Vasya had an array of $n$ integers, each element of the array was from $1$ to $n$. He chose $m$ pairs of different positions and wrote them down to a sheet of paper. Then Vasya compared the elements at these positions, and wrote down the results of the comparisons to another sheet of paper. For each pair he wrote either "greater", "less", or "equal".

After several years, he has found the first sheet of paper, but he couldn't find the second one. Also he doesn't remember the array he had. In particular, he doesn't remember if the array had equal elements. He has told this sad story to his informatics teacher Dr Helen.

She told him that it could be the case that even if Vasya finds his second sheet, he would still not be able to find out whether the array had two equal elements. 

Now Vasya wants to find two arrays of integers, each of length $n$. All elements of the first array must be distinct, and there must be two equal elements in the second array. For each pair of positions Vasya wrote at the first sheet of paper, the result of the comparison must be the same for the corresponding elements of the first array, and the corresponding elements of the second array. 

Help Vasya find two such arrays of length $n$, or find out that there are no such arrays for his sets of pairs.


-----Input-----

The first line of input contains two integers $n$, $m$ — the number of elements in the array and number of comparisons made by Vasya ($1 \le n \le 100\,000$, $0 \le m \le 100\,000$).

Each of the following $m$ lines contains two integers $a_i$, $b_i$  — the positions of the $i$-th comparison ($1 \le a_i, b_i \le n$; $a_i \ne b_i$). It's guaranteed that any unordered pair is given in the input at most once.


-----Output-----

The first line of output must contain "YES" if there exist two arrays, such that the results of comparisons would be the same, and all numbers in the first one are distinct, and the second one contains two equal numbers. Otherwise it must contain "NO".

If the arrays exist, the second line must contain the array of distinct integers, the third line must contain the array, that contains at least one pair of equal elements. Elements of the arrays must be integers from $1$ to $n$.


-----Examples-----
Input
1 0

Output
NO

Input
3 1
1 2

Output
YES
1 3 2 
1 3 1 

Input
4 3
1 2
1 3
2 4

Output
YES
1 3 4 2 
1 3 4 1

Difficulty: MEDIUM_HARD
Tags: Constructive algorithms

Starter code:

Solutions:
(n, m) = map(int, input().split())
c = [[0, i, []] for i in range(n)]
for i in range(m):
	(a, b) = map(int, input().split())
	c[a - 1][0] += 1
	c[a - 1][2].append(b - 1)
	c[b - 1][0] += 1
	c[b - 1][2].append(a - 1)
if n == 1:
	print('NO')
else:
	ans = n * (n - 1) // 2
	if m >= ans:
		print('NO')
	else:
		c.sort(key=lambda x: x[0])
		vall = c[0][1]
		c[0][2].append(vall)
		c[0][2].sort()
		final = -1
		for i in range(len(c[0][2])):
			if c[0][2][i] != i and i != vall:
				final = i
				break
		if final == -1:
			final = len(c[0][2])
		print('YES')
		flag = True
		s1 = ''
		s2 = ''
		val = 1
		temp = min(vall, final)
		temp2 = max(vall, final)
		for i in range(n):
			if i == temp:
				s1 += str(n) + ' '
				s2 += str(n) + ' '
			elif i == temp2:
				s1 += str(n - 1) + ' '
				s2 += str(n) + ' '
			else:
				s1 += str(val) + ' '
				s2 += str(val) + ' '
				val += 1
		print(s1[:-1])
		print(s2[:-1])


import math
import heapq, bisect
import sys
from collections import deque, defaultdict
from fractions import Fraction
import sys
mod = 10 ** 9 + 7
mod1 = 998244353
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
sys.setrecursionlimit(300000)

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')

class TreeNode:

	def __init__(self, k, v):
		self.key = k
		self.value = v
		self.left = None
		self.right = None
		self.parent = None
		self.height = 1
		self.num_left = 1
		self.num_total = 1

class AvlTree:

	def __init__(self):
		self._tree = None

	def add(self, k, v):
		if not self._tree:
			self._tree = TreeNode(k, v)
			return
		node = self._add(k, v)
		if node:
			self._rebalance(node)

	def _add(self, k, v):
		node = self._tree
		while node:
			if k < node.key:
				if node.left:
					node = node.left
				else:
					node.left = TreeNode(k, v)
					node.left.parent = node
					return node.left
			elif node.key < k:
				if node.right:
					node = node.right
				else:
					node.right = TreeNode(k, v)
					node.right.parent = node
					return node.right
			else:
				node.value = v
				return

