253, 127, 255, 253, 255, 255, 247, 253, 255, 245, 255, 247, 255, 255, 255, 245, 95, 255, 255, 255, 255, 255, 125, 255, 255, 255, 247, 255, 125, 255, 245, 127, 255, 255, 253, 223, 247, 223, 255, 253, 223, 255, 255, 125, 215, 127, 223, 255, 253, 223, 255, 247, 127, 255, 255, 255, 255, 125, 253, 223, 127, 223, 223, 119, 255, 247, 255, 255, 255, 255, 125, 255, 253, 255, 215, 255, 255, 255, 245, 253, 223, 255, 255, 255, 247, 255, 215, 127, 127, 215, 255, 223, 255, 127, 255, 255, 255, 221, 247, 247, 255, 223, 255, 255, 247, 253, 255, 223, 125, 255, 215, 247, 127, 247, 255, 223, 215, 255, 255, 247, 127, 127, 223, 255, 223, 255, 127, 255, 255, 255, 223, 255, 253, 255, 255, 245, 95, 223, 119, 223, 255, 255, 255, 255, 253, 127, 223, 255, 255, 215, 255, 255, 255, 255, 255, 255, 127, 127, 255, 247, 253, 215, 255, 255, 255, 255, 223, 223, 247, 255, 255, 127, 221, 255, 247, 125, 255, 255, 253, 247, 119, 255, 223, 253, 253, 255, 255, 127, 247, 253, 125, 223, 255, 127, 215, 253, 127, 255, 247, 255, 223, 127, 221, 255, 245, 223, 223, 127, 255, 223, 127, 255, 255, 253, 223, 223, 247, 223, 255, 247, 223, 223, 255, 255, 215, 247, 255, 255, 253, 223, 247, 247, 127, 255, 255, 255, 215, 255, 255, 255, 255, 255, 223, 255, 221, 255, 127, 127, 255, 253, 127, 255, 253, 127, 247, 127, 255, 255, 255, 223, 255, 255, 223, 247, 247, 221, 223, 255, 255, 255, 255, 255, 255, 119, 253, 247, 127, 127, 255, 253, 223, 255, 253, 255, 215, 255, 255, 223, 253, 253, 255, 127, 255, 247, 255, 127, 247, 127, 253, 223, 255, 95, 255, 255, 255, 215, 247, 255, 255, 247, 95, 255, 255, 255, 215, 253, 255, 223, 253, 223, 247, 255, 221, 247, 255, 253, 255, 127, 255, 255, 127, 255, 255, 119, 255, 223, 247, 253, 247, 255, 255, 255, 253, 253, 247, 255, 95, 223, 247, 255, 215, 247, 93, 255, 255, 127, 215, 255, 255, 223, 127, 95, 255, 245, 253, 255, 127, 127, 247, 247, 221, 255, 127, 253, 255, 119, 127, 255, 127, 255, 255, 255, 221, 247, 247, 255, 255, 253, 255, 223, 255, 223, 223, 125, 255, 255, 127, 223, 255, 247, 127, 255, 127, 253, 223, 253, 127, 255, 117, 255, 247, 255, 223, 255, 255, 255, 223, 127, 255, 223, 255, 255, 223, 255, 253, 255, 255, 255, 255, 253, 253, 255, 255, 255, 247, 127, 255, 223, 253, 255, 215, 255, 255, 255, 253, 223, 255, 255, 125, 255, 245, 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n = int(input())
mm = []
m = 100002
for i in range(12500):
	u = cx(mmm[i])
	for j in range(8):
		mm.append(u[j])
mm.append(2)
mm.append(2)
if n == 1:
	print(1)
	print(1)
elif n == 2:
	print(1)
	print(1, 1)
else:
	print(2)
	s = [1 if i >= m else mm[i] for i in range(n + 2)]
	for i in range(m, math.ceil(math.sqrt(n + 1)) + 1):
		if s[i] == 1:
			for j in range(i + 1, n + 2):
				if j % i == 0:
					s[j] = 2
	print(' '.join([str(s[i]) for i in range(2, n + 2)]))


def isprime(n):
	d = 3
	if n == 2:
		return True
	if n % 2 == 0:
		return False
	while d * d <= n:
		if n % d == 0:
			return False
		d += 2
	return True
n = int(input())
if n == 1:
	print(1)
	print(1)
elif n == 2:
	print(1)
	print(1, 1)
else:
	print(2)
	for i in range(2, n + 2):
		if isprime(i):
			print(1, end=' ')
		else:
			print(2, end=' ')
	print('')


from sys import stdin, stdout, exit
import math
import sys

def target_X():
	n = int(stdin.readline())
	if n < 3:
		print(1)
		for x in range(n):
			print(1, end=' ')
		sys.exit()
	isPrime = ['true'] * (n + 2)
	isPrime[0] = 'false'
	isPrime[1] = 'false'
	i = 2
	while i * i <= n + 1:
		if isPrime[i] == 'true':
			j = i * i
			while j <= n + 1:
				isPrime[j] = 'false'
				j += i
		i += 1
	print(2)
	for i in range(1, n + 1):
		if isPrime[i + 1] == 'true':
			print(2, end=' ')
		else:
			print(1, end=' ')
target_X()


n = int(input())
prizes = [1 for i in range(n)]
for j in range(int(n ** (1 / 2))):
	if prizes[j] == 1:
		for i in range(2 * j + 2, n, j + 2):
			prizes[i] = 2
if n > 2:
	print(2)
else:
	print(1)
for num in prizes:
	print(num, end=' ')


import math
n = int(input())
answer = ''
if n <= 2:
	print(1)
else:
	print(2)
m = n + 2
numbers = [True] * m
numbers[0] = False
numbers[1] = False
for i in range(2, int(math.sqrt(m)) + 1):
	j = 0
	while i ** 2 + j * i < m:
		numbers[i ** 2 + j * i] = False
		j += 1
for i in range(2, m):
	if numbers[i]:
		answer += '1 '
	else:
		answer += '2 '
answer = answer[:-1]
print(answer)


def main():
	(n, one) = (int(input()) + 2, '1')
	l = [one] * n
	for p in range(2, n):
		if l[p] is one:
			pp = p * p
			if pp > n:
				break
			for q in range(pp, n, p):
				l[q] = '2'
	print(2 if n > 4 else 1)
	print(' '.join(l[2:]))
main()


import sys
import re
input = lambda : sys.stdin.readline()
import functools

@functools.lru_cache(maxsize=10000)
def prime_factors(n):
	i = 2
	factors = []
	while i * i <= n:
		if n % i:
			i += 1
		else:
			n //= i
			factors.append(i)
	if n > 1:
		factors.append(n)
	return factors

def is_prim(n):
	return not re.match('^1?$|^(11+?)\\1+$', n * '1')

def is_prime(n):
	for i in range(2, int(n ** 0.5) + 1):
		if n % i == 0:
			return False
	return True

def Main():
	n = int(input())
	if n == 1:
		print(1, '\n', 1)
		return 0
	if n == 2:
		print(1)
		print(1, 1)
		return 0
	A = []
	for i in range(2, n + 2):
		if is_prime(i):
			A.append(1)
		else:
			A.append(2)
	print(2)
	print(*A)
Main()


n = int(input()) + 1
a = [1] * (n + 1)
a[0] = 2
a[1] = 2
for i in range(2, n + 1):
	if a[i] == 1:
		for j in range(2, n // i + 1):
			a[i * j] = 2
print(1 if n == 2 or n == 3 else 2)
print(*a[2:])


a = ['2'] * 1000100
a[1] = '1'
for i in range(2, 1000010):
	if a[i] == '2':
		for j in range(i * i, 1000010, i):
			a[j] = '1'
n = int(input())
if n <= 2:
	print(1)
	print(' '.join(['1'] * n))
else:
	print(2)
	print(' '.join(a[2:n + 2]))


from sys import stdin, stdout
n = int(stdin.readline())
ans = [1 for i in range(n + 10)]
for i in range(2, n + 5):
	if ans[i] == 1:
		for j in range(i * i, n + 5, i):
			ans[j] = 2
s = set()
for i in range(2, n + 2):
	s.add(ans[i])
stdout.write(str(len(s)) + '\n' + ' '.join(list(map(str, ans[2:n + 2]))))


n = int(input())
if n == 2:
	print('1\n1 1')
elif n == 1:
	print('1\n1')
else:
	a = [True for i in range(n + 2)]
	for i in range(2, n + 2):
		if a[i]:
			for j in range(i * 2, n + 2, i):
				a[j] = False
	print(2, 1, sep='\n', end='')
	for i in range(1, n):
		print('', 2 - a[i + 2], end='')


n = int(input())
a = [True] * (n + 2)
for i in range(2, n + 2):
	if not a[i]:
		continue
	j = i * i
	while j < n + 2:
		a[j] = False
		j += i
if n <= 2:
	print(1)
else:
	print(2)
print(' '.join(('1' if x else '2' for x in a[2:])))


import math

def sieve(n):
	s = [1] * (n + 2)
	for i in range(2, n + 2):
		if s[i] == 1:
			count = 2
			for j in range(i ** 2, n + 2, i):
				s[j] = count
	return s[2:]
n = int(input())
prime = sieve(n)
print(len(set(prime)))
print(*prime)


import math
n = int(input())
k = int(math.sqrt(n))
k += 1
p = [1] * (n + 2)
a = [1] * (n + 2)
for i in range(2, k + 1):
	if p[i] == 1:
		a[i] = 1
		for j in range(i * i, n + 2, i):
			if p[j] == 1:
				p[j] = 0
				a[j] = 2
if n < 3:
	print(1)
else:
	print(2)
for i in range(2, n + 2):
	print(a[i], end=' ')
print()


def isPrime(n):
	if n <= 1:
		return False
	if n <= 3:
		return True
	if n % 2 == 0 or n % 3 == 0:
		return False
	i = 5
	while i * i <= n:
		if n % i == 0 or n % (i + 2) == 0:
			return False
		i = i + 6
	return True
n = int(input())
if n == 1:
	print(1)
	print(1)
	exit()
if n == 2:
	print(1)
	print('1 1')
	exit(0)
arr = []
for i in range(2, n + 2):
	arr.append(i)
d = [1 for i in range(n)]
for i in range(n):
	if isPrime(arr[i]) == False:
		d[i] = 2
print(2)
print(*d)


n = int(input())
a = [1] * (n + 2)
for i in range(2, n + 2):
	if a[i] != 2:
		j = 2 * i
		while j <= n + 1:
			a[j] = 2
			j = j + i
if n > 2:
	print('2')
else:
	print('1')
c = a[2:]
print(*c, sep=' ')


import math

def sieve_of_eratosthenes(limit):
	is_prime_array = [False] * 2 + [True] * (limit - 1)
	for num in range(2, int(math.sqrt(limit)) + 1):
		if is_prime_array[num]:
			is_prime_array[num * 2::num] = [False] * len(is_prime_array[num * 2::num])
	return set((num for num in range(len(is_prime_array)) if is_prime_array[num]))
n = int(input())
s_p = sieve_of_eratosthenes(n + 2)
print(1 if n <= 2 else 2)
for i in range(2, n + 2):
	if i in s_p:
		print('1', end=' ')
	else:
		print('2', end=' ')


n = int(input())
N = n + 2
mark = [1] * N
for i in range(2, N):
	if mark[i] == 1:
		for j in range(i * i, N, i):
			mark[j] = 2
print(len(set(mark[2:])))
print(*mark[2:])


from sys import stdout, stdin
import math
r = lambda : int(input())
ra = lambda : [*map(int, input().split())]
raw = lambda : [*stdin.readline()]
out = lambda a: stdout.write(''.join(a))

def s(a):
	if a <= 1:
		return False
	else:
		for i in range(2, int(math.sqrt(a)) + 1):
			if a % i == 0:
				return False
		return True
n = r()
di = {}
k = 1
res = ''
p = [i + 2 for i in range(n)]
for i in range(n):
	if s(p[i]):
		res += '1 '
	else:
		res += '2 '
if '2' in res:
	k = 2
print(k)
out(res)


import sys
(mod, MOD) = (1000000007, 998244353)

def get_array():
	return list(map(int, sys.stdin.readline().strip().split()))

def get_ints():
	return map(int, sys.stdin.readline().strip().split())

def input():
	return sys.stdin.readline().strip()
n = int(input())
result = [0] * (n + 2)
for i in range(2, int((n + 1) ** 0.5) + 1):
	if result[i] == 0:
		result[i] = 1
		for j in range(i + i, n + 2, i):
			result[j] = 2
result = result[2:]
for i in range(len(result)):
	if result[i] == 0:
		result[i] = 1
print(max(result))
print(*result)


n = int(input())
seive = [1] * (n + 2)
seive[0] = -1
seive[1] = -1
for i in range(n + 2):
	if seive[i] == 1:
		for j in range(i * 2, n + 2, i):
			seive[j] = 2
if n == 1 or n == 2:
	print(1)
	for i in range(2, n + 2):
		print(seive[i], end=' ')
elif n == 0:
	print(0)
else:
	print(2)
	for i in range(2, n + 2):
		print(seive[i], end=' ')


def soa(n):
	lst = [0 for _ in range(n + 1)]
	p = 2
	while p * p <= n:
		if lst[p] == 0:
			c = 2
			lst[p] = 1
			for i in range(p * p, n + 1, p):
				lst[i] = 2
		p += 1
	return lst
num = int(input())
lst = soa(num + 1)
lst = lst[2:]
lst = [x if not x == 0 else 1 for x in lst]
new = set(lst)
count = len(new)
print(count)
for j in lst:
	print(j, end=' ')


def prime_factors():
	n = 100001
	seive = [i for i in range(n + 1)]
	i = 2
	while i * i <= n:
		for j in range(i * i, n + 1, i):
			if seive[j] % i == 0:
				seive[j] = 2
		i += 1
	for k in range(2, n + 1):
		if seive[k] == k:
			seive[k] = 1
	seive[0] = 1
	seive[1] = 1
	return seive
seive = prime_factors()
n = int(input())
if n < 3:
	print(1)
else:
	print(2)
i = 1
c = 0
for j in range(i + 1, n + 2):
	if seive[j] == 1:
		print(1, end=' ')
	else:
		print(2, end=' ')


n = int(input()) + 2
C = [1] * n
for i in range(2, n):
	for j in range(i * i, n, i):
		C[j] = 2
print(len(set(C[2:])))
print(*C[2:])


n = int(input())
res = 1
piece = [1 for i in range(n + 2)]
for i in range(2, n + 2):
	if piece[i] != 1:
		continue
	for j in range(i + i, n + 2, i):
		piece[j] = 2
for p in piece:
	res = max(p, res)
print(res)
print(' '.join(map(str, piece[2:])))


def main(n):
	prime = [True for i in range(n + 2)]
	p = 2
	k = 1
	ans = [1 for i in range(n)]
	while p * p <= n + 1:
		if prime[p] == True:
			for i in range(p * 2, n + 2, p):
				if prime[i] == True:
					prime[i] = False
					ans[i - 2] += 1
					k = 2
		p += 1
	print(k)
	for i in range(n):
		print(ans[i], end=' ')
n = int(input())
main(n)


