Dasha decided to have a rest after solving the problem. She had been ready to start her favourite activity — origami, but remembered the puzzle that she could not solve.  [Image] 

The tree is a non-oriented connected graph without cycles. In particular, there always are n - 1 edges in a tree with n vertices.

The puzzle is to position the vertices at the points of the Cartesian plane with integral coordinates, so that the segments between the vertices connected by edges are parallel to the coordinate axes. Also, the intersection of segments is allowed only at their ends. Distinct vertices should be placed at different points. 

Help Dasha to find any suitable way to position the tree vertices on the plane.

It is guaranteed that if it is possible to position the tree vertices on the plane without violating the condition which is given above, then you can do it by using points with integral coordinates which don't exceed 10^18 in absolute value.


-----Input-----

The first line contains single integer n (1 ≤ n ≤ 30) — the number of vertices in the tree. 

Each of next n - 1 lines contains two integers u_{i}, v_{i} (1 ≤ u_{i}, v_{i} ≤ n) that mean that the i-th edge of the tree connects vertices u_{i} and v_{i}.

It is guaranteed that the described graph is a tree.


-----Output-----

If the puzzle doesn't have a solution then in the only line print "NO".

Otherwise, the first line should contain "YES". The next n lines should contain the pair of integers x_{i}, y_{i} (|x_{i}|, |y_{i}| ≤ 10^18) — the coordinates of the point which corresponds to the i-th vertex of the tree.

If there are several solutions, print any of them. 


-----Examples-----
Input
7
1 2
1 3
2 4
2 5
3 6
3 7
Output
YES
0 0
1 0
0 1
2 0
1 -1
-1 1
0 2
Input
6
1 2
2 3
2 4
2 5
2 6

Output
NO

Input
4
1 2
2 3
3 4
Output
YES
3 3
4 3
5 3
6 3


-----Note-----

In the first sample one of the possible positions of tree is: [Image]

Source: codeforces | Difficulty: HARD
Tags: Graph algorithms

Graph traversal

Constructive algorithms

Greedy algorithms

Tree algorithms


Solutions:
def dfs(v, x, y, t, l, pr):
	ans[v] = (x, y)
	p = [(0, 1, 3), (0, 1, 2), (1, 2, 3), (0, 2, 3)][t]
	g[v] = [u for u in g[v] if u != pr]
	for i in range(min(len(p), len(g[v]))):
		newx = x + nx[p[i]][0] * l
		newy = y + nx[p[i]][1] * l
		dfs(g[v][i], newx, newy, p[i], l // 4, v)
read = lambda : map(int, input().split())
n = int(input())
g = [list() for i in range(n + 1)]
for i in range(n - 1):
	(u, v) = read()
	g[u].append(v)
	g[v].append(u)
root = 1
for i in range(n + 1):
	if len(g[i]) > 4:
		print('NO')
		return
ans = [0] * (n + 1)
ans[root] = (0, 0)
inf = 10 ** 18
l = inf // 4
nx = ((1, 0), (0, -1), (-1, 0), (0, 1))
for i in range(len(g[root])):
	dfs(g[root][i], nx[i][0] * l, nx[i][1] * l, i, l // 4, root)
print('YES')
[print(*i) for i in ans[1:]]


from collections import *

def ri():
	return map(int, input().split())
d = [[1, 0], [0, 1], [-1, 0], [0, -1]]

def bfs(s, adj, v, l):
	if v[s] == 1:
		return 0
	q = deque()
	q.append(s)
	v[s] = 1
	while q:
		n = q.popleft()
		for a in adj[n]:
			if v[a] == 0:
				for i in range(4):
					if dv[n][i] == 0:
						dv[n][i] = 1
						break
				pos[a][0] = pos[n][0] + d[i][0] * 2 ** (31 - l[n])
				pos[a][1] = pos[n][1] + d[i][1] * 2 ** (31 - l[n])
				if i == 0:
					dv[a][2] = 1
				elif i == 1:
					dv[a][3] = 1
				elif i == 2:
					dv[a][0] = 1
				elif i == 3:
					dv[a][1] = 1
				l[a] = l[n] + 1
				q.append(a)
				v[a] = 1
n = int(input())
adj = [set() for i in range(n)]
v = [0 for i in range(n)]
l = [0 for i in range(n)]
dv = [[0, 0, 0, 0] for i in range(n)]
pos = [[0, 0] for i in range(n)]
for i in range(n - 1):
	(a, b) = ri()
	a -= 1
	b -= 1
	adj[a].add(b)
	adj[b].add(a)
for i in range(n):
	if len(adj[i]) > 4:
		print('NO')
		exit()
bfs(0, adj, v, l)
print('YES')
for i in range(n):
	print(pos[i][0], pos[i][1])


def solve():