	@staticmethod
	def get_height(x):
		return x.height if x else 0

	@staticmethod
	def get_num_total(x):
		return x.num_total if x else 0

	def _rebalance(self, node):
		n = node
		while n:
			lh = self.get_height(n.left)
			rh = self.get_height(n.right)
			n.height = max(lh, rh) + 1
			balance_factor = lh - rh
			n.num_total = 1 + self.get_num_total(n.left) + self.get_num_total(n.right)
			n.num_left = 1 + self.get_num_total(n.left)
			if balance_factor > 1:
				if self.get_height(n.left.left) < self.get_height(n.left.right):
					self._rotate_left(n.left)
				self._rotate_right(n)
			elif balance_factor < -1:
				if self.get_height(n.right.right) < self.get_height(n.right.left):
					self._rotate_right(n.right)
				self._rotate_left(n)
			else:
				n = n.parent

	def _remove_one(self, node):
		replacement = node.left or node.right
		if node.parent:
			if AvlTree._is_left(node):
				node.parent.left = replacement
			else:
				node.parent.right = replacement
			replacement.parent = node.parent
			node.parent = None
		else:
			self._tree = replacement
			replacement.parent = None
		node.left = None
		node.right = None
		node.parent = None
		self._rebalance(replacement)

	def _remove_leaf(self, node):
		if node.parent:
			if AvlTree._is_left(node):
				node.parent.left = None
			else:
				node.parent.right = None
			self._rebalance(node.parent)
		else:
			self._tree = None
		node.parent = None
		node.left = None
		node.right = None

	def remove(self, k):
		node = self._get_node(k)
		if not node:
			return
		if AvlTree._is_leaf(node):
			self._remove_leaf(node)
			return
		if node.left and node.right:
			nxt = AvlTree._get_next(node)
			node.key = nxt.key
			node.value = nxt.value
			if self._is_leaf(nxt):
				self._remove_leaf(nxt)
			else:
				self._remove_one(nxt)
			self._rebalance(node)
		else:
			self._remove_one(node)

	def get(self, k):
		node = self._get_node(k)
		return node.value if node else -1

	def _get_node(self, k):
		if not self._tree:
			return None
		node = self._tree
		while node:
			if k < node.key:
				node = node.left
			elif node.key < k:
				node = node.right
			else:
				return node
		return None

	def get_at(self, pos):
		x = pos + 1
		node = self._tree
		while node:
			if x < node.num_left:
				node = node.left
			elif node.num_left < x:
				x -= node.num_left
				node = node.right
			else:
				return (node.key, node.value)
		raise IndexError('Out of ranges')

	@staticmethod
	def _is_left(node):
		return node.parent.left and node.parent.left == node

	@staticmethod
	def _is_leaf(node):
		return node.left is None and node.right is None

	def _rotate_right(self, node):
		if not node.parent:
			self._tree = node.left
			node.left.parent = None
		elif AvlTree._is_left(node):
			node.parent.left = node.left
			node.left.parent = node.parent
		else:
			node.parent.right = node.left
			node.left.parent = node.parent
		bk = node.left.right
		node.left.right = node
		node.parent = node.left
		node.left = bk
		if bk:
			bk.parent = node
		node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1
		node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right)
		node.num_left = 1 + self.get_num_total(node.left)

	def _rotate_left(self, node):
		if not node.parent:
			self._tree = node.right
			node.right.parent = None
		elif AvlTree._is_left(node):
			node.parent.left = node.right
			node.right.parent = node.parent
		else:
			node.parent.right = node.right
			node.right.parent = node.parent
		bk = node.right.left
		node.right.left = node
		node.parent = node.right
		node.right = bk
		if bk:
			bk.parent = node
		node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1
		node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right)
		node.num_left = 1 + self.get_num_total(node.left)