N = 1000010
primes = [1] * N
for i in range(2, N):
	if 1 == primes[i]:
		for j in range(i * i, N, i):
			primes[j] = 2
n = int(input())
ans = primes[2:n + 2]
print(len(set(ans)))
print(*ans)


def sieve(n):
	np = [0] * (n + 1)
	for i in range(2, n + 1):
		if np[i] == 0:
			np[i] = '1'
			for j in range(i * i, n + 1, i):
				np[j] = '2'
	return np
n = int(input())
t = sieve(n + 1)
if n == 1 or n == 2:
	print(1)
else:
	print(2)
print(' '.join(t[2:]))


import math, string, itertools, fractions, heapq, collections, re, array, bisect, sys, copy, functools
import random
sys.setrecursionlimit(10 ** 7)
inf = 10 ** 20
eps = 1.0 / 10 ** 10
mod = 10 ** 9 + 7
dd = [(-1, 0), (0, 1), (1, 0), (0, -1)]
ddn = [(-1, 0), (-1, 1), (0, 1), (1, 1), (1, 0), (1, -1), (0, -1), (-1, -1)]

def LI():
	return list(map(int, sys.stdin.readline().split()))

def LLI():
	return [list(map(int, l.split())) for l in sys.stdin.readlines()]

def LI_():
	return [int(x) - 1 for x in sys.stdin.readline().split()]

def LF():
	return [float(x) for x in sys.stdin.readline().split()]

def LS():
	return sys.stdin.readline().split()

def I():
	return int(sys.stdin.readline())

def F():
	return float(sys.stdin.readline())

def S():
	return input()

def pf(s):
	return print(s, flush=True)

def pe(s):
	return print(str(s), file=sys.stderr)

def main():
	n = I()
	a = [0] * n
	for i in range(2, n + 2, 2):
		a[i - 2] = min(2, i // 2)
	for i in range(3, n + 2, 2):
		if a[i - 2] > 0:
			continue
		for j in range(i, n + 2, i):
			a[j - 2] = min(2, j // i)
	return '{}\n{}'.format(max(a), ' '.join(map(str, a)))
print(main())


n = int(input())
prime = [0 for i in range(n + 2)]
p = 2
while p * p <= n + 1:
	if prime[p] == 0:
		for i in range(p * p, n + 2, p):
			prime[i] = 1
	p = p + 1
if n < 3:
	print(1)
else:
	print(2)
for i in range(2, n + 2):
	prime[i] = prime[i] + 1
s = ' '.join((str(e) for e in prime[2:n + 2]))
print(s)


def main():
	n = int(input())
	if n == 1:
		print('1')
		print('1')
		return
	elif n == 2:
		print('1')
		print('1 1')
		return
	elif n == 3:
		print('2')
		print('1 1 2')
		return
	else:
		numbers = [True] * (n + 3)
		for prime in range(2, n + 3):
			for i in range(2 * prime, n + 3, prime):
				numbers[i] = False
		print(2)
		print(' '.join([str(1) if numbers[i + 2] else str(2) for i in range(n)]))
main()


def isPrime(n):
	if n == 2 or n == 3:
		return True
	if n % 2 == 0 or n % 3 == 0:
		return False
	i = 5
	w = 2
	sqN = int(pow(n, 0.5))
	while i <= sqN:
		if n % i == 0:
			return False
		i += w
		w = 6 - w
	return True
n = int(input().strip())
arr = [1 if isPrime(i) else 2 for i in range(2, n + 2)]
print(max(arr))
print(*arr)


def prime(n: int):
	for i in range(2, int(n ** 0.5) + 1):
		if n % i == 0:
			return False
	return True
n = int(input())
if n < 3:
	print(1)
	for i in range(n):
		print(1, end=' ')
else:
	print(2)
	for i in range(2, n + 2):
		if prime(i):
			print('1', end=' ')
		else:
			print('2', end=' ')


class Solution:

	def __init__(self):
		self.sieve = []
		self.spf = []

	def buildsieve(self, n):
		self.spf = [-1] * (n - 2)
		a = [-1] * (n - 2)
		for i in range(0, n - 2):
			fac = i + 2
			if a[i] == -1:
				while i + fac < n - 2:
					if a[i + fac] == -1:
						self.spf[i + fac] = 0
					a[i + fac] = 0
					i = i + fac
		self.sieve = a

	def primeFactors(self, N):
		if len(self.sieve) < 1:
			self.buildsieve(N + 5)
		if N > 2:
			print(2)
		else:
			print(1)
		for i in range(0, N):
			if self.sieve[i] == 0:
				print(2, end=' ')
			else:
				print(1, end=' ')
ob = Solution()
ob.primeFactors(int(input()))


n = int(input()) + 2
prime = [i % 2 for i in range(n)]
prime[1] = 0
prime[2] = 1
for p in range(3, int(n ** 0.5) + 2, 2):
	if not prime[p]:
		continue
	for q in range(p * p, n, p + p):
		prime[q] = 0
l = [2 - x for x in prime[2:]]
print(max(l))
print(' '.join(map(str, l)))


from math import sqrt
n = int(input())
l = [1] * (n + 2)
for i in range(2, int(sqrt(n + 2) + 1)):
	if l[i] == 1:
		for j in range(i * i, n + 2, i):
			l[j] = 2
if n >= 3:
	print(2)
	print(*l[2:n + 2])
else:
	print(1)
	print(*[1] * n)


import math
n = input()
n = int(n)
if n == 1:
	print('1')
	print('1')
if n == 2:
	print('1')
	print('1 1')
if n > 2:
	print('2')
	s = ''
	for i in range(2, n + 2):
		flag = 0
		for j in range(2, math.ceil(math.sqrt(n)) + 1):
			if j * j > i:
				break
			if i % j == 0:
				flag = 1
		if flag > 0:
			print(2, end=' ')
		else:
			print(1, end=' ')


n = int(input())
if n <= 2:
	print(1)
	for i in range(n):
		print(1, end=' ')
else:
	prime = [1] * (n + 2)
	for i in range(2, n + 2):
		if prime[i]:
			k = i
			while k + i < n + 2:
				k += i
				prime[k] = 0
	print(2)
	for i in range(2, n + 2):
		if prime[i]:
			print(1, end=' ')
		else:
			print(2, end=' ')


def is_prime(n):
	if n == 2 or n == 3:
		return True
	if n < 2 or n % 2 == 0:
		return False
	if n < 9:
		return True
	if n % 3 == 0:
		return False
	r = int(n ** 0.5)
	f = 5
	while f <= r:
		if n % f == 0:
			return False
		if n % (f + 2) == 0:
			return False
		f += 6
	return True
n = int(input())
colors = []
for i in range(2, n + 2):
	if not is_prime(i):
		colors.append(str(2))
	else:
		colors.append(str(1))
if n >= 3:
	print(2)
else:
	print(1)
print(' '.join(colors))


n = int(input())
if n == 1:
	print(1)
	print(1)
	exit()
if n == 2:
	print(1)
	print(1, 1)
	exit()
a = [1] * (n + 2)
for i in range(2, n + 2):
	if a[i] == 1:
		for j in range(2 * i, n + 2, i):
			a[j] = 2
a = a[2:]
print(2)
print(*a)


n = int(input())
s = [False] * (n + 2)
for i in range(2, n + 2):
	if not s[i]:
		for j in range(2 * i, n + 2, i):
			s[j] = True
print(1 if n <= 2 else 2)
print(' '.join(('12'[si] for si in s[2:])))


n = int(input())
if n == 1:
	print('1\n1')
	exit()
if n == 2:
	print('1\n1 1')
	exit()
lis = [1 for i in range(n + 2)]

def snt(n):
	for i in range(2, int(n ** 0.5) + 1):
		if n % i == 0:
			return False
	return True
for i in range((n + 1) // 2 + 1):
	if snt(i):
		lis[i] = 2
print(2)
print(*lis[2:])


import math
n = int(input())
z = []
for i in range(2, n + 2):
	c = 0
	for j in range(2, int(math.pow(i, 0.5)) + 1):
		if i % j == 0:
			c += 1
			break
	if c == 0:
		z.append('1')
	else:
		z.append('2')
if z.count('1') > 0 and z.count('2') > 0:
	print(2)
else:
	print(1)
print(' '.join(z))


n = int(input())
a = [1] * (n + 2)
if n < 3:
	print(1)
	b = [1] * n
	print(*b)
else:
	for i in range(2, n + 2):
		if a[i] == 2:
			continue
		else:
			for j in range(i + i, n + 2, i):
				a[j] = 2
	print(2)
	print(*a[2:])


import math
n = int(input())
n += 1
prime = [True for i in range(n + 1)]
color = [1 for i in range(n + 1)]
prime[1] = False
lim = math.floor(math.sqrt(n))
for i in range(2, lim + 1):
	if prime[i] == True:
		p = i * i
		while p <= n:
			prime[p] = False
			color[p] = color[i] + 1
			p += i
k = max(color)
print(k)
for i in range(2, n + 1):
	print(color[i], end=' ')


n = int(input())

def genPrimeList(n):
	isPrime = ['1' for i in range(n + 2)]
	for i in range(2, n + 1):
		for j in range(2 * i, n + 2, i):
			isPrime[j] = '2'
	return isPrime
if n < 3:
	print('1')
	for x in genPrimeList(n)[2:]:
		print(x, end=' ')
else:
	print('2')
	for x in genPrimeList(n)[2:]:
		print(x, end=' ')


import math

def prime(n):
	j = 0
	if n == 2 or n == 3:
		return 1
	for i in range(2, int(math.sqrt(n)) + 1):
		if n % i == 0:
			j = 1
			break
	if j == 1:
		return 0
	else:
		return 1
n = int(input())
if n == 1 or n == 2:
	print(1)
else:
	print(2)
for i in range(2, n + 2):
	if prime(i):
		print(1, end=' ')
	else:
		print(2, end=' ')


def rwh_primes(n):
	sieve = [True] * n
	for i in range(3, int(n ** 0.5) + 1, 2):
		if sieve[i]:
			sieve[i * i::2 * i] = [False] * ((n - i * i - 1) // (2 * i) + 1)
	return [2] + [i for i in range(3, n, 2) if sieve[i]]
n = int(input())
primes = set(rwh_primes(n + 2))
res = [1 if i + 2 in primes else 2 for i in range(n)]
print(2 if 2 in res else 1)
print(*res)


n = int(input())
arr = [1] * n
for i in range(2, n + 2):
	if arr[i - 2]:
		for j in range(i * i, n + 2, i):
			arr[j - 2] = 0
print(len(set(arr)))
print(' '.join(('1' if arr[i - 2] == 1 else '2' for i in range(2, n + 2))))


n = int(input())
r = [1 for i in range(n + 2)]
for i in range(2, n + 2):
	if r[i] == 1:
		for j in range(i * i, n + 2, i):
			r[j] = 2
if n < 3:
	print(1)
else:
	print(2)
print(*r[2:])


def is_prime(n):
	if n == 2 or n == 3:
		return True
	if n < 2 or n % 2 == 0:
		return False
	if n < 9:
		return True
	if n % 3 == 0:
		return False
	r = int(n ** 0.5)
	f = 5
	while f <= r:
		if n % f == 0:
			return False
		if n % (f + 2) == 0:
			return False
		f += 6
	return True
n = int(input())
value_color = []
primes = set()
for i in range(0, n):
	value = i + 2
	if is_prime(value):
		value_color.append('1')
	else:
		value_color.append('2')
if n == 1:
	print('1')
	print('1')
elif n == 2:
	print('1')
	print('1 1')
else:
	print('2')
	print(' '.join(value_color))


n = int(input())
a = [0] * (n + 2)
for i in range(2, n + 2):
	for j in range(i, n + 2, i):
		a[j] += 1
if n > 2:
	print(2)
else:
	print(1)
for i in range(2, n + 2):
	if a[i] == 1:
		print(1, end=' ')
	else:
		print(2, end=' ')


