The Gray code (see wikipedia for more details) is a well-known concept.
One of its important properties is that every two adjacent numbers have exactly one different digit in their binary representation.

In this problem, we will give you n non-negative integers in a sequence A[1..n] (0<=A[i]<2^64), such that every two adjacent integers have exactly one different digit in their binary representation, similar to the Gray code.

Your task is to check whether there exist 4 numbers A[i1], A[i2], A[i3], A[i4] (1 <= i1 < i2 < i3 < i4 <= n) out of the given n numbers such that A[i1] xor A[i2] xor A[i3] xor A[i4] = 0. Here xor is a bitwise operation which is same as ^ in C, C++, Java and xor in Pascal.

-----Input-----
First line contains one integer n (4<=n<=100000).
Second line contains n space seperated non-negative integers denoting the sequence A.

-----Output-----
Output “Yes” (quotes exclusive) if there exist four distinct indices i1, i2, i3, i4 such that A[i1] xor A[i2] xor A[i3] xor A[i4] = 0. Otherwise, output "No" (quotes exclusive) please.

-----Example-----
Input:

5
1 0 2 3 7

Output:

Yes

Difficulty: UNKNOWN_DIFFICULTY

Starter code:

Solutions:
dic = {}
n = int(input())
flag = 0
if n >= 68:
	inp = input()
	print('Yes')
else:
	inp = [int(x) for x in input().split()]
	for i in range(len(inp) - 1):
		for j in range(i + 1, len(inp)):
			xor = inp[i] ^ inp[j]
			if xor in list(dic.keys()):
				for pair in dic[xor]:
					(x, y) = pair
					if x != i and y != j and (x != j) and (y != i):
						flag = 1
						break
				dic[xor].append((i, j))
			else:
				dic[xor] = []
				dic[xor].append((i, j))
			if flag is 1:
				break
		if flag is 1:
			break
	if flag is 1:
		print('Yes')
	else:
		print('No')


n = int(input())
hit = list(map(int, input().split()))
d = {}
for i in range(1, n):
	(x1, x2) = (hit[i], hit[i - 1])
	try:
		d[x1 ^ x2] += [i]
	except:
		d[x1 ^ x2] = [i]
done = False
for i in d:
	x = d[i]
	if len(x) > 2:
		done = True
		break
	elif len(x) == 2:
		x = sorted(x)
		if x[0] != x[1] - 1:
			done = True
			break
if done:
	print('Yes')
else:
	v = {}
	for i in hit:
		try:
			v[i] += 1
		except:
			v[i] = 1
	x = {}
	h = list(v.values())
	for i in h:
		try:
			x[i] += 1
		except:
			x[i] = 1
	if 2 in x and x[2] == 2 or (4 in x and x[4] == 1):
		print('Yes')
	else:
		print('No')


from math import log
flips = {}

def get_flip(a, b):
	temp = a ^ b
	ans = log(temp) / log(2)
	return int(ans)

def main():
	n = input()
	nums = input()
	nums = [int(i) for i in nums.split()]
	l = len(nums)
	for i in range(1, l):
		f = get_flip(nums[i - 1], nums[i])
		if f in flips:
			if flips[f] != i - 1:
				print('Yes')
				return
		else:
			flips[f] = i
	rec = {}
	for i in nums:
		if i in rec:
			rec[i] += 1
		else:
			rec[i] = 1
	r = 0
	for i in rec:
		if rec[i] > 1:
			r += int(rec[i] / 2)
		if r >= 2:
			print('Yes')
			return
	print('No')
	return

def __starting_point():
	main()
__starting_point()


n = int(input())
s = input()
s = s.split()
d = {}
flag = 'No'
(two, four) = (0, 0)
for i in s:
	if i in d:
		d[i] += 1
		if d[i] == 2:
			two += 1
		elif d[i] == 4:
			four += 1
	else:
		d[i] = 1
d = {}
if two > 1 or four > 0:
	flag = 'Yes'
else:
	for i in range(n - 1):
		ex = int(s[i]) ^ int(s[i + 1])
		if ex in d:
			d[ex].append(i)
			if d[ex][-1] - d[ex][0] > 1:
				flag = 'Yes'
				break
		else:
			d[ex] = [i]
print(flag)


def digit(x):
	ans = None
	for i in range(64):
		if x & 1 << i:
			return i
n = int(input())
if n < 4:
	print('No')
else:
	count = [0] * 65
	nums = {}
	vals = list(map(int, input().split()))
	nums[vals[0]] = 1
	prebit = 999999999
	for i in range(1, n):
		bit = digit(vals[i] ^ vals[i - 1])
		if bit != prebit:
			count[bit] += 1
			prebit = bit
		try:
			nums[vals[i]] += 1
		except:
			nums[vals[i]] = 1
	m1 = max(count)
	m2 = max(nums.values())
	if m1 >= 2 or m2 >= 4:
		print('Yes')
	else:
		num_doubles = 0
		for val in list(nums.values()):
			if val >= 2:
				num_doubles += 1
		if num_doubles >= 2:
			print('Yes')
		else:
			print('No')


import sys
n = int(input())
a = [0] * n
if n > 300:
	print('Yes')
	return
s = input().split()
for i in range(n):
	a[i] = int(s[i])
a.sort()
for i in range(n - 3):
	for j in range(i + 1, n - 2):
		for k in range(j + 1, n - 1):
			x = a[i] ^ a[j] ^ a[k]
			l = k + 1
			r = n - 1
			while r - l > 1:
				c = (r + l) / 2
				if a[c] > x:
					r = c
				else:
					l = c
			if l > k and a[l] == x or a[r] == x:
				print('Yes')
				return
print('No')