	@staticmethod
	def _get_next(node):
		if not node.right:
			return node.parent
		n = node.right
		while n.left:
			n = n.left
		return n

class SegmentTree1:

	def __init__(self, data, default=0, func=lambda a, b: max(a, b)):
		self._default = default
		self._func = func
		self._len = len(data)
		self._size = _size = 1 << (self._len - 1).bit_length()
		self.data = [default] * (2 * _size)
		self.data[_size:_size + self._len] = data
		for i in reversed(range(_size)):
			self.data[i] = func(self.data[i + i], self.data[i + i + 1])

	def __delitem__(self, idx):
		self[idx] = self._default

	def __getitem__(self, idx):
		return self.data[idx + self._size]

	def __setitem__(self, idx, value):
		idx += self._size
		self.data[idx] = value
		idx >>= 1
		while idx:
			self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
			idx >>= 1

	def __len__(self):
		return self._len

	def query(self, start, stop):
		if start == stop:
			return self.__getitem__(start)
		stop += 1
		start += self._size
		stop += self._size
		res = self._default
		while start < stop:
			if start & 1:
				res = self._func(res, self.data[start])
				start += 1
			if stop & 1:
				stop -= 1
				res = self._func(res, self.data[stop])
			start >>= 1
			stop >>= 1
		return res

	def __repr__(self):
		return 'SegmentTree({0})'.format(self.data)

class SegmentTree:

	def __init__(self, data, default=0, func=lambda a, b: a + b):
		self._default = default
		self._func = func
		self._len = len(data)
		self._size = _size = 1 << (self._len - 1).bit_length()
		self.data = [default] * (2 * _size)
		self.data[_size:_size + self._len] = data
		for i in reversed(range(_size)):
			self.data[i] = func(self.data[i + i], self.data[i + i + 1])

	def __delitem__(self, idx):
		self[idx] = self._default

	def __getitem__(self, idx):
		return self.data[idx + self._size]

	def __setitem__(self, idx, value):
		idx += self._size
		self.data[idx] = value
		idx >>= 1
		while idx:
			self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
			idx >>= 1

	def __len__(self):
		return self._len

	def query(self, start, stop):
		if start == stop:
			return self.__getitem__(start)
		stop += 1
		start += self._size
		stop += self._size
		res = self._default
		while start < stop:
			if start & 1:
				res = self._func(res, self.data[start])
				start += 1
			if stop & 1:
				stop -= 1
				res = self._func(res, self.data[stop])
			start >>= 1
			stop >>= 1
		return res

	def __repr__(self):
		return 'SegmentTree({0})'.format(self.data)

class Factorial:

	def __init__(self, MOD):
		self.MOD = MOD
		self.factorials = [1, 1]
		self.invModulos = [0, 1]
		self.invFactorial_ = [1, 1]

	def calc(self, n):
		if n <= -1:
			print('Invalid argument to calculate n!')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		if n < len(self.factorials):
			return self.factorials[n]
		nextArr = [0] * (n + 1 - len(self.factorials))
		initialI = len(self.factorials)
		prev = self.factorials[-1]
		m = self.MOD
		for i in range(initialI, n + 1):
			prev = nextArr[i - initialI] = prev * i % m
		self.factorials += nextArr
		return self.factorials[n]

	def inv(self, n):
		if n <= -1:
			print('Invalid argument to calculate n^(-1)')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		p = self.MOD
		pi = n % p
		if pi < len(self.invModulos):
			return self.invModulos[pi]
		nextArr = [0] * (n + 1 - len(self.invModulos))
		initialI = len(self.invModulos)
		for i in range(initialI, min(p, n + 1)):
			next = -self.invModulos[p % i] * (p // i) % p
			self.invModulos.append(next)
		return self.invModulos[pi]

	def invFactorial(self, n):
		if n <= -1:
			print('Invalid argument to calculate (n^(-1))!')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		if n < len(self.invFactorial_):
			return self.invFactorial_[n]
		self.inv(n)
		nextArr = [0] * (n + 1 - len(self.invFactorial_))
		initialI = len(self.invFactorial_)
		prev = self.invFactorial_[-1]
		p = self.MOD
		for i in range(initialI, n + 1):
			prev = nextArr[i - initialI] = prev * self.invModulos[i % p] % p
		self.invFactorial_ += nextArr
		return self.invFactorial_[n]

class Combination:

	def __init__(self, MOD):
		self.MOD = MOD
		self.factorial = Factorial(MOD)

	def ncr(self, n, k):
		if k < 0 or n < k:
			return 0
		k = min(k, n - k)
		f = self.factorial
		return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD

def powm(a, n, m):
	if a == 1 or n == 0:
		return 1
	if n % 2 == 0:
		s = powm(a, n // 2, m)
		return s * s % m
	else:
		return a * powm(a, n - 1, m) % m

def sort_list(list1, list2):
	zipped_pairs = zip(list2, list1)
	z = [x for (_, x) in sorted(zipped_pairs)]
	return z

def product(l):
	por = 1
	for i in range(len(l)):
		por *= l[i]
	return por

def binarySearchCount(arr, n, key):
	left = 0
	right = n - 1
	count = 0
	while left <= right:
		mid = int((right + left) / 2)
		if arr[mid] < key:
			count = mid + 1
			left = mid + 1
		else:
			right = mid - 1
	return count

def countdig(n):
	c = 0
	while n > 0:
		n //= 10
		c += 1
	return c

def binary(x, length):
	y = bin(x)[2:]
	return y if len(y) >= length else '0' * (length - len(y)) + y

def countGreater(arr, n, k):
	l = 0
	r = n - 1
	leftGreater = n
	while l <= r:
		m = int(l + (r - l) / 2)
		if arr[m] >= k:
			leftGreater = m
			r = m - 1
		else:
			l = m + 1
	return n - leftGreater
(n, m) = map(int, input().split())
c = defaultdict(int)
ans = [i for i in range(1, n + 1)]
ori = [i for i in range(1, n + 1)]
s = set()
ma = defaultdict(int)
con = defaultdict(list)
for i in range(m):
	(a, b) = map(int, input().split())
	c[a] += 1
	c[b] += 1
	ma[a] = max(ma[a], b)
	ma[b] = max(ma[b], a)
	con[a].append(b)
	con[b].append(a)
	s.add((a, b))
e = -1
if m == n * (n - 1) // 2:
	print('NO')
	sys.exit(0)
for i in range(1, n + 1):
	if (i, i + 1) not in s and (i + 1, i) not in s and (i + 1 <= n):
		e = 1
		ans[i + 1 - 1] = ans[i - 1]
		break
	if (i, i - 1) not in s and (i - 1, i) not in s and (i - 1 >= 1):
		e = 1
		ans[i - 1 - 1] = ans[i - 1]
		break
if e == -1:
	for i in range(1, n + 1):
		if e == 1:
			break
		if c[i] == 0:
			e = 1
			ans[i - 1] = 1
			break
		for j in range(i + 1, n + 1):
			if (i, j) not in s and (j, i) not in s:
				e = 1
				ori[0] = ori[i - 1]
				ori[1] = ori[j - 1]
				ori[i - 1] = 1
				ori[j - 1] = 2
				ans[0] = ans[i - 1]
				ans[1] = ans[j - 1]
				ans[i - 1] = 1
				ans[j - 1] = 1
				break
	if e == -1:
		print('NO')
		sys.exit(0)
print('YES')
print(*ori)
print(*ans)


(n, m) = map(int, input().split())
s = set()
for i in range(m):
	(x, y) = map(int, input().split())
	s.add((x, y))
if m * 2 == n * (n - 1) or n < 2 or (n == 2 and m == 1):
	print('NO')
	return
(x, y) = (0, 0)
for i in range(1, n + 1):
	for j in range(i + 1, n + 1):
		if (i, j) not in s and (j, i) not in s:
			x = i
			y = j
			break
x -= 1
y -= 1
print('YES')
l = list(range(1, n + 1))
if x == 1:
	(y, x) = (x, y)
if y == 0:
	(x, y) = (y, x)
(l[x], l[0]) = (1, l[x])
(l[y], l[1]) = (2, l[y])
print(*l)
l[y] = 1
print(*l)


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

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

def li():
	return list(mi())
(n, m) = mi()
g = [[] for i in range(n + 1)]
e = []
for i in range(m):
	(a, b) = mi()
	e.append((a, b))
	g[a].append(b)
	g[b].append(a)
eq = None
if n > 1:
	for i in range(1, n + 1):
		if len(g[i]) == n - 1:
			continue
		s = set(g[i])
		for j in range(1, n + 1):
			if i != j and j not in s:
				eq = (i, j)
				break
		if eq:
			break
if eq:
	(a, b) = ([0] * n, [0] * n)
	a[eq[0] - 1] = 1
	a[eq[1] - 1] = 2
	b[eq[0] - 1] = b[eq[1] - 1] = 1
	c = 3
	for i in range(n):
		if not a[i]:
			a[i] = b[i] = c
			c += 1
	for (i, j) in e:
		if (a[i - 1] < a[j - 1]) != (b[i - 1] < b[j - 1]):
			eq = None
			break
if eq:
	print('YES')
	print(*a)
	print(*b)
else:
	print('NO')