IL = lambda : list(map(int, input().split()))
IS = lambda : input().split()
I = lambda : int(input())
S = lambda : input()
n = I()
primes = [True for i in range(n + 2)]
for i in range(2, n + 2):
	if primes[i]:
		for j in range(i * 2, n + 2, i):
			primes[j] = False
print(1 if n < 3 else 2)
print(' '.join(['1' if i else '2' for i in primes[2:]]))


import math
n = int(input())
if n <= 2:
	print(1)
	for i in range(2, n + 2):
		print(1, end=' ')
else:
	print(2)
	ans = [0] * (n + 2)
	for i in range(2, n + 2):
		flag = True
		for j in range(2, math.floor(math.sqrt(i)) + 1):
			if i % j == 0:
				flag = False
				break
		ans[i] = flag + 1
	for i in range(2, n + 2):
		print(ans[i], end=' ')


def dfs(v, col):
	used[v] = col
	for u in g[v]:
		if used[u] == -1:
			dfs(u, col ^ 1)
n = int(input())
used = [1 for i in range(n)]
for i in range(2, n + 2):
	if used[i - 2] == 1:
		for j in range(i * i, n + 2, i):
			used[j - 2] = 2
print(max(used))
print(*used)


n = int(input())
n += 2
u = [1] * n
for i in range(2, n):
	if u[i] == 1:
		for j in range(i * i, n, i):
			u[j] = 2
print(max(u[2:]))
print(' '.join(map(str, u[2:])))


n = int(input())
if n > 2:
	l = [0 for i in range(n)]
	i = 0
	while i < n:
		if l[i] == 0:
			c = 1
			l[i] = c
			for j in range((i + 2) * (i + 2) - 2, n, i + 2):
				if l[j] == 0:
					l[j] = 2
		i += 1
	print(2)
	print(*l)
else:
	print(1)
	l = [1] * n
	print(*l)


from collections import Counter
n = int(input())
primes = [-1 for i in range(n + 2)]
spf = [1 for i in range(n + 2)]
primes[0] = 0
primes[1] = 0
for i in range(1, n + 2):
	if primes[i] == -1:
		for j in range(i, (n + 1) // i + 1):
			if primes[i * j] == -1:
				spf[i * j] = 2
				primes[i * j] = 0
arr = Counter(spf)
print(len(arr))
for i in range(2, n + 2):
	print(spf[i], end=' ')


from math import sqrt
n = int(input())
f = 0
ans = []
for k in range(n + 2):
	ans.append('y')
for i in range(2, n + 2):
	if ans[i] == 'y':
		for j in range(2 * i, n + 2, i):
			ans[j] = 'n'
			f += 1
if f == 0:
	print(1)
else:
	print(2)
s = ''
for l in range(2, n + 2):
	if ans[l] == 'y':
		s += '1 '
	else:
		s += '2 '
print(s)


import math
n = int(input())
if n == 1 or n == 2:
	print(1)
	for i in range(n):
		print(1)
else:
	print(2)
	ans = [1, 1]
	for i in range(4, n + 2):
		if i % 2 == 0 or i % 3 == 0:
			ans.append(2)
		else:
			j = 5
			f = True
			while j <= math.sqrt(i):
				if i % j == 0:
					ans.append(2)
					f = False
					break
				j += 2
			if f == True:
				ans.append(1)
	print(*ans)


from collections import deque as de

class My_stack:

	def __init__(self):
		self.data = []

	def my_push(self, x):
		return self.data.append(x)

	def my_pop(self):
		return self.data.pop()

	def my_peak(self):
		return self.data[-1]

	def my_contains(self, x):
		return self.data.count(x)

	def my_show_all(self):
		return self.data

	def isEmpty(self):
		return len(self.data) == 0
arrStack = My_stack()

def isPrime(n):
	if n <= 1:
		return False
	if n <= 3:
		return True
	if n % 2 == 0 or n % 3 == 0:
		return False
	i = 5
	while i * i <= n:
		if n % i == 0 or n % (i + 2) == 0:
			return False
		i = i + 6
	return True
n = int(input())
if n == 1:
	print(1)
	print(1)
elif n == 2:
	print(1)
	print(1, 1)
else:
	print(2, sep='\n')
	for i in range(n):
		if isPrime(i + 2):
			print(1, end=' ')
		else:
			print(2, end=' ')


import math

def isprime(n):
	for i in range(2, int(math.sqrt(n)) + 1):
		if n % i == 0:
			return 0
	return 1
n = int(input())
a = []
prime = []
for i in range(1, n + 1):
	a.append(i + 1)
for i in range(0, len(a)):
	if isprime(a[i]) == 0:
		prime.append(2)
	else:
		prime.append(1)
if n >= 3:
	print(2)
	print(*prime)
else:
	print(1)
	print(*prime)


n = int(input())
array = [0 for x in range(n + 2)]
for i in range(2, n + 2):
	if array[i] == 0:
		for j in range(2 * i, n + 2, i):
			array[j] = 1
if n > 2:
	print(2)
else:
	print(1)
for x in range(2, n + 2):
	if array[x] == 1:
		print('2 ', end=' ')
	else:
		print('1 ', end=' ')


def isprime(n):
	if n == 2:
		return 1
	else:
		for i in range(2, int(n ** 0.5) + 2):
			if n % i == 0:
				return 0
		return 1
n = int(input())
if n <= 2:
	print(1)
	for i in range(n):
		print(1, end=' ')
else:
	print(2)
	for i in range(2, n + 2):
		if isprime(i):
			print(1, end=' ')
		else:
			print(2, end=' ')


from sys import stdin, stdout
cin = stdin.readline
cout = stdout.write
mp = lambda : list(map(int, cin().split()))
(n,) = mp()
prime = [1] * (n + 2)
for i in range(2, n + 2):
	if prime[i] == 1:
		for j in range(i + i, n + 2, i):
			prime[j] = 2
if n <= 2:
	cout('1\n')
else:
	cout('2\n')
for i in range(2, n + 2):
	cout(str(prime[i]) + ' ')


def main():
	n = int(input())
	primes = [True for i in range(n)]
	for i in range(n):
		if primes[i]:
			j = 1 + i
			while True:
				index = i + (i + 2) * j
				if index >= n:
					break
				primes[index] = False
				j += 1
	if n <= 2:
		print(1)
	else:
		print(2)
	for prime in primes:
		if prime:
			print(1, end=' ')
		else:
			print(2, end=' ')
	print()
main()


n = int(input())
isPrime = [True] * (n + 2)
for x in range(2, int((n + 1) ** 0.5 + 1), 1):
	if isPrime[x]:
		for y in range(x ** 2, n + 2, x):
			isPrime[y] = False
if n > 2:
	print(2)
else:
	print(1)
for p in range(2, n + 2):
	if isPrime[p]:
		print(1, end=' ')
	else:
		print(2, end=' ')


from math import sqrt
n = int(input())

def prost(a):
	x = int(sqrt(a) + 1)
	for i in range(2, x):
		if a % i == 0:
			return False
	return True
if n <= 2:
	print(1)
else:
	print(2)
for i in range(2, n + 2):
	if i == 2 or i == 5:
		print(1, end=' ')
	elif i % 2 == 0 or i % 5 == 0:
		print(2, end=' ')
	elif prost(i) == True:
		print(1, end=' ')
	else:
		print(2, end=' ')


n = int(input())
output = []
for k in range(n):
	output.append(1)
for numb in range(2, (n + 1) // 2 + 1):
	if output[numb - 2] == 1:
		next_idx = 2 * numb - 2
		while next_idx <= n - 1:
			output[next_idx] = 2
			next_idx += numb
str_output = ''
for k in range(n):
	str_output += str(output[k]) + ' '
if n < 3:
	print(str(1))
else:
	print(str(2))
print(str_output)


def sieve(n):
	rn = round(n ** 0.5) + 1
	primes = [1] * (n + 2)
	i = 2
	while i < rn:
		if primes[i] == 1:
			for j in range(i * 2, n + 2, i):
				primes[j] = 2
		i += 1
	primes.remove(1)
	primes.remove(1)
	print(2)
	print(*primes)
n = int(input())
if n < 3:
	print(1)
	ls = [1] * n
	print(*ls)
else:
	sieve(n)


def main():
	n = int(input())
	color = [2] * n
	for i in range(n):
		if color[i] == 1:
			continue
		m = i + 2
		t = 2 * m
		if t > n + 1:
			color[i] = 1
		while t <= n + 1:
			color[t - 2] = 1
			t += m
	k = 1
	for x in color:
		if x == 2:
			k = 2
			break
	print(k)
	for x in color:
		print(x, end=' ')
main()


n = int(input())
a = []
for i in range(n + 2):
	a.append(1)
for i in range(2, n + 2):
	if a[i] == 1:
		j = i * 2
		while j <= n + 1:
			if a[j] == a[i]:
				a[j] += 1
			j += i
d = {}
for i in range(2, n + 2):
	ele = a[i]
	if ele not in d:
		d[ele] = 1
	else:
		d[ele] += 1
count = 0
for ele in d:
	count += 1
print(count)
for i in range(2, n + 2):
	print(a[i], sep='', end=' ')


n = int(input())
a = [True for i in range(n + 2)]
(a[0], a[1]) = (False, False)
for i in range(2, n + 2):
	if a[i]:
		j = i * i
		while j < n + 2:
			a[j] = False
			j = j + i
c = 0
for i in range(2, n + 2):
	if a[i] == True:
		c = c + 1
if n <= 2:
	print(1)
	if n == 1:
		print(1)
	else:
		print(1, ' ', 1)
else:
	print(2)
	for i in range(1, n + 1):
		if a[i + 1] == True:
			print(1, end=' ')
		else:
			print(2, end=' ')


n = int(input())
a = [1] * (n + 2)
for i in range(2, n + 2):
	j = 2
	while a[i] == 1 and i * j < n + 2:
		a[i * j] = 2
		j += 1
print(len(set(a[2:])))
print(*a[2:])


n = int(input())
prime = [True for i in range(n + 2)]
prime[0] = False
prime[1] = False
for i in range(2, n + 2):
	if prime[i]:
		for j in range(i ** 2, n + 2, i):
			prime[j] = False
print(2 if n > 2 else 1)
for i in range(n):
	if prime[i + 2]:
		print(1, end=' ')
	else:
		print(2, end=' ')


def divider(n):
	i = 2
	while i ** 2 <= n:
		if n % i == 0:
			return False
		i += 1
	return True
n = int(input())
ans = []
for i in range(2, n + 2):
	if divider(i):
		ans.append(1)
	else:
		ans.append(2)
print(len(set(ans)))
print(*ans)


def sieve(n):
	l = [1] * n
	for i in range(2, n):
		if l[i] == 1:
			for j in range(i * i, n, i):
				l[j] = 0
	l[1] = 0
	l[0] = 0
	if n == 4:
		print(1)
	else:
		print(2)
	for i in range(2, len(l)):
		if l[i] == 1:
			print(1, end=' ')
		else:
			print(2, end=' ')
n = int(input())
if n == 1:
	print(1)
	print(1)
else:
	sieve(n + 2)


n = int(input())
if n == 1:
	print(1)
	print(1)
elif n == 2:
	print(1)
	print('1 1')
else:
	print(2)
	ans = []

	def prime(q):
		j = 2
		while j * j <= q:
			if q % j == 0:
				return False
			j += 1
		return True
	for i in range(2, n + 2):
		if prime(i):
			ans.append('1')
		else:
			ans.append('2')
	print(' '.join(ans))


n = int(input())
color = []
prime = []
c = 0
for i in range(0, n + 2):
	prime.append(1)
	color.append(1)
i = 2
while i * i <= n + 1:
	if prime[i] == 1:
		for j in range(2 * i, n + 2, i):
			prime[j] = 0
			color[j] = 2
	i += 1
for i in range(2, n + 2):
	if color[i] == 2:
		c = 1
		break
if c == 1:
	print(2)
else:
	print(1)
for i in range(2, n + 2):
	print(str(color[i]), end=' ')


def main(n):
	MAX = int(n * 3)
	is_prime = [True] * MAX
	is_prime[0] = False
	is_prime[1] = False
	for i in range(2, n + 1):
		if is_prime[i]:
			for j in range(i * i, n + 3, i):
				is_prime[j] = False
	if n == 1:
		print('1\n1')
		return
	elif n == 2:
		print('1\n1 1')
		return
	print(2)
	ret = []
	for i in range(2, n + 2):
		if not is_prime[i]:
			ret.append(1)
		else:
			ret.append(2)
	print(' '.join(list(map(str, ret))))
main(int(input()))


n = int(input())
if n == 1 or n == 2:
	print(1)
	print(*[1] * n)
else:
	prime = [1] * (n + 2)
	prime[0] = prime[1] = 0
	i = 2
	while i * i <= n + 1:
		if prime[i] != 2:
			for j in range(i * i, n + 2, i):
				prime[j] = 2
		i += 1
	print(2)
	print(*prime[2:])