	def push(u, v, g):
		if u not in g:
			g[u] = []
		if v not in g:
			g[v] = []
		g[u].append(v)
		g[v].append(u)
	n = int(input())
	g = {}
	for _ in range(n - 1):
		(u, v) = map(int, input().split())
		push(u, v, g)
	for u in g:
		if len(g[u]) > 4:
			return ('NO', None)
	d = {}
	build(1, 0, 0, 0, 31, -1, d, g)
	s = ''
	for u in range(1, n + 1):
		(x, y) = d[u]
		s += str(x) + ' ' + str(y)
		s += '\n'
	return ('YES', s)

def cal_pos(dir_, cur_x, cur_y, cur_base):
	if dir_ == 0:
		return (cur_x, cur_y + (1 << cur_base))
	elif dir_ == 1:
		return (cur_x + (1 << cur_base), cur_y)
	elif dir_ == 2:
		return (cur_x, cur_y - (1 << cur_base))
	else:
		return (cur_x - (1 << cur_base), cur_y)

def build(u, p, cur_x, cur_y, cur_base, pre_dir, d, g):
	d[u] = [cur_x, cur_y]
	type_ = [0, 1, 2, 3]
	if pre_dir in type_:
		type_.remove(pre_dir)
	if u in g:
		for v in g[u]:
			if v != p:
				dir_ = type_.pop()
				(next_x, next_y) = cal_pos(dir_, cur_x, cur_y, cur_base)
				build(v, u, next_x, next_y, cur_base - 1, (dir_ - 2) % 4, d, g)
(ans, s) = solve()
if ans == 'NO':
	print(ans)
else:
	print(ans)
	print(s)


n = int(input())
p = [set() for i in range(n)]
for k in range(n - 1):
	(u, v) = map(int, input().split())
	p[u - 1].add(v - 1)
	p[v - 1].add(u - 1)
s = [(0, 0)] * n
t = [(0, 1 << 30, 7)]
l = [1, 0, -1, 0, 1]
while t:
	(u, d, j) = t.pop()
	(x, y) = s[u]
	i = 0
	for v in p[u]:
		if i == j:
			i += 1
		if i > 3:
			exit(print('NO'))
		p[v].remove(u)
		s[v] = (x + l[i] * d, y + l[i + 1] * d)
		t.append((v, d >> 1, (i + 2) % 4))
		i += 1
print('YES')
for (x, y) in s:
	print(x, y)


n = int(input())
adj = [[] for _ in range(n)]
for _ in range(n - 1):
	(u, v) = list(map(int, input().split()))
	adj[u - 1].append(v - 1)
	adj[v - 1].append(u - 1)
from collections import deque

def bfs(v):
	vis = [i == v for i in range(n)]
	paths = deque([[v]])
	while paths:
		p = paths.popleft()
		for nv in adj[p[-1]]:
			if not vis[nv]:
				vis[nv] = True
				paths.append(p + [nv])
	return p
diameter = bfs(0)
diameter = bfs(diameter[-1])
p = diameter[len(diameter) // 2]
start = (0, 0)
move = [(0, 1), (1, 0), (0, -1), (-1, 0)]
gpt = lambda pt, i, dis: (pt[0] + move[i][0] * dis, pt[1] + move[i][1] * dis)
vis = [False] * n
dis = 2 ** (len(diameter) + 1)
ans = [0] * n
q = deque([(p, start, -1, dis)])
while q:
	(p, start, dr, dis) = q.popleft()
	vis[p] = True
	ans[p] = start
	if len(adj[p]) > 4:
		print('NO')
		return
	if dr == -1:
		drs = [i for i in range(4)]
	else:
		drs = [i for i in range(4) if gpt(move[i], dr, 1) != (0, 0)]
	for nv in adj[p]:
		if not vis[nv]:
			(vis[nv], dr) = (True, drs.pop())
			npt = gpt(start, dr, dis)
			q.append((nv, npt, dr, dis // 2))
			ans[nv] = npt
print('YES')
for pt in ans:
	print(*pt)


import math
import random
import heapq, bisect
import sys
from collections import deque, defaultdict
from fractions import Fraction
import sys
from collections import defaultdict
mod = 10 ** 9 + 7
mod1 = 998244353
import os
import sys
from io import BytesIO, IOBase
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')

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=300006, func=lambda a, b: min(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

class TrieNode:

	def __init__(self):
		self.children = [None] * 26
		self.isEndOfWord = False

class Trie:

	def __init__(self):
		self.root = self.getNode()

	def getNode(self):
		return TrieNode()

	def _charToIndex(self, ch):
		return ord(ch) - ord('a')

	def insert(self, key):
		pCrawl = self.root
		length = len(key)
		for level in range(length):
			index = self._charToIndex(key[level])
			if not pCrawl.children[index]:
				pCrawl.children[index] = self.getNode()
			pCrawl = pCrawl.children[index]
		pCrawl.isEndOfWord = True

	def search(self, key):
		pCrawl = self.root
		length = len(key)
		for level in range(length):
			index = self._charToIndex(key[level])
			if not pCrawl.children[index]:
				return False
			pCrawl = pCrawl.children[index]
		return pCrawl != None and pCrawl.isEndOfWord

class Node:

	def __init__(self, data):
		self.data = data
		self.height = 0
		self.left = None
		self.right = None

class BinaryTrie:

	def __init__(self):
		self.root = Node(0)

	def insert(self, pre_xor):
		self.temp = self.root
		for i in range(31, -1, -1):
			val = pre_xor & 1 << i
			if val == 0:
				if not self.temp.right:
					self.temp.right = Node(0)
				self.temp = self.temp.right
			elif val >= 1:
				if not self.temp.left:
					self.temp.left = Node(0)
				self.temp = self.temp.left

	def do(self, temp):
		if not temp:
			return 0
		ter = temp
		temp.height = self.do(ter.left) + self.do(ter.right)
		if temp.height == 0:
			temp.height += 1
		return temp.height

	def query(self, xor):
		self.temp = self.root
		cur = 0
		i = 31
		while i > -1:
			val = xor & 1 << i
			if not self.temp:
				return cur
			if val >= 1:
				self.opp = self.temp.right
				if self.temp.left:
					self.temp = self.temp.left
				else:
					return cur
			else:
				self.opp = self.temp.left
				if self.temp.right:
					self.temp = self.temp.right
				else:
					return cur
			if self.temp.height == pow(2, i):
				cur += 1 << i
				self.temp = self.opp
			i -= 1
		return cur
n = int(input())
if n == 1:
	print('YES')
	print(0, 0)
	sys.exit(0)
ans = [(0, 0) for i in range(n)]
done = set()

def dfs(v, a, b, d, p, rem):
	ans[v] = (a, b)
	t = 0
	rem = (-1 * rem[0], -1 * rem[1])
	w = [(1, 0), (0, 1), (-1, 0), (0, -1), (0, 0)]
	w.remove(rem)
	for i in graph[v]:
		if i == p:
			continue
		dfs(i, a + d * w[t][0], b + d * w[t][1], d // 2, v, w[t])
		t += 1
graph = defaultdict(list)
d = defaultdict(int)
for i in range(n - 1):
	(x, y) = map(int, input().split())
	d[x - 1] += 1
	d[y - 1] += 1
	graph[x - 1].append(y - 1)
	graph[y - 1].append(x - 1)
if max(d.values()) > 4:
	print('NO')
else:
	dfs(0, 0, 0, 2 ** 58, -1, (0, 0))
	print('YES')
	for i in range(n):
		print(*ans[i])


from collections import deque
n = int(input())
dx = [-1, 0, 1, 0]
dy = [0, -1, 0, 1]
gr = [[] for i in range(n)]
for i in range(n - 1):
	(a, b) = [int(i) for i in input().split()]
	a -= 1
	b -= 1
	gr[a].append(b)
	gr[b].append(a)
for i in range(n):
	if len(gr[i]) > 4:
		print('NO')
		exit(0)
print('YES')
d = deque()
d.append((0, 10 ** 18 // 2, 10 ** 18 // 2, -1, -1, 50))
ans = [0] * n
while len(d) > 0:
	v = d[0][0]
	x = d[0][1]
	y = d[0][2]
	ans[v] = (d[0][1], d[0][2])
	p = d[0][4]
	dr = d[0][3]
	pw = d[0][5]
	d.popleft()
	if p != -1:
		gr[v].pop(gr[v].index(p))
	cur = 0
	for i in range(4):
		if i == dr:
			continue
		if cur == len(gr[v]):
			break
		ngh = gr[v][cur]
		d.append((ngh, x + 2 ** pw * dx[i], y + 2 ** pw * dy[i], (i + 2) % 4, v, pw - 1))
		cur += 1
for i in ans:
	print(*i)


def main():
	n = int(input())
	graph = [[] for i in range(n)]
	ans = [(0, 0)] * n
	for _ in range(n - 1):
		(u, v) = [int(el) for el in input().split()]
		u -= 1
		v -= 1
		graph[u].append(v)
		graph[v].append(u)
	for l in graph:
		if len(l) > 4:
			print('NO')
			return
	step = 1 << 28
	used = [False] * n

	def dfs(v, direction, step, koord):
		used[v] = True
		if direction == 'u':
			my_koord = (koord[0] + step, koord[1])
			dirs = ['u', 'l', 'r']
		elif direction == 'd':
			my_koord = (koord[0] - step, koord[1])
			dirs = ['d', 'l', 'r']
		elif direction == 'l':
			my_koord = (koord[0], koord[1] - step)
			dirs = ['u', 'd', 'l']
		elif direction == 'r':
			my_koord = (koord[0], koord[1] + step)
			dirs = ['u', 'd', 'r']
		elif direction == '':
			my_koord = (0, 0)
			dirs = ['u', 'd', 'l', 'r']
		ans[v] = my_koord
		d = 0
		for u in graph[v]:
			if not used[u]:
				dfs(u, dirs[d], step >> 1, my_koord)
				d += 1
	dfs(0, '', step, (0, 0))
	print('YES')
	for k in ans:
		print(k[0], k[1])
main()