Given n, find n consecutive positive integers. However, all numbers must have divisors other than 1 and the number itself.

Hint

In Sample Output 2, 8, 9 and 10 are selected as three consecutive integers.
The second and third lines output 3, as a divisor of 9, and the fourth line outputs 5, as a divisor of 10.



Input

The input is given in the following format.


n


The input meets the following constraints.
1 ≤ n ≤ 1,500

Output

Print the smallest of the n consecutive positive integers you choose on the first line.
Output the divisor for each value from the 2nd line to the n + 1 line.
Any value may be output unless the divisor is 1 or the number itself.
Let x be the number output on the first line, and output the divisor of x + i-2 on the i line.

The output value must not exceed 5,000 digits.

Examples

Input

2


Output

8
2
3


Input

3


Output

8
2
3
5

Source: aizu | Difficulty: UNKNOWN_DIFFICULTY


Solutions:
import sys
n = int(input())
if n == 1:
	print(4, 2, sep='\n')
	sys.exit(0)
ans = 1
for i in range(2, n + 2):
	ans *= i
print(ans + 2)
for i in range(2, n + 2):
	print(i)


import sys
import os
import math
n = int(input())
if n == 1:
	print(4)
	print(2)
elif n == 2:
	print(8)
	print(4)
	print(3)
else:
	a = 1
	for i in range(1, n + 2):
		a *= i
	print(a - n - 1)
	for i in range(n + 1, 1, -1):
		print(i)


n = int(input())
if n == 1:
	print(4)
	print(2)
elif n == 2:
	print(14)
	print(2)
	print(3)
else:
	ans = 1
	for i in range(2, 2 + n):
		ans *= i
	print(ans - n - 1)
	for i in range(n + 1, 1, -1):
		print(i)


def main():
	num = 2
	i = 3
	for _ in range(1500 // 2):
		num *= i
		i += 2
	n = int(input())
	print(num + 2)
	for i in range(n):
		a = i + 2
		if i % 2 == 0:
			a = 2
		print(a)
main()


import sys
sys.setrecursionlimit(1000000)
memo = {0: 1}

def fact(num):
	if num in memo:
		return memo[num]
	memo[num] = num * fact(num - 1)
	return memo[num]
n = int(input())
print(fact(n + 1) + 2)
for i in range(n):
	print(i + 2)


import math
n = int(input())
print(math.factorial(n + 1) + 2)
for i in range(2, n + 2):
	print(i)


from functools import reduce
n = int(input())
n1500 = 48119977967797748601669900935813797818348080406726138081308559411630575189001095591292230585206733851868464009619343585194052091124618166270271481881393331431627962810299844149333789044689395510487167879769325303699470467829234399263326545652860748605075746366928323606645492277541120083438086727369377887676000211405318480244354207419604864176969950581435222198851194568984095705945549589054568321792338919149442985919957734792959402499096845643020401869381175603964424333222114125974374817804242633309769804293952870034619354125014210045647664063240162007560108665290568646128342557147350985358724154623253371867470765120422073867963935775258692109753041762094343569050497470353531764481503174750911858230906998361066084787758316110585736013365377431860738572261325738233656835271947352695180865573043834027955539012765489372645042504406597752357481931532872356635411224578334040522294746402829585458478708778346379431862368824819009177091444034885941394319343910223168655869761799669075059527608502465593181398566214786801211651657222004123456498258513120359126022843038535083709796101565934859483203933443308601475813108363074118562404412420191947127585482919172173045961122122701434297870691932154082986945954748251105782181586397275820342101470457300633590139512919549474113721711616912519714191760699935509810254849967087635936181176363954224186031346682928878492872249485456690138831610135377916327940503701400290125509132140782614640495733518048670983360134097860364762638658894873174499870133559364805443430831459505987809215393353387232078177562975021460595422358573128085417162336030235138652735438053034531962620811566019896879275257163988352090874930346115518331202927263708446729394381879888839549731876978682249320628599631628662375508826209854754631984276392670919216923002770077734756077549035942976209159416211581439461484509549370357486770276807687544580164314647595031368948490282897173328013518435758700056425922638411889496527975846052717958044813737086806600171993703579485864029383208714528950303253881360812631162134750100307772634337467012820470715650810714689905121432259528505483053930402217400686061612471659630192434864094539828085677465383026128353771071152304197549798870706139893609140045659756285435787771636258253666592102151236142132724425850991205720020493660580896600891888594659612927724357866265934517615841298789154462249169688860092640284756382431746120357767933119589280468687348061788072986362788582227019465263474828590646048451070702923434422714349595857654843699542321849363652767771978314681013589442955219879702008068934096624650625769705233333462826013860098698155180331145365652453482955497979915586438474687345677874451117702250441711504844638414485210092261397271970571029038581873069951161330495772310508760528249706514238384269808639507080418298318311361373628512041716415196868334254119137139589149597210032153545941114666530498906529240798164804007394775927836045668573993316428972539932745757171947402454257142633700815922407278403640595355142075599446056337986717212316223257763412164180899532722039383244462511410346646148863397237096276822656157561194665545757017429842404840309758925618650507921043007241637877939825811059339138925526124514467627126548126795078784022672860886251974581362141782786407402896309678008909663263987018538107050886193489012497405005820727271232733728141775132722013860591169620692789290456794698409808557447756701311883266010859016027592252397754508251628808293537776536569608111330584797160694847898923196743970244451842702266403326317319092117151143971679500042590269255093130215984418097418435474300467281949798227102529873732749027992079700287275900856241172902880909546551703263202853584498085358955307673717177961902081098618729046348849060249600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002
print(n1500)
for i in range(0, n):
	print(i + 2)