last = 1
n = int(input())
arr = [1] * (n + 2)
for i in range(2, n + 2):
	if arr[i] != 1:
		continue
	for j in range(2 * i, n + 2, i):
		if arr[j] == arr[i]:
			arr[j] += 1
			last = max(last, arr[j])
print(last)
print(' '.join(map(str, arr[2:])))


def prime_sieve():
	sieve = [1] * 1000001
	sieve[0] = 0
	sieve[1] = 0
	for i in range(2, 1001):
		if sieve[i] == 1:
			for j in range(i * i, 1000001, i):
				sieve[j] = 0
	return sieve
sieve = prime_sieve()
n = int(input())
if n == 1 or n == 2:
	print(1)
	l = [1] * n
else:
	l = []
	for i in range(2, n + 2):
		if sieve[i] == 1:
			l.append(1)
		else:
			l.append(2)
	print(2)
print(*l)


n = int(input())
l = [1] * 1000001
l[0] = 0
l[1] = 0
for i in range(2, 1000001):
	if l[i] == 1:
		for j in range(i * i, 1000001, i):
			l[j] = 2
k = set(l[2:n + 2])
print(len(k))
print(*l[2:n + 2])


from math import *
from sys import *
input = stdin.readline
n = int(input())
l = []
m = 2
for i in range(2, n + 2):
	f = 0
	for j in range(2, int(sqrt(i)) + 1):
		if i % j == 0:
			f = 1
			break
	if f == 1:
		l.append(m)
	else:
		l.append(1)
print(len(set(l)))
print(*l)


def sieve(n):
	mark = [True] * (n + 1)
	p = 2
	while p * p <= n:
		if mark[p]:
			for i in range(p * p, n + 1, p):
				mark[i] = False
		p += 1
	for i in range(2, n + 1):
		if mark[i]:
			print(1, end=' ')
		else:
			print(2, end=' ')
n = int(input())
if n == 1 or n == 2:
	print(1)
else:
	print(2)
sieve(n + 1)


vis = [0] * int(100000.0 + 3)

def sieve():
	for i in range(2, int(100000.0 + 3)):
		if vis[i]:
			continue
		j = i * i
		while j < int(100000.0 + 3):
			vis[j] = 1
			j += i
sieve()
n = int(input())
print(1 if n <= 2 else 2)
for i in range(2, n + 2):
	vis[i] += 1
print(*vis[2:n + 2])


import math

def check_prime(num):
	if all((num % i != 0 for i in range(2, int(math.sqrt(num)) + 1))):
		return 1
	else:
		return 0
n = int(input())
if n >= 3:
	print(2)
else:
	print(1)
for i in range(2, n + 2):
	if check_prime(i):
		print(1, end=' ')
	else:
		print(2, end=' ')
print()


import math
n = int(input())
a = [1] * n
a[0] = 1
if n >= 3:
	print(2)
	a[2] = 2
else:
	print(1)
for i in range(2, n + 2):
	if a[i - 2] == 1:
		for j in range(2 * i, n + 2, i):
			a[j - 2] = 2
print(*a)


sieve = [0] * 100002
for i in range(2, 100002):
	if sieve[i]:
		continue
	for j in range(i * 2, 100002, i):
		sieve[j] = i
n = int(input())
print(1 if n <= 2 else 2)
ans = ''
for i in range(2, n + 2):
	if sieve[i]:
		ans += '2 '
	else:
		ans += '1 '
print(ans)


def isPrime(n):
	for i in range(2, int(n ** 0.5) + 1):
		if n % i == 0:
			return False
	return True
n = int(input())
x = []
for i in range(n):
	x.append(1 if isPrime(i + 2) else 2)
print(len(list(set(x))))
print(*x)


def prime(n):
	if n == 1:
		print(1)
		print(1)
		return
	if n == 2:
		print(1)
		print(1, 1)
		return
	arr = list(range(2, n + 2))
	for i in range(len(arr)):
		p = arr[i]
		if p == True or p == False:
			continue
		arr[i] = True
		for j in range(p * p, n + 2, p):
			arr[j - 2] = False
	d = {True: 1, False: 2}
	for i in range(len(arr)):
		arr[i] = d[arr[i]]
	print(2)
	print(*arr)
prime(int(input()))


def sakurajima(n):
	if n < 9:
		return ['0', '1', '1', '2', '1', '2', '1', '2'][1:n + 1]
	n += 1
	l = [1] * n
	for i in range(2, int(n ** 0.5) + 1):
		if l[i - 1] == 1:
			for j in range(i ** 2, n + 1, i):
				if j % i == 0:
					l[j - 1] = 2
	l[0] = 0
	return [str(i) for i in l[1:]]
n = int(input())
if n <= 2:
	print(1)
	print(' '.join(['1'] * n))
else:
	print(2)
	print(' '.join(sakurajima(n)))


n = int(input())
s = [i for i in range(n + 2)]
p = [1 for i in range(n + 2)]
p[1] = 1
p[2] = 1
x = 2
while x <= n + 1:
	while x <= n + 1 and p[x] == 2:
		x += 1
	y = 2
	while y * x <= n + 1:
		p[y * x] = 2
		y += 1
	x += 1
res = p[2:]
m = 1
for i in range(len(res)):
	m = max(m, res[i])
print(m)
print(' '.join(map(str, res)))


import sys

def debug(x, table):
	for (name, val) in table.items():
		if x is val:
			print('DEBUG:{} -> {}'.format(name, val), file=sys.stderr)
			return None

def solve():
	n = int(input())
	if n <= 2:
		k = 1
		ans = [1] * n
		print(k)
		print(*ans)
	else:
		k = 2
		ans = color(n)
		print(k)
		print(*ans)

def color(n):
	res = [1] * (n + 2)
	for p in range(2, n + 2):
		if res[p] != 1:
			continue
		for q in range(p * p, n + 2, p):
			res[q] = 2
	return res[2:]

def __starting_point():
	solve()
__starting_point()


import random, math
from copy import deepcopy as dc
MAXN = 100005
primes = [1] * MAXN
primes[0] = 0
primes[1] = 0

def seive():
	i = 2
	while i * i < MAXN:
		if primes[i] == 1:
			for j in range(i * i, MAXN, i):
				primes[j] = 2
		i += 1

def solution(n):
	cur = 1
	out = []
	for i in range(2, n + 2):
		out.append(primes[i])
	return (max(out), out)

def input_test():
	n = int(input())
	(out, li) = solution(n)
	print(out)
	print(' '.join(list(map(str, li))))
seive()
input_test()


maxn = 100005
pri = [1] * 100005
pri[0] = pri[1] = 0
for i in range(2, maxn):
	if not pri[i]:
		continue
	for j in range(i * i, maxn, i):
		pri[j] = 0
n = int(input())
if n < 3:
	print(1)
else:
	print(2)
for i in range(2, n + 2):
	if pri[i]:
		print(1, end=' ')
	else:
		print(2, end=' ')


import sys
read = lambda : sys.stdin.readline().strip()
write = lambda x: sys.stdout.write(x + '\n')
N = int(read())
ps = [i for i in range(N + 2)]
pn = 0
cs = [0] * (N + 2)
for i in range(2, N + 2):
	if not cs[i]:
		ps[pn] = i
		pn += 1
		for j in range(i ** 2, N + 2, i):
			cs[j] = 1
if N <= 2:
	write('1')
else:
	write('2')
write(' '.join((str(c + 1) for c in cs[2:])))


import math
n = int(input())

def isPrime(n):
	for i in range(2, int(math.sqrt(n)) + 1):
		if n % i == 0:
			return False
	return True
if n == 1:
	print(1)
	print(1)
elif n == 2:
	print(1)
	print('1 1')
else:
	print(2)
	answerlist = []
	for i in range(2, n + 2):
		if isPrime(i):
			answerlist.append('1')
		else:
			answerlist.append('2')
	print(' '.join(answerlist))


sieve = [True] * 100005
prime = []
for i in range(2, 100005):
	if sieve[i]:
		prime.append(i)
		for j in range(i * i, 100005, i):
			sieve[j] = False
n = int(input())
if n <= 2:
	print(1)
	print('1 ' * n)
else:
	print(2)
	for i in range(2, n + 2):
		print(sieve[i] + 1, end=' ')


def primefun(n2):
	cnt = 0
	seive = [1 for i in range(n2 + 1)]
	i = 2
	while i * i <= n2 + 1:
		if seive[i] == 1:
			for j in range(i * i, n2 + 1, i):
				seive[j] = 0
		i = i + 1
	seive[0] = 0
	seive[1] = 0
	return seive
n = int(input())
seive = primefun(100001)
if n > 2:
	print(2)
else:
	print(1)
for i in range(2, n + 2):
	if seive[i] == 1:
		print(1, end=' ')
	else:
		print(2, end=' ')


import math
n = int(input())
if n == 1:
	print(1)
	print(1)
	exit(0)
prime = [2]
ans = [1]
for i in range(3, n + 2):
	curr = 0
	sq = math.floor(math.sqrt(i))
	isPrime = True
	while curr < len(prime) and prime[curr] <= sq:
		if i % prime[curr] == 0:
			isPrime = False
			break
		curr += 1
	if isPrime:
		prime.append(i)
		ans.append(1)
	else:
		ans.append(2)
print(2 if n > 2 else 1)
print(' '.join(map(str, ans)))


from sys import stdin, stdout, maxsize
tup = lambda : map(int, stdin.readline().split())
I = lambda : int(stdin.readline())
lint = lambda : [int(x) for x in stdin.readline().split()]
stpr = lambda x: stdout.write(f'{x}' + '\n')
star = lambda x: print(' '.join(map(str, x)))
from _collections import defaultdict

def count(n):
	i = 2
	while i * i <= n:
		if n % i == 0:
			return 2
		i += 1
	return 1
dd = defaultdict(int)
n = I()
ans = []
for i in range(2, n + 2):
	ans.append(count(i))
stpr(len(set(ans)))
star(ans)


def is_prime(x):
	i = 2
	while i * i <= x:
		if x % i == 0:
			return False
		i += 1
	return True
n = int(input())
ans = []
for i in range(2, n + 2):
	if is_prime(i):
		ans.append(1)
	else:
		ans.append(2)
if n == 1:
	print(1)
	print(1)
elif n == 2:
	print(1)
	print(1, 1)
else:
	print(2)
	print(' '.join((str(num) for num in ans)))


n = int(input())
l = [1] * (n + 2)
t = 1
for i in range(2, n + 2):
	if l[i] == 1:
		for j in range(i + i, n + 2, i):
			l[j] = 2
			t = max(t, l[j])
print(t)
print(*l[2:])


N = int(input()) + 2
is_prime = N * [1]
color = N * [2]
for i in range(N):
	if i < 2:
		continue
	if is_prime[i]:
		j = 2 * i
		while j < N:
			is_prime[j] = 0
			j += i
		color[i] = 1
print(max(color[2:N]), ' '.join(map(str, color[2:N])), sep='\n')