(n, m) = map(int, input().split())
d = [set() for q in range(n)]
for q in range(m):
	(l, r) = map(int, input().split())
	(l, r) = (l - 1, r - 1)
	d[l].add(r)
	d[r].add(l)
ans = -1
for q in range(n):
	if len(d[q]) < n - 1:
		ans = q
		break
if ans == -1:
	print('NO')
else:
	for q in range(n):
		if q != ans and q not in d[ans]:
			ans = [ans, q]
			break
	(ans, ans1) = (min(ans), max(ans))
	a = []
	s = []
	for q in range(ans + 1):
		a.append(1 + q)
		s.append(1 + q)
	for q in range(ans + 1, ans1):
		a.append(2 + q)
		s.append(2 + q)
	a.append(ans + 1)
	s.append(ans + 2)
	for q in range(ans1 + 1, n):
		a.append(1 + q)
		s.append(1 + q)
	print('YES')
	print(*s)
	print(*a)


import sys
input = sys.stdin.buffer.readline
for _ in range(1):
	(n, m) = map(int, input().split())
	ans = [0] * (n + 1)
	a = []
	for i in range(m):
		(l, r) = map(int, input().split())
		if l > r:
			(l, r) = (r, l)
		a.append([l, r])
	if m == int(n * (n - 1) // 2):
		print('NO')
		continue
	a.sort()
	f = -1
	s = -1
	count = 0
	(l, r) = (1, 2)
	add = n * (n - 1) // 2
	for i in range(add):
		if r == n + 1:
			l += 1
			r = l + 1
		if i == m:
			f = l
			s = r
			break
		if a[i][0] != l or a[i][1] != r:
			f = l
			s = r
			break
		r += 1
	if l != n - 1 or r != n:
		f = l
		s = r
	ans1 = [0] * (n + 1)
	ans2 = [0] * (n + 1)
	ans1[f] = ans2[f] = ans1[s] = 1
	ans2[s] = 2
	count = 3
	i = 1
	while i <= n:
		if ans1[i] == 0:
			ans1[i] = ans2[i] = count
			count += 1
		i += 1
	if f == -1:
		print('NO')
	else:
		print('YES')
		print(*ans2[1:])
		print(*ans1[1:])


(n, m) = map(int, input().split())
member = [0 for _ in range(n + 1)]
linked = set()
for i in range(m):
	(a, b) = map(int, input().split())
	linked.add(str(a) + '-' + str(b))
	linked.add(str(b) + '-' + str(a))
	member[a] += 1
	member[b] += 1
num = 0
for i in range(1, n + 1):
	if member[i] < n - 1:
		num = i
		break
if num:
	for i in range(1, n + 1):
		if i != num:
			text = str(num) + '-' + str(i)
			if text not in linked:
				pair = i
				break
	arr = [num, pair]
	arr.sort()
	sa = [0] * n
	sb = [0] * n
	sa[arr[0] - 1] = 1
	sa[arr[1] - 1] = 2
	sb[arr[0] - 1] = 1
	sb[arr[1] - 1] = 1
	cur = 3
	for i in range(n):
		if sa[i] == 0:
			sa[i] = cur
			sb[i] = cur
			cur += 1
	print('YES')
	print(*sa)
	print(*sb)
else:
	print('NO')


def read(type=1):
	if type:
		file = open('input.dat', 'r')
		line = list(map(int, file.readline().split()))
		n = line[0]
		m = line[1]
		a = []
		for i in range(m):
			line = tuple(map(int, file.readline().split()))
			if line[0] < line[1]:
				a.append(line)
			else:
				a.append([line[1], line[0]])
		file.close()
	else:
		line = list(map(int, input().strip().split()))
		n = line[0]
		m = line[1]
		a = []
		for i in range(m):
			line = tuple(map(int, input().strip().split()))
			if line[0] < line[1]:
				a.append(line)
			else:
				a.append([line[1], line[0]])
	return (n, m, a)