n = [int(x) for x in input().split()]
n = n[0]
primals = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, 10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, 10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, 10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 10957, 10973, 10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251, 11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399, 11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, 11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, 11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, 12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553, 12569, 12577, 12583, 12589, 12601, 12611, 12613, 12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, 12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, 13009, 13033, 13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, 13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, 13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, 13591, 13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687, 13691, 13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757, 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38501, 38543, 38557, 38561, 38567, 38569, 38593, 38603, 38609, 38611, 38629, 38639, 38651, 38653, 38669, 38671, 38677, 38693, 38699, 38707, 38711, 38713, 38723, 38729, 38737, 38747, 38749, 38767, 38783, 38791, 38803, 38821, 38833, 38839, 38851, 38861, 38867, 38873, 38891, 38903, 38917, 38921, 38923, 38933, 38953, 38959, 38971, 38977, 38993, 39019, 39023, 39041, 39043, 39047, 39079, 39089, 39097, 39103, 39107, 39113, 39119, 39133, 39139, 39157, 39161, 39163, 39181, 39191, 39199, 39209, 39217, 39227, 39229, 39233, 39239, 39241, 39251, 39293, 39301, 39313, 39317, 39323, 39341, 39343, 39359, 39367, 39371, 39373, 39383, 39397, 39409, 39419, 39439, 39443, 39451, 39461, 39499, 39503, 39509, 39511, 39521, 39541, 39551, 39563, 39569, 39581, 39607, 39619, 39623, 39631, 39659, 39667, 39671, 39679, 39703, 39709, 39719, 39727, 39733, 39749, 39761, 39769, 39779, 39791, 39799, 39821, 39827, 39829, 39839, 39841, 39847, 39857, 39863, 39869, 39877, 39883, 39887, 39901, 39929, 39937, 39953, 39971, 39979, 39983, 39989, 40009, 40013, 40031, 40037, 40039, 40063, 40087, 40093, 40099, 40111, 40123, 40127, 40129, 40151, 40153, 40163, 40169, 40177, 40189, 40193, 40213, 40231, 40237, 40241, 40253, 40277, 40283, 40289, 40343, 40351, 40357, 40361, 40387, 40423, 40427, 40429, 40433, 40459, 40471, 40483, 40487, 40493, 40499, 40507, 40519, 40529, 40531, 40543, 40559, 40577, 40583, 40591, 40597, 40609, 40627, 40637, 40639, 40693, 40697, 40699, 40709, 40739, 40751, 40759, 40763, 40771, 40787, 40801, 40813, 40819, 40823, 40829, 40841, 40847, 40849, 40853, 40867, 40879, 40883, 40897, 40903, 40927, 40933, 40939, 40949, 40961, 40973, 40993, 41011, 41017, 41023, 41039, 41047, 41051, 41057, 41077, 41081, 41113, 41117, 41131, 41141, 41143, 41149, 41161, 41177, 41179, 41183, 41189, 41201, 41203, 41213, 41221, 41227, 41231, 41233, 41243, 41257, 41263, 41269, 41281, 41299, 41333, 41341, 41351, 41357, 41381, 41387, 41389, 41399, 41411, 41413, 41443, 41453, 41467, 41479, 41491, 41507, 41513, 41519, 41521, 41539, 41543, 41549, 41579, 41593, 41597, 41603, 41609, 41611, 41617, 41621, 41627, 41641, 41647, 41651, 41659, 41669, 41681, 41687, 41719, 41729, 41737, 41759, 41761, 41771, 41777, 41801, 41809, 41813, 41843, 41849, 41851, 41863, 41879, 41887, 41893, 41897, 41903, 41911, 41927, 41941, 41947, 41953, 41957, 41959, 41969, 41981, 41983, 41999, 42013, 42017, 42019, 42023, 42043, 42061, 42071, 42073, 42083, 42089, 42101, 42131, 42139, 42157, 42169, 42179, 42181, 42187, 42193, 42197, 42209, 42221, 42223, 42227, 42239, 42257, 42281, 42283, 42293, 42299, 42307, 42323, 42331, 42337, 42349, 42359, 42373, 42379, 42391, 42397, 42403, 42407, 42409, 42433, 42437, 42443, 42451, 42457, 42461, 42463, 42467, 42473, 42487, 42491, 42499, 42509, 42533, 42557, 42569, 42571, 42577, 42589, 42611, 42641, 42643, 42649, 42667, 42677, 42683, 42689, 42697, 42701, 42703, 42709, 42719, 42727, 42737, 42743, 42751, 42767, 42773, 42787, 42793, 42797, 42821, 42829, 42839, 42841, 42853, 42859, 42863, 42899, 42901, 42923, 42929, 42937, 42943, 42953, 42961, 42967, 42979, 42989, 43003, 43013, 43019, 43037, 43049, 43051, 43063, 43067, 43093, 43103, 43117, 43133, 43151, 43159, 43177, 43189, 43201, 43207, 43223, 43237, 43261, 43271, 43283, 43291, 43313, 43319, 43321, 43331, 43391, 43397, 43399, 43403, 43411, 43427, 43441, 43451, 43457, 43481, 43487, 43499, 43517, 43541, 43543, 43573, 43577, 43579, 43591, 43597, 43607, 43609, 43613, 43627, 43633, 43649, 43651, 43661, 43669, 43691, 43711, 43717, 43721, 43753, 43759, 43777, 43781, 43783, 43787, 43789, 43793, 43801, 43853, 43867, 43889, 43891, 43913, 43933, 43943, 43951, 43961, 43963, 43969, 43973, 43987, 43991, 43997, 44017, 44021, 44027, 44029, 44041, 44053, 44059, 44071, 44087, 44089, 44101, 44111, 44119, 44123, 44129, 44131, 44159, 44171, 44179, 44189, 44201, 44203, 44207, 44221, 44249, 44257, 44263, 44267, 44269, 44273, 44279, 44281, 44293, 44351, 44357, 44371, 44381, 44383, 44389, 44417, 44449, 44453, 44483, 44491, 44497, 44501, 44507, 44519, 44531, 44533, 44537, 44543, 44549, 44563, 44579, 44587, 44617, 44621, 44623, 44633, 44641, 44647, 44651, 44657, 44683, 44687, 44699, 44701, 44711, 44729, 44741, 44753, 44771, 44773, 44777, 44789, 44797, 44809, 44819, 44839, 44843, 44851, 44867, 44879, 44887, 44893, 44909, 44917, 44927, 44939, 44953, 44959, 44963, 44971, 44983, 44987, 45007, 45013, 45053, 45061, 45077, 45083, 45119, 45121, 45127, 45131, 45137, 45139, 45161, 45179, 45181, 45191, 45197, 45233, 45247, 45259, 45263, 45281, 45289, 45293, 45307, 45317, 45319, 45329, 45337, 45341, 45343, 45361, 45377, 45389, 45403, 45413, 45427, 45433, 45439, 45481, 45491, 45497, 45503, 45523, 45533, 45541, 45553, 45557, 45569, 45587, 45589, 45599, 45613, 45631, 45641, 45659, 45667, 45673, 45677, 45691, 45697, 45707, 45737, 45751, 45757, 45763, 45767, 45779, 45817, 45821, 45823, 45827, 45833, 45841, 45853, 45863, 45869, 45887, 45893, 45943, 45949, 45953, 45959, 45971, 45979, 45989, 46021, 46027, 46049, 46051, 46061, 46073, 46091, 46093, 46099, 46103, 46133, 46141, 46147, 46153, 46171, 46181, 46183, 46187, 46199, 46219, 46229, 46237, 46261, 46271, 46273, 46279, 46301, 46307, 46309, 46327, 46337, 46349, 46351, 46381, 46399, 46411, 46439, 46441, 46447, 46451, 46457, 46471, 46477, 46489, 46499, 46507, 46511, 46523, 46549, 46559, 46567, 46573, 46589, 46591, 46601, 46619, 46633, 46639, 46643, 46649, 46663, 46679, 46681, 46687, 46691, 46703, 46723, 46727, 46747, 46751, 46757, 46769, 46771, 46807, 46811, 46817, 46819, 46829, 46831, 46853, 46861, 46867, 46877, 46889, 46901, 46919, 46933, 46957, 46993, 46997, 47017, 47041, 47051, 47057, 47059, 47087, 47093, 47111, 47119, 47123, 47129, 47137, 47143, 47147, 47149, 47161, 47189, 47207, 47221, 47237, 47251, 47269, 47279, 47287, 47293, 47297, 47303, 47309, 47317, 47339, 47351, 47353, 47363, 47381, 47387, 47389, 47407, 47417, 47419, 47431, 47441, 47459, 47491, 47497, 47501, 47507, 47513, 47521, 47527, 47533, 47543, 47563, 47569, 47581, 47591, 47599, 47609, 47623, 47629, 47639, 47653, 47657, 47659, 47681, 47699, 47701, 47711, 47713, 47717, 47737, 47741, 47743, 47777, 47779, 47791, 47797, 47807, 47809, 47819, 47837, 47843, 47857, 47869, 47881, 47903, 47911, 47917, 47933, 47939, 47947, 47951, 47963, 47969, 47977, 47981, 48017, 48023, 48029, 48049, 48073, 48079, 48091, 48109, 48119, 48121, 48131, 48157, 48163, 48179, 48187, 48193, 48197, 48221, 48239, 48247, 48259, 48271, 48281, 48299, 48311, 48313, 48337, 48341, 48353, 48371, 48383, 48397, 48407, 48409, 48413, 48437, 48449, 48463, 48473, 48479, 48481, 48487, 48491, 48497, 48523, 48527, 48533, 48539, 48541, 48563, 48571, 48589, 48593, 48611, 48619, 48623, 48647, 48649, 48661, 48673, 48677, 48679, 48731, 48733, 48751, 48757, 48761, 48767, 48779, 48781, 48787, 48799, 48809, 48817, 48821, 48823, 48847, 48857, 48859, 48869, 48871, 48883, 48889, 48907, 48947, 48953, 48973, 48989, 48991, 49003, 49009, 49019, 49031, 49033, 49037, 49043, 49057, 49069, 49081, 49103, 49109, 49117, 49121, 49123, 49139, 49157, 49169, 49171, 49177, 49193, 49199, 49201, 49207, 49211, 49223, 49253, 49261, 49277, 49279, 49297, 49307, 49331, 49333, 49339, 49363, 49367, 49369, 49391, 49393, 49409, 49411, 49417, 49429, 49433, 49451, 49459, 49463, 49477, 49481, 49499, 49523, 49529, 49531, 49537, 49547, 49549, 49559, 49597, 49603, 49613, 49627, 49633, 49639, 49663, 49667, 49669, 49681, 49697, 49711, 49727, 49739, 49741, 49747, 49757, 49783, 49787, 49789, 49801, 49807, 49811, 49823, 49831, 49843, 49853, 49871, 49877, 49891, 49919, 49921, 49927, 49937, 49939, 49943, 49957, 49991, 49993, 49999, 50021, 50023, 50033, 50047]
if n == 1:
	print(1)
	print(1)
elif n == 2:
	print(1)
	print('1 1')
else:
	print(2)
	a = (1 + n) / 2
	s = ''
	for i in range(2, n + 2):
		if i <= a:
			if i == primals[0]:
				del primals[0]
				s = s + ' 1'
			else:
				s = s + ' 2'
		else:
			for _ in range(i, n + 2):
				s = s + ' 2'
			break
	print(s[1:])


n = int(input())
arr = [1] * (n + 2)
arr[0] = 2
arr[1] = 2
i = 2
while True:
	for j in range(2 * i, n + 2, i):
		arr[j] = 2
	try:
		i = arr.index(1, i + 1)
	except:
		break
if n == 1 or n == 2:
	print(1)
else:
	print(2)
for i in range(2, n + 2):
	print(arr[i], end=' ')
print()


from math import sqrt
(n, k) = (int(input()) + 1, 1)
t = [1] * (n - 1)
for i in range(2, int(sqrt(n)) + 1):
	for j in range(i * i, n + 1, i):
		(t[j - 2], k) = (2, 2)
print(k)
print(*t)


n = int(input())
a = [1 for i in range(n + 2)]
for i in range(2, int(n ** 0.5) + 2):
	if a[i] != 2:
		for j in range(i * 2, n + 2, i):
			a[j] = 2
print(len(set(a)))
print(*a[2:])


def print_color(n):
	(d, k) = ([1] * (n + 2), 1)
	for i in range(2, n + 2):
		for j in range(i * i, n + 2, i):
			d[j] = 2
	print(len(set(d[2:])))
	print(*d[2:])
n = int(input())
print_color(n)


import os
import sys
import math
import itertools
from io import BytesIO, IOBase
import os.path
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))
mod = 10 ** 9 + 7
pi = 3.141592653589793

def i1():
	return int(sys.stdin.readline())

def sf():
	return sys.stdin.readline()

def mi():
	return map(int, sys.stdin.readline().split())

def arr():
	return list(map(int, sys.stdin.readline().split()))

def pf(ans):
	return sys.stdout.write(str(ans) + '\n')

def gcd(a, b):
	if a == 0:
		return b
	elif b == 0:
		return a
	if a > b:
		return gcd(a % b, b)
	else:
		return gcd(a, b % a)

def lcm(a, b):
	return a * b // gcd(a, b)
if os.path.exists('input_file.txt'):
	sys.stdin = open('input_file.txt', 'r')
	sys.stdout = open('output_file.txt', 'w')

def SOE(n):
	prime = [True for i in range(n + 1)]
	p = 2
	while p * p <= n:
		if prime[p] == True:
			for i in range(p * 2, n + 1, p):
				prime[i] = False
		p += 1
	prime[0] = False
	prime[1] = False
	return prime

def solve(p):
	l = []
	n = int(input())
	if n == 1:
		print(1)
	else:
		for i in range(2, n + 2):
			if i == 1:
				l.append(1)
			elif p[i]:
				l.append(1)
			else:
				l.append(2)
	if n == 2 or n == 1:
		print(1)
	else:
		print(2)
	for i in l:
		print(i, end=' ')
tc = 1
p = SOE(1000002)
for t in range(tc):
	solve(p)


import math
n = int(input())
prime = [True] * (n + 2)
for i in range(2, int(math.sqrt(n + 1)) + 1):
	if prime[i]:
		for j in range(2 * i, n + 2, i):
			if j < len(prime):
				prime[j] = False
if n == 1 or n == 2:
	print(1)
else:
	print(2)
for i in range(2, n + 2):
	if prime[i]:
		print(1, end=' ')
	else:
		print(2, end=' ')


from math import sqrt
n = int(input())
if n <= 2:
	print(1)
else:
	print(2)

def isprime(x):
	for i in range(2, int(sqrt(x)) + 1):
		if x % i == 0:
			return 0
	return 1
for j in range(2, n + 2):
	if isprime(j):
		print(1, end=' ')
	else:
		print(2, end=' ')


n = int(input())
l = []
for i in range(n):
	l.append(i + 2)

def SieveOfEratosthenes(n):
	prime = [True for i in range(n + 1)]
	p = 2
	while p * p <= n:
		if prime[p] == True:
			for i in range(p * p, n + 1, p):
				prime[i] = False
		p += 1
	return prime
x = SieveOfEratosthenes(n + 1)
for i in range(1, n + 2):
	if x[i] == True:
		l[i - 2] = 1
	else:
		l[i - 2] = 2
if False in x:
	print(2)
else:
	print(1)
for i in l:
	print(i, end=' ')
print()


def prime_nums_finder(n):
	is_prime = [True for i in range(n + 1)]
	is_prime[0] = False
	for i in range(1, int(n ** 0.5)):
		if is_prime[i]:
			for j in range((i + 1) ** 2 - 1, n, i + 1):
				is_prime[j] = False
	return is_prime
n = int(input())
prime_nums = prime_nums_finder(n + 2)
if n < 3:
	print('1\n' + '1 ' * n)
else:
	print('2\n' + ' '.join(['1' if prime_nums[i + 1] else '2' for i in range(n)]))


a = int(input())
z = [0] + [0] * (a + 1)
if a < 3:
	print(1)
else:
	print(2)
for i in range(2, a + 2):
	if not z[i]:
		for j in range(2 * i, a + 2, i):
			z[j] = 2
		z[i] = 1
print(*z[2:])


n = int(input())
color = [0 for _ in range(0, n + 2)]
total = set()
for i in range(2, n + 2):
	if color[i] == 0:
		color[i] = 1
		total.add(1)
		for i in range(i * 2, n + 2, i):
			color[i] = 2
			total.add(2)
print(len(total))
print(*color[2:n + 2])


from math import sqrt

def prime(a):
	if a < 2:
		return False
	for x in range(2, int(sqrt(a)) + 1):
		if a % x == 0:
			return False
	return True
prime_lst = []
n = int(input())
if n < 3:
	print(1)
else:
	print(2)
for i in range(2, n + 2):
	if prime(i):
		print(1, end=' ')
	else:
		print(2, end=' ')


n = int(input())
t = [1] * (n + 2)
p = 2
while p ** 2 <= n + 1:
	if t[p] == 1:
		for j in range(p * 2, n + 2, p):
			t[j] = 2
	p += 1
if n == 1:
	print(1)
	print(1)
elif n == 2:
	print(1)
	print(1, 1)
else:
	f = []
	for j in range(1, n + 1):
		if t[j + 1] == 1:
			f.append(1)
		else:
			f.append(2)
	print(2)
	print(*f)


n = int(input())
arr = []
for i in range(n + 2):
	arr.append(1)
x = 2
while x * x <= n + 1:
	if arr[x] == 1:
		if 2 * x <= n + 1:
			for j in range(x * 2, n + 2, x):
				arr[j] = 2
	x += 1
if n == 1 or n == 2:
	print(1)
else:
	print(2)
for y in range(2, n + 2):
	print(arr[y], end=' ')


a = [0] * 100002
for i in range(2, 100002):
	if not a[i]:
		j = 2 * i
	while j <= 100001:
		a[j] = 1
		j += i
n = int(input())
if n <= 2:
	print('1')
else:
	print('2')
for i in range(2, n + 2):
	print(a[i] + 1, end=' ')


import math

def eratosthenes(n):
	is_composite = [False for _ in range(n + 1)]
	is_composite[0] = is_composite[1] = True
	b = math.floor(math.sqrt(n)) + 1
	for p in range(2, b + 1):
		if is_composite[p]:
			continue
		x = 2 * p
		while x <= n:
			is_composite[x] = True
			x += p
	return is_composite
n = int(input())
is_composite = eratosthenes(n + 1)
if n >= 3:
	print(2)
else:
	print(1)
print(*(1 if not is_composite[k] else 2 for k in range(2, n + 2)))


def get_primes(n):
	if n == 1:
		numbers = ['1']
		return numbers
	m = n + 2
	numbers = ['1'] * m
	for i in range(2, int(n ** 0.5 + 1) + 2):
		if numbers[i] == '1':
			for j in range(i * i, m, i):
				numbers[j] = '2'
	return numbers[2:]
n = int(input())
if n <= 2:
	print('1')
	print(' '.join(get_primes(n)))
else:
	print('2')
	print(' '.join(get_primes(n)))


import math

def isPrime(i):
	if sieve[i]:
		for j in range(i * i, n + 2, i):
			sieve[j] = 2
n = int(input())
sieve = [1 for i in range(n + 2)]
rnge = int(math.sqrt(n))
for i in range(2, rnge + 2):
	isPrime(i)
if n >= 3:
	print(2)
else:
	print(1)
for i in range(2, n + 2):
	print(sieve[i], end=' ')


from sys import stdin, stdout

def sieve(n, till):
	if till <= 2:
		print(1)
		for i in range(till):
			print(1, end=' ')
		return
	print(2)
	numbers_till_n = [True for i in range(n + 1)]
	initial_value = 2
	while initial_value ** 2 <= n:
		if numbers_till_n[initial_value]:
			for i in range(initial_value ** 2, n + 1, initial_value):
				numbers_till_n[i] = False
		initial_value += 1
	for i in range(2, till + 2):
		if numbers_till_n[i]:
			print(1, end=' ')
		else:
			print(2, end=' ')
	return
sieve(10 ** 5 + 2, int(stdin.readline()))


import math

def main():
	n = int(input())
	sieve = [True] * 100005
	sieve[0] = False
	sieve[1] = False
	for i in range(2, int(math.sqrt(100005)) + 1):
		if sieve[i]:
			for j in range(2 * i, 100005, i):
				sieve[j] = False
	if n == 1:
		print('1\n1')
	elif n == 2:
		print('1\n1 1')
	else:
		print('2')
		for i in range(2, n + 2):
			if sieve[i]:
				print('1', end=' ')
			else:
				print('2', end=' ')
main()


n = int(input())
a = [0 for i in range(n + 2)]
color = 1
for i in range(2, n + 2):
	if a[i] == 0:
		a[i] = 1
		for j in range(i * i, n + 2, i):
			a[j] = a[i] + 1
			color = max(color, a[j])
print(color)
for i in a[2:]:
	print(i, end=' ')


p = 10 ** 5 + 2

def Sieve():
	l = [True] * p
	i = 2
	while i * i <= p:
		if l[i]:
			for j in range(2 * i, p, i):
				l[j] = False
		i += 1
	return l
isprime = Sieve()
n = int(input())
if n == 1:
	print(1)
	print(1)
elif n == 2:
	print(1)
	print(1, 1)
else:
	print(2)
	for i in range(2, n + 2):
		if isprime[i]:
			print(1, end=' ')
		else:
			print(2, end=' ')


n = int(input())
primes = [True] * (n + 2)
for i in range(2, (n + 1) // 2 + 1):
	for j in range(2, (n + 1) // i + 1):
		primes[i * j] = False
if n <= 2:
	print(1)
else:
	print(2)
for i in range(2, n + 2):
	if primes[i]:
		print(1, end=' ')
	else:
		print(2, end=' ')


import math as mt
import sys, string, bisect
input = sys.stdin.readline
from collections import deque
L = lambda : list(map(int, input().split()))
Ls = lambda : list(input().split())
M = lambda : map(int, input().split())
I = lambda : int(input())
MAXN = 10 ** 5 + 5
spf = [0 for i in range(MAXN)]

def sieve():
	spf[1] = 1
	for i in range(2, MAXN):
		spf[i] = i
	for i in range(4, MAXN, 2):
		spf[i] = 2
	for i in range(3, mt.ceil(mt.sqrt(MAXN))):
		if spf[i] == i:
			for j in range(i * i, MAXN, i):
				if spf[j] == j:
					spf[j] = i
sieve()
n = I()
if n < 3:
	print(1)
else:
	print(2)
for i in range(2, n + 2):
	if spf[i] == i:
		print('1', end=' ')
	else:
		print('2', end=' ')


n = int(input())
prime = [True] * (n + 2)
prime[0] = prime[1] = False
for m in range(2, n + 2):
	if prime[m]:
		for i in range(2 * m, n + 2, m):
			prime[i] = False
print('2' if n > 2 else '1')
colors = ['1' if prime[m] else '2' for m in range(2, n + 2)]
print(' '.join(colors))


import sys
fin = sys.stdin
fout = sys.stdout
n = int(fin.readline())
colors = [1] * n
allCount = 1
for i in range(2, n + 2):
	if colors[i - 2] == 1 and i * i <= n + 1:
		allCount += 1
		for j in range(i * i, n + 2, i):
			colors[j - 2] = 2
fout.write(str(max(colors)) + '\n')
fout.write(' '.join(map(str, colors)))


from math import sqrt

def isprime(t):
	for i in range(2, int(sqrt(t)) + 1):
		if t % i == 0:
			return 0
	return 1
n = int(input())
s = []
cnt = 1
r = []
for i in range(2, n + 2):
	if isprime(i):
		r.append(1)
	else:
		r.append(2)
print(max(r), '\n', *r)


n = int(input())
isp = [1] * (n + 2)
for i in range(2, n + 2):
	if isp[i] == 1:
		for j in range(i * i, n + 2, i):
			isp[j] = 2
print(1 if n <= 2 else 2)
print(' '.join((str(isp[i]) for i in range(2, n + 2))))


import sys
import collections
from collections import Counter
import itertools
import math
import timeit

def sieve(n):
	if n < 2:
		return list()
	prime = [True for _ in range(n + 1)]
	p = 3
	while p * p <= n:
		if prime[p]:
			for i in range(p * 2, n + 1, p):
				prime[i] = False
		p += 2
	r = [2]
	for p in range(3, n + 1, 2):
		if prime[p]:
			r.append(p)
	return r

def divs(n, start=1):
	divisors = []
	for i in range(start, int(math.sqrt(n) + 1)):
		if n % i == 0:
			if n / i == i:
				divisors.append(i)
			else:
				divisors.extend([i, n // i])
	return divisors

def divn(n, primes):
	divs_number = 1
	for i in primes:
		if n == 1:
			return divs_number
		t = 1
		while n % i == 0:
			t += 1
			n //= i
		divs_number *= t

def flin(d, x, default=-1):
	left = right = -1
	for i in range(len(d)):
		if d[i] == x:
			if left == -1:
				left = i
			right = i
	if left == -1:
		return (default, default)
	else:
		return (left, right)

def ceil(n, k):
	return n // k + (n % k != 0)

def ii():
	return int(input())

def mi():
	return map(int, input().split())

def li():
	return list(map(int, input().split()))

def lcm(a, b):
	return abs(a * b) // math.gcd(a, b)

def prr(a, sep=' '):
	print(sep.join(map(str, a)))

def dd():
	return collections.defaultdict(int)

def ddl():
	return collections.defaultdict(list)
n = ii()
d = sieve(n + 1)
res = [2] * n
for i in d:
	res[i - 2] = 1
print(2 if n > 2 else 1)
prr(res)


def soe(n):
	temp = []
	prime = [True for i in range(n + 1)]
	p = 2
	while p * p <= n:
		if prime[p] == True:
			for i in range(p * p, n + 1, p):
				prime[i] = False
		p += 1
	for p in range(2, n + 1):
		if prime[p]:
			temp.append(p)
	return temp
n = int(input())
temp = soe(n + 1)
temp = set(temp)
if len(temp) == 0:
	print(1)
	for i in range(2, n + 2):
		print(1, end=' ')
elif n < 3:
	print(1)
	for i in range(n):
		print(1, end=' ')
else:
	print(2)
	for i in range(2, n + 2):
		if i in temp:
			print(1, end=' ')
		else:
			print(2, end=' ')


num = [0] * 100009
n = int(input())
m = 1
for i in range(2, n + 2, 1):
	if num[i] == 0:
		num[i] = 1
		for j in range(i + i, n + 2, i):
			num[j] = 2
			m = 2
print(m)
for i in range(2, n + 2, 1):
	print(num[i], end=' ')


def get_primes(n):
	m = n + 2
	numbers = ['1'] * m
	for i in range(2, int(n ** 0.5 + 1)):
		if numbers[i] == '1':
			for j in range(i * i, m, i):
				numbers[j] = '2'
	return numbers[2:]
entrada = int(input())
if entrada == 1:
	print('1\n1')
elif entrada == 2:
	print('1\n1 1')
elif entrada == 3:
	print('2\n1 1 2')
else:
	print('2')
	print(' '.join(get_primes(entrada)))


n = int(input())
res = []
for i in range(n):
	u = i + 2
	if u == 2:
		res.append(1)
	else:
		e = int(u ** 0.5)
		lock = 0
		for j in range(2, e + 1):
			if u % j == 0:
				lock = 1
				break
		if lock == 1:
			res.append(2)
		else:
			res.append(1)
print(len(set(res)))
print(*res)


n = int(input())
l = [-1 for i in range(n)]

def evklid(a):
	for i in range(2, int(a ** 0.5) + 1):
		if a % i == 0:
			return i
	return 0
p = 2
for i in range(2, n + 2):
	d = evklid(i)
	if d == 0:
		l[i - 2] = 1
	else:
		l[i - 2] = 2
print(len(set(l)))
print(*l)


from collections import deque

def solve(x):
	if x <= 1:
		return False
	if x <= 3:
		return True
	if x % 2 == 0 or x % 3 == 0:
		return False
	i = 5
	while i * i <= x:
		if x % i == 0 or x % (i + 2) == 0:
			return False
		i += 6
	return True
n = int(input())
arr = deque()
for i in range(1, n + 1):
	arr.append(i + 1)
cnt = 0
res = deque()
for i in range(n):
	if solve(arr[i]) == False:
		cnt += 1
		res.append(2)
	else:
		res.append(1)
if cnt > 0:
	print(2)
	print(*res)
else:
	print(1)
	print(*res)


n = int(input())
a = [0] * (n + 2)

def max(a, b):
	if a > b:
		return a
	return b
mx = 1
for i in range(2, n + 2):
	if a[i]:
		mx = 2
		a[i] = 2
		continue
	j = i
	c = 1
	while j <= n + 1:
		a[j] += 1
		j += i
print(mx)
for i in range(2, n + 2):
	print(a[i], end=' ')


import math

def is_prime(n):
	raiz = math.floor(math.sqrt(n))
	if n == 2 or n == 3:
		return True
	for i in range(2, raiz + 1):
		if n % i == 0:
			return False
	return True
n = int(input())
primos = set()
count = 1
salida = ''
for i in range(2, n + 2):
	if is_prime(i):
		salida += '1 '
	else:
		salida += '2 '
		count = 2
print(count)
print(salida)