def write(sol, x):
	print('YES')
	print(' '.join(map(str, sol[1:-1])))
	sol[x[1]] = sol[x[0]]
	print(' '.join(map(str, sol[1:-1])))

def solve(a):
	if len(a) == n * (n - 1) // 2:
		print('NO')
		return 0
	a = sorted(a, key=lambda x: (x[0], x[1]))
	x = [1, 2]
	for t in a:
		if list(t) != x:
			break
		if x[1] == n:
			x[0] += 1
			x[1] = x[0] + 1
		else:
			x[1] += 1
	sol = [0 for i in range(n + 2)]
	sol[x[0]] = 1
	sol[x[1]] = 2
	v = 3
	for i in range(1, n + 1):
		if i not in x:
			sol[i] = v
			v += 1
	write(sol, x)
(n, m, a) = read(0)
solve(a)


import os
import sys
from bisect import bisect_left, bisect_right
from collections import Counter, defaultdict
from functools import reduce
from io import BytesIO, IOBase
from itertools import combinations
from math import gcd, inf, sqrt, ceil, floor

def lcm(a, b):
	return a * b // gcd(a, b)
MAXN = 1000004
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, ceil(sqrt(MAXN))):
		if spf[i] == i:
			for j in range(i * i, MAXN, i):
				if spf[j] == j:
					spf[j] = i

def getFactorization(x):
	ret = Counter()
	while x != 1:
		ret[spf[x]] += 1
		x = x // spf[x]
	return ret

def printDivisors(n):
	i = 2
	z = [1, n]
	while i <= sqrt(n):
		if n % i == 0:
			if n / i == i:
				z.append(i)
			else:
				z.append(i)
				z.append(n // i)
		i = i + 1
	return z

def create(n, x, f):
	pq = len(bin(n)[2:])
	if f == 0:
		tt = min
	else:
		tt = max
	dp = [[inf] * n for _ in range(pq)]
	dp[0] = x
	for i in range(1, pq):
		for j in range(n - (1 << i) + 1):
			dp[i][j] = tt(dp[i - 1][j], dp[i - 1][j + (1 << i - 1)])
	return dp

def enquiry(l, r, dp, f):
	if l > r:
		return inf if not f else -inf
	if f == 1:
		tt = max
	else:
		tt = min
	pq1 = len(bin(r - l + 1)[2:]) - 1
	return tt(dp[pq1][l], dp[pq1][r - (1 << pq1) + 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 * p, n + 1, p):
				prime[i] = False
		p += 1
	x = []
	for i in range(2, n + 1):
		if prime[i]:
			x.append(i)
	return x

def main():
	from collections import defaultdict
	import sys
	(n, m) = map(int, input().split())
	c = defaultdict(int)
	ans = [i for i in range(1, n + 1)]
	ori = [i for i in range(1, n + 1)]
	s = set()
	ma = defaultdict(int)
	con = defaultdict(list)
	for i in range(m):
		(a, b) = map(int, input().split())
		c[a] += 1
		c[b] += 1
		ma[a] = max(ma[a], b)
		ma[b] = max(ma[b], a)
		con[a].append(b)
		con[b].append(a)
		s.add((a, b))
	e = -1
	if m == n * (n - 1) // 2:
		print('NO')
		sys.exit(0)
	for i in range(1, n + 1):
		if (i, i + 1) not in s and (i + 1, i) not in s and (i + 1 <= n):
			e = 1
			ans[i + 1 - 1] = ans[i - 1]
			break
		if (i, i - 1) not in s and (i - 1, i) not in s and (i - 1 >= 1):
			e = 1
			ans[i - 1 - 1] = ans[i - 1]
			break
	if e == -1:
		for i in range(1, n + 1):
			if e == 1:
				break
			if c[i] == 0:
				e = 1
				ans[i - 1] = 1
				break
			for j in range(i + 1, n + 1):
				if (i, j) not in s and (j, i) not in s:
					e = 1
					ori[0] = ori[i - 1]
					ori[1] = ori[j - 1]
					ori[i - 1] = 1
					ori[j - 1] = 2
					ans[0] = ans[i - 1]
					ans[1] = ans[j - 1]
					ans[i - 1] = 1
					ans[j - 1] = 1
					break
		if e == -1:
			print('NO')
			sys.exit(0)
	print('YES')
	print(*ori)
	print(*ans)
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')
main()