int_inp = lambda : int(input())
strng = lambda : input().strip()
strl = lambda : list(input().strip())
mul = lambda : map(int, input().strip().split())
mulf = lambda : map(float, input().strip().split())
seq = lambda : list(map(int, input().strip().split()))
import math
from collections import Counter, defaultdict
n = int(input()) + 1
a = [1] * (n + 1)
a[0] = 2
a[1] = 2
for i in range(2, n + 1):
	if a[i] == 1:
		for j in range(2, n // i + 1):
			a[i * j] = 2
print(1 if n == 2 or n == 3 else 2)
print(*a[2:])


import sys
n = int(input())
A = [True] * (n + 2)
found = False

def solve():
	for i in range(2, n + 2):
		if A[i] == True:
			for j in range(i + i, n + 2, i):
				A[j] = False
solve()
if n > 2:
	print(2)
else:
	print(1)
for i in range(2, n + 2):
	if A[i] == True:
		print(1, end=' ')
	else:
		print(2, end=' ')


def is_prime(x):
	k = 2
	while k * k <= x:
		if x % k == 0:
			return False
		k += 1
	return True
n = int(input())
col = 1
ans = [1] * n
for i in range(2, n + 2):
	if not is_prime(i):
		col = 2
		ans[i - 2] = 2
print(col)
print(*ans)


import sys
sys.setrecursionlimit(10000000)
mod = 10 ** 9 + 7
digl = ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']
ii = lambda : int(input())
si = lambda : input()
dgl = lambda : list(map(int, input()))
f = lambda : map(int, input().split())
il = lambda : list(map(int, input().split()))
ls = lambda : list(input())
n = ii()
l = [i for i in range(2, n + 2)]
lc = []

def isprime(n):
	return any((n % i == 0 for i in range(2, int(n ** 0.5) + 1)))
for i in l:
	lc.append(isprime(i) + 1)
print(max(lc))
print(*lc)


n = int(input())
primes = [0] * (n + 2)
res = []
for i in range(2, n + 2):
	if primes[i] == 0:
		res.append(1)
		for j in range(i, n + 2, i):
			primes[j] = 1
	else:
		res.append(2)
if n < 3:
	print(1)
else:
	print(2)
print(' '.join(map(str, res)))


import math
n = int(input())
if n < 3:
	print(1)
else:
	print(2)
for i in range(2, n + 2):
	sq = int(math.sqrt(i)) + 1
	for j in range(2, sq):
		if i % j == 0:
			print(2, end=' ')
			break
	else:
		print(1, end=' ')


import timeit

def seive(n):
	prime = [True for i in range(n + 2)]
	prime[1] = False
	prime[0] = False
	for p in range(2, int(n ** 0.5) + 1):
		if prime[p]:
			for i in range(p * 2, n + 1, p):
				prime[i] = False
	return prime
n = int(input())
primes = seive(n + 2)
if n > 2:
	print('2')
else:
	print('1')
for i in range(2, n + 2):
	if primes[i] == True:
		primes[i] = 1
	else:
		primes[i] = 2
print(' '.join([str(primes[i]) for i in range(2, n + 2)]))


n = int(input())
sieve = [0 for x in range(n + 5)]
for i in range(2, n + 2):
	if sieve[i] is 0:
		j = 2 * i
		while j <= n + 1:
			sieve[j] = 1
			j += i
if n > 2:
	print(2)
else:
	print(1)
for s in range(2, n + 2):
	if sieve[s] is 0:
		print(1, end=' ')
	else:
		print(2, end=' ')


n = int(input())
if n == 1:
	print(1)
	print(1)
elif n == 2:
	print(1)
	print(1, 1)
else:
	print(2)
	np = [False for i in range(n + 1 + 1)]
	for i in range(2, n + 1 + 1):
		if np[i]:
			print(2, end=' ')
		else:
			print(1, end=' ')
			for j in range(i + i, n + 1 + 1, i):
				np[j] = True
	print()


x = int(input())
p = []
if x > 2:
	print(2)
else:
	print(1)
for i in range(2, x + 2):
	new = False
	for j in p:
		if not i % j:
			new = True
			break
	if new:
		print(2, end=' ')
	else:
		print(1, end=' ')
		p.append(i)


sieve = [False for _ in range(100005)]
n = int(input())
for i in range(2, n + 2):
	if not sieve[i]:
		j = 2 * i
		while j <= n + 1:
			sieve[j] = True
			j += i
if n > 2:
	print('2')
else:
	print('1')
for i in range(2, n + 2):
	print('1' if not sieve[i] else '2', end=' ')


x = [0] * 100010
for i in range(2, 100010):
	if x[i] == 0:
		j = 2 * i
		while j < 100010:
			x[j] = 1
			j += i
n = int(input())
if n <= 2:
	print(1)
	if n == 1:
		print(1)
	else:
		print(1, 1)
	exit()
print(2)
for i in range(2, n + 2):
	if x[i] == 0:
		print(1, end=' ')
	else:
		print(2, end=' ')
print()


n = int(input())
li = [0] * (n + 2)
li[0] = li[1] = 10 ** 6
for i in range(2, n + 1 // 2 + 1):
	if li[i] == 0:
		for j in range(i * 2, n + 2, i):
			li[j] += 1
value = n + 2 - li.count(0) - 2
if value >= 1:
	value = 2
else:
	value = 1
print(value)
for i in range(2, n + 2):
	if li[i] == 0:
		print(1, end=' ')
	else:
		print(2, end=' ')


n = int(input())
p = [1] * (n + 2)
if n <= 2:
	print(1)
else:
	print(2)
for i in range(2, n + 2):
	if p[i] == 1:
		for j in range(2, (n + 1) // i + 1):
			p[i * j] = 2
print(*p[2:n + 2])


n = int(input())
l = [1] * 1000001
l[0] = 0
l[1] = 0
for i in range(2, 1000001):
	if l[i] == 1:
		for j in range(i * i, 1000001, i):
			l[j] = 2
if n > 2:
	print(2)
else:
	print(1)
print(*l[2:n + 2])


from math import sqrt

class Solution:

	def countPrimes(self, n):
		prime_array = [1] * (n + 2)
		count = 0
		for i in range(2, (n + 2) // 2 + 1):
			if prime_array[i] == 1:
				for j in range(2, (n + 1) // i + 1):
					if prime_array[i * j] < 2:
						prime_array[i * j] += 1
		print(max(prime_array))
		for i in range(2, n + 2):
			print(prime_array[i], end=' ')
val = int(input())
a = Solution()
a.countPrimes(val)


n = int(input())
if n <= 2:
	print(1)
else:
	print(2)
primes = []
for i in range(2, n + 2):
	for p in primes:
		if i % p == 0:
			print(2, end=' ')
			break
	else:
		print(1, end=' ')
		primes.append(i)


from math import sqrt
n = int(input())
nums = [1] * n
for i in range(2, n + 2):
	if nums[i - 2]:
		for j in range(2, (n + 1) // i + 1):
			nums[i * j - 2] = 0
if n > sum(nums):
	print(2)
else:
	print(1)
for i in range(n):
	if nums[i]:
		print(1, end=' ')
	else:
		print(2, end=' ')


import sys
n = int(input())
col = [1 for i in range(n + 2)]
curprime = 1
ans = 0
if n <= 2:
	print(1)
	for i in range(n):
		print(1, end=' ')
	return
while True:
	prime = curprime + 1
	while prime <= n + 1 and col[prime] == 2:
		prime += 1
	if prime >= n + 1:
		break
	for i in range(prime + prime, n + 2, prime):
		col[i] = 2
	curprime = prime
print(2)
for i in range(2, n + 2):
	print(col[i], end=' ')


def Sieve(n):
	l = [True for i in range(n + 1)]
	p = 2
	while p * p <= n:
		if l[p]:
			for i in range(p * p, n + 1, p):
				l[i] = False
		p += 1
	for i in range(n + 1):
		if l[i]:
			l[i] = 1
		else:
			l[i] = 2
	return l
n = int(input())
if n == 1:
	print(1)
	print(1)
elif n == 2:
	print(1)
	print(1, 1)
else:
	print(2)
	print(*Sieve(n + 1)[2:])


from typing import List
import math

class Solution:

	def prime_factors(self, n) -> int:
		f_map = {}
		self.smallest_prime_factor = [-1] * (n + 2)
		self.primes_or_not = [1] * (n + 2)
		self.primes_or_not[1] = 0
		for i in range(2, int(math.sqrt(n)) + 1):
			if self.primes_or_not[i] == 1:
				j = i
				while i * j <= n:
					if self.primes_or_not[i * j] == 1:
						self.primes_or_not[i * j] = 0
					j += 1
		self.primes = [i for i in range(2, n + 1) if self.primes_or_not[i] == 1]
sol = Solution()
sol.prime_factors(10 ** 5 + 2)
n = int(input())
ans = []
for i in range(2, n + 2):
	val = 1 if sol.primes_or_not[i] == 1 else 2
	ans.append(str(val))
if n <= 2:
	print(1)
else:
	print(2)
print(' '.join(ans))


class node:

	def __init__(self):
		self.data = 1
		self.boo = True

def clr_count(n):
	li = []
	for z in range(n + 2):
		li.append(node())
	c = 1
	for i in range(2, int((n + 2) ** (1 / 2)) + 1):
		if li[i].boo == True:
			for j in range(i * i, len(li), i):
				li[j].boo = False
				if li[i].data == li[j].data:
					if c == li[j].data:
						c += 1
				li[j].data = c
	print(c)
	for i in li[2:]:
		print(i.data, end=' ')
n = int(input())
clr_count(n)


n = int(input())
l = list(range(2, n + 2))
l = [0, 0] + l
for i in range(2, n + 2):
	if 2 * l[i] > n + 1 or (i != 2 and l[i] == 2):
		continue
	for j in range(2 * l[i], n + 2, l[i]):
		if l[j] > 2:
			l[j] = 2
for i in range(2, n + 2):
	if l[i] > 2:
		l[i] = 1
l[2] = 1
print(len(set(l)) - 1)
for i in range(2, n + 2):
	print(l[i], end=' ')


import math
n = int(input())
prime_num = [1] * (n + 2)
prime_num[1] = 0
for i in range(2, math.ceil(n ** 0.5) + 1):
	if prime_num[i]:
		for j in range(i ** 2, n + 2, i):
			prime_num[j] = 0
if n > 2:
	print(2)
	for i in range(2, n + 2):
		if prime_num[i]:
			print(1, end=' ')
		else:
			print(2, end=' ')
else:
	print(1)
	for i in range(n):
		print(1, end=' ')


n = int(input())
C = [1] * n
for i in range(2, 1 + int((n + 1) ** 0.5)):
	for j in range(i * i, n + 2, i):
		C[j - 2] = 2
print(2 - (n < 3))
print(*C)


n = int(input())
p = [0, 1] + [i + 1 for i in range(1, n + 1)]
ans = [0] + [1] * (n + 1)
m = 2
p[1] = 0
while m < n:
	if p[m] != 0:
		j = m * 2
		ans[m] = 1
		c = 2
		while j <= n + 1:
			p[j] = 0
			if ans[j] == 1:
				ans[j] = c
			j += m
	m += 1
print(max(ans[2:]))
print(*ans[2:])


n = int(input())
a = [True] * (n + 2)
a[0] = a[1] = False
for i in range(2, n + 2):
	if a[i] == True:
		m = 2 * i
		while m < n + 2:
			a[m] = False
			m = m + i
na = []
for i in range(2, n + 2):
	if a[i] == True:
		na.append(1)
	else:
		na.append(2)
if n > 2:
	print(2)
else:
	print(1)
for i in range(len(na)):
	print(na[i], end=' ')


def f(n):
	if n == 2:
		return True
	for i in range(2, int(n ** 0.5) + 1):
		if n % i == 0:
			return False
	return True
s = int(input())
if s > 2:
	print(2)
	q = [1] * s
	for i in range(2, s + 2):
		if f(i):
			q[i - 2] = 2
	print(' '.join([str(w) for w in q]))
elif s == 1:
	print(1)
	print(1)
else:
	print(1)
	print('1 1')


def SieveOfEratosthenes(n):
	prime = [True for i in range(n + 1)]
	p = 2
	while p * p <= n:
		if prime[p] == True:
			for i in range(p * 2, n + 1, p):
				prime[i] = False
		p += 1
	nuPrime = prime[2:n]
	return nuPrime
n = int(input())
prime = SieveOfEratosthenes(n + 2)
if n == 1:
	print(1)
	print(1)
elif n == 2:
	print(1)
	print('1 1')
else:
	print(2)
	for i in range(n):
		if prime[i]:
			print('1 ', end='')
		else:
			print('2 ', end='')


from math import ceil

def sieve_wheel_30(N):
	__smallp = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997)
	wheel = (2, 3, 5)
	const = 30
	if N < 2:
		return []
	if N <= const:
		pos = 0
		while __smallp[pos] <= N:
			pos += 1
		return list(__smallp[:pos])
	offsets = (7, 11, 13, 17, 19, 23, 29, 1)
	p = [2, 3, 5]
	dim = 2 + N // const
	tk1 = [True] * dim
	tk7 = [True] * dim
	tk11 = [True] * dim
	tk13 = [True] * dim
	tk17 = [True] * dim
	tk19 = [True] * dim
	tk23 = [True] * dim
	tk29 = [True] * dim
	tk1[0] = False
	d = {}
	for x in offsets:
		for y in offsets:
			res = x * y % const
			if res in offsets:
				d[x, res] = y
	tmptk = {1: tk1, 7: tk7, 11: tk11, 13: tk13, 17: tk17, 19: tk19, 23: tk23, 29: tk29}
	(pos, prime, lastadded, stop) = (0, 0, 0, int(ceil(N ** 0.5)))

	def del_mult(tk, start, step):
		for k in range(start, len(tk), step):
			tk[k] = False
	cpos = const * pos
	while prime < stop:
		if tk7[pos]:
			prime = cpos + 7
			p.append(prime)
			lastadded = 7
			for off in offsets:
				tmp = d[7, off]
				start = pos + prime if off == 7 else prime * (const * (pos + 1 if tmp < 7 else 0) + tmp) // const
				del_mult(tmptk[off], start, prime)
		if tk11[pos]:
			prime = cpos + 11
			p.append(prime)
			lastadded = 11
			for off in offsets:
				tmp = d[11, off]
				start = pos + prime if off == 11 else prime * (const * (pos + 1 if tmp < 11 else 0) + tmp) // const
				del_mult(tmptk[off], start, prime)
		if tk13[pos]:
			prime = cpos + 13
			p.append(prime)
			lastadded = 13
			for off in offsets:
				tmp = d[13, off]
				start = pos + prime if off == 13 else prime * (const * (pos + 1 if tmp < 13 else 0) + tmp) // const
				del_mult(tmptk[off], start, prime)
		if tk17[pos]:
			prime = cpos + 17
			p.append(prime)
			lastadded = 17
			for off in offsets:
				tmp = d[17, off]
				start = pos + prime if off == 17 else prime * (const * (pos + 1 if tmp < 17 else 0) + tmp) // const
				del_mult(tmptk[off], start, prime)
		if tk19[pos]:
			prime = cpos + 19
			p.append(prime)
			lastadded = 19
			for off in offsets:
				tmp = d[19, off]
				start = pos + prime if off == 19 else prime * (const * (pos + 1 if tmp < 19 else 0) + tmp) // const
				del_mult(tmptk[off], start, prime)
		if tk23[pos]:
			prime = cpos + 23
			p.append(prime)
			lastadded = 23
			for off in offsets:
				tmp = d[23, off]
				start = pos + prime if off == 23 else prime * (const * (pos + 1 if tmp < 23 else 0) + tmp) // const
				del_mult(tmptk[off], start, prime)
		if tk29[pos]:
			prime = cpos + 29
			p.append(prime)
			lastadded = 29
			for off in offsets:
				tmp = d[29, off]
				start = pos + prime if off == 29 else prime * (const * (pos + 1 if tmp < 29 else 0) + tmp) // const
				del_mult(tmptk[off], start, prime)
		pos += 1
		cpos = const * pos
		if tk1[pos]:
			prime = cpos + 1
			p.append(prime)
			lastadded = 1
			for off in offsets:
				tmp = d[1, off]
				start = pos + prime if off == 1 else prime * (const * pos + tmp) // const
				del_mult(tmptk[off], start, prime)
	if lastadded == 1:
		p.pop()
	while pos < len(tk1):
		cpos = const * pos
		if tk1[pos]:
			p.append(cpos + 1)
		if tk7[pos]:
			p.append(cpos + 7)
		if tk11[pos]:
			p.append(cpos + 11)
		if tk13[pos]:
			p.append(cpos + 13)
		if tk17[pos]:
			p.append(cpos + 17)
		if tk19[pos]:
			p.append(cpos + 19)
		if tk23[pos]:
			p.append(cpos + 23)
		if tk29[pos]:
			p.append(cpos + 29)
		pos += 1
	pos = len(p) - 1
	while p[pos] > N:
		pos -= 1
	if pos < len(p) - 1:
		del p[pos + 1:]
	return p
n = int(input())
primes = set(sieve_wheel_30(n // 2 + 2))
if n < 3:
	print(1)
else:
	print(2)
for i in range(2, n + 2):
	if i in primes:
		print(1, end=' ')
	else:
		print(2, end=' ')


arr = []

def SieveOfEratosthenes(n):
	prime = [True for i in range(n + 1)]
	p = 2
	while p * p <= n:
		if prime[p] == True:
			for i in range(p * 2, n + 1, p):
				prime[i] = False
		p += 1
	prime[0] = False
	prime[1] = False
	for p in range(n + 1):
		if prime[p]:
			arr.append(p)
SieveOfEratosthenes(10 ** 5)
n = int(input())
if n == 1:
	print(1)
	print(1)
	exit()
if n == 2:
	print(1)
	print(1, 1)
	exit()
print(2)
ans = []
for i in range(2, n + 2):
	if i in arr:
		ans.append(1)
	else:
		ans.append(2)
print(*ans)


import math as ma
n = int(input())
maxN = 100001
primes = [0] * (n + 2)
color = [0] * (n + 2)
c = 1
for p in range(2, n + 2):
	if primes[p] == 0:
		for l in range(p, n + 2 - p, p):
			primes[p + l] = 1
ncolors = 1
for p in range(2, n + 2):
	if primes[p] == 0:
		color[p] = 1
	else:
		color[p] = 2
		ncolors = 2
print(ncolors)
for p in range(2, n + 2):
	print(color[p], end=' ')


import sys
input = sys.stdin.readline

def ceil(x):
	if x != int(x):
		x = int(x) + 1
	return x

def factorial(x, m):
	val = 1
	while x > 0:
		val = val * x % m
		x -= 1
	return val

def fact(x):
	val = 1
	while x > 0:
		val *= x
		x -= 1
	return val

def swaparr(arr, a, b):
	temp = arr[a]
	arr[a] = arr[b]
	arr[b] = temp

def gcd(a, b):
	if b == 0:
		return a
	return gcd(b, a % b)

def lcm(a, b):
	return a * b // gcd(a, b)

def nCr(n, k):
	if k > n:
		return 0
	if k > n - k:
		k = n - k
	res = 1
	for i in range(k):
		res = res * (n - i)
		res = res / (i + 1)
	return int(res)

def upper_bound(a, x, lo=0, hi=None):
	if hi == None:
		hi = len(a)
	while lo < hi:
		mid = (lo + hi) // 2
		if a[mid] < x:
			lo = mid + 1
		else:
			hi = mid
	return lo

def primefs(n):
	primes = {}
	while n % 2 == 0 and n > 0:
		primes[2] = primes.get(2, 0) + 1
		n = n // 2
	for i in range(3, int(n ** 0.5) + 2, 2):
		while n % i == 0 and n > 0:
			primes[i] = primes.get(i, 0) + 1
			n = n // i
	if n > 2:
		primes[n] = primes.get(n, 0) + 1
	return primes

def power(x, y, p):
	res = 1
	x = x % p
	if x == 0:
		return 0
	while y > 0:
		if y & 1 == 1:
			res = res * x % p
		y = y >> 1
		x = x * x % p
	return res

def swap(a, b):
	temp = a
	a = b
	b = temp
	return (a, b)

def find(x, link):
	p = x
	while p != link[p]:
		p = link[p]
	while x != p:
		nex = link[x]
		link[x] = p
		x = nex
	return p

def union(x, y, link, size):
	x = find(x, link)
	y = find(y, link)
	if size[x] < size[y]:
		(x, y) = swap(x, y)
	if x != y:
		size[x] += size[y]
		link[y] = x

def sieve(n):
	prime = [True for i in range(n + 1)]
	(prime[0], prime[1]) = (False, False)
	p = 2
	while p * p <= n:
		if prime[p] == True:
			for i in range(p * p, n + 1, p):
				prime[i] = False
		p += 1
	return prime

def phi(n):
	result = n
	p = 2
	while p * p <= n:
		if n % p == 0:
			while n % p == 0:
				n = n // p
			result = result * (1.0 - 1.0 / float(p))
		p = p + 1
	if n > 1:
		result = result * (1.0 - 1.0 / float(n))
	return int(result)
MAXN = int(100000.0 + 5)

def spf_sieve():
	spf[1] = 1
	for i in range(2, MAXN):
		spf[i] = i
	for i in range(4, MAXN, 2):
		spf[i] = 2
	for i in range(3, ceil(MAXN ** 0.5), 2):
		if spf[i] == i:
			for j in range(i * i, MAXN, i):
				if spf[j] == j:
					spf[j] = i
spf = [0 for i in range(MAXN)]

def factoriazation(x):
	res = []
	for i in range(2, int(x ** 0.5) + 1):
		while x % i == 0:
			res.append(i)
			x //= i
	if x != 1:
		res.append(x)
	return res

def factors(n):
	res = []
	for i in range(1, int(n ** 0.5) + 1):
		if n % i == 0:
			res.append(i)
			res.append(n // i)
	return list(set(res))

def int_array():
	return list(map(int, input().strip().split()))

def float_array():
	return list(map(float, input().strip().split()))

def str_array():
	return input().strip().split()
MOD = int(1000000000.0) + 7
CMOD = 998244353
INF = float('inf')
NINF = -float('inf')
from itertools import permutations
import math
from bisect import bisect_left

def solve():
	n = int(input())
	if n <= 2:
		print(1)
		print(*[1] * n)
		return
	primes = sieve(n + 1)
	val = []
	for x in primes[2:]:
		if x:
			val.append(1)
		else:
			val.append(2)
	print(2)
	print(*val)
for _ in range(1):
	solve()


import math
n = int(input())
is_Prime = [True for i in range(n + 2)]
limit = int(math.sqrt(len(is_Prime)))

def displaySieve():
	for i in range(len(is_Prime)):
		print(i, is_Prime[i])
for i in range(2, limit + 1, 1):
	if is_Prime[i]:
		for j in range(i + i, len(is_Prime), i):
			is_Prime[j] = False
output = []
if False in is_Prime:
	print(2)
	for i in range(2, len(is_Prime), 1):
		if is_Prime[i]:
			output.append('1')
		else:
			output.append('2')
else:
	print('1')
	for i in range(2, len(is_Prime), 1):
		output.append('1')
print(' '.join(output))


n = int(input())
ans = [1 for _ in range(n + 2)]
for i in range(2, int(n ** 0.5) + 2):
	if ans[i] == 2:
		continue
	for j in range(i * 2, n + 2, i):
		ans[j] = 2
print(len(set(ans)))
print(*ans[2:])


n = int(input())
if n <= 2:
	print(1)
else:
	print(2)
n += 2
result = ['1'] * n
for i in range(2, int(n ** 0.5) + 1):
	j = 0
	while i ** 2 + j * i < n:
		result[i ** 2 + j * i] = '2'
		j += 1
print(' '.join(result[2:]))


import os
import sys
from math import *
from collections import *
from bisect import *
from io import BytesIO, IOBase

def vsInput():
	sys.stdin = open('input.txt', 'r')
	sys.stdout = open('output.txt', 'w')
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')

def value():
	return tuple(map(int, input().split()))

def array():
	return [int(i) for i in input().split()]

def Int():
	return int(input())

def Str():
	return input()

def arrayS():
	return [i for i in input().split()]

def prime(n):
	color = [1] * (n + 1)
	c = 1
	pr = [True] * (n + 1)
	pr[0] = False
	pr[1] = False
	p = 2
	while p * p <= n:
		if pr[p] == True:
			color[p] = c
			ct = 2
			for j in range(p * p, n + 1, p):
				color[j] = ct
				pr[j] = False
		p += 1
	return color[2:]
n = Int()
ans = prime(n + 1)
print(max(ans))
print(*ans)


import sys
LI = lambda : list(map(int, sys.stdin.readline().split()))
MI = lambda : map(int, sys.stdin.readline().split())
SI = lambda : sys.stdin.readline().strip('\n')
II = lambda : int(sys.stdin.readline())
n = II()
if n < 3:
	print(1)
	print(*[1] * n)
	exit()
ok = [2] * (n + 2)
for i in range(2, n + 2):
	if ok[i] == 2:
		for j in range(i + i, n + 2, i):
			ok[j] = 1
print(2)
print(*ok[2:])


userInput = int(input())

def colorPrimeSieve(n):
	x = [0] * (n - 1)
	primes = []
	for i in range(2, n + 1):
		if x[i - 2] == 0:
			x[i - 2] = 1
			for j in range(i, int(n / i) + 1):
				x[i * j - 2] = 2
	return x
primes = colorPrimeSieve(userInput + 1)
if userInput > 2:
	print(2)
else:
	print(1)
outputColor = ''
for x in primes:
	outputColor = outputColor + str(x) + ' '
print(outputColor)


import math

def soe(n):
	is_prime = [True for i in range(n + 2)]
	is_prime[0] = False
	is_prime[1] = False
	color = [1 for i in range(n + 2)]
	for i in range(2, n + 2):
		if is_prime[i]:
			for j in range(2 * i, n + 2, i):
				is_prime[j] = False
				color[j] = 2
	return color
colors = soe(pow(10, 5))
n = int(input())
if n > 2:
	print(2)
else:
	print(1)
print(*colors[2:n + 2])


def is_prime(n):
	i = 2
	while i * i <= n:
		if n % i == 0:
			return 2
		i += 1
	return 1
n = int(input())
ans = []
for i in range(2, n + 2):
	ans.append(is_prime(i))
print(len(set(ans)))
print(*ans)