Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well.

In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned.

Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023.

Input

The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines.

Next n lines contain commands. A command consists of a character that represents the operation ("&", "|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023.

Output

Output an integer k (0 ≤ k ≤ 5) — the length of your program.

Next k lines must contain commands in the same format as in the input.

Examples

Input

3
| 3
^ 2
| 1


Output

2
| 3
^ 2


Input

3
&amp; 1
&amp; 3
&amp; 5


Output

1
&amp; 1


Input

3
^ 1
^ 2
^ 3


Output

0

Note

You can read about bitwise operations in <https://en.wikipedia.org/wiki/Bitwise_operation>.

Second sample:

Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs.
n = int(raw_input())
temp = ''
o = []
a = []
x = []
val = 10
first = ''
second = ''
third = ''
for i in range(n):
	temp = raw_input().split()
	if(first==''):
		first = temp[0] 
	elif(first != temp[0] and second==''):
		second = temp[0]
	elif(first != temp[0] and second!=temp[0] and third==''):
		third = temp[0]
	if(temp[0]=='|'):
		o.append(int(temp[1]))
		val|=int(temp[1])
	if(temp[0]=='&'):
		a.append(int(temp[1]))
		val&=int(temp[1])
	if(temp[0]=='^'):
		x.append(int(temp[1]))
		val^=int(temp[1])
ans_x = 0
for i in x:
	ans_x^=i
ans_o = 0
for i in o:
	ans_o|=i
if(len(a)>=1):
	ans_a = a[0]
	for i in range(1,len(a)):
		ans_a&=a[i]
else:
	ans_a=-1

count = 0
if(ans_x!=0):
	count+=1
if(ans_o!=0):
	count+=1
if(ans_a!=-1):
	count+=1
val_1 = 10

def q1():
	global val_1
	if(ans_o!=0):
		val_1|=ans_o
		# print '| ' + str(ans_o)
def w1():
	global val_1
	if(ans_x!=0):
		# print '^ ' + str(ans_x)
		val_1^=ans_x
def e1():
	global val_1
	if(ans_a!=-1):
		val_1&=ans_a
		# print '& ' + str(ans_a)
if(first=='|'):
	q1()
elif(first=='&'):
	e1()
elif(first=='^'):
	w1()
if(second=='|'):
	q1()
elif(second=='&'):
	e1()
elif(second=='^'):
	w1()
if(third=='|'):
	q1()
elif(third=='&'):
	e1()
elif(third=='^'):
	w1()
if(val_1!=val):
	print count+1
else:

	print count

def q():
	global val_1
	if(ans_o!=0):
		# val_1|=ans_o
		print '| ' + str(ans_o)
def w():
	global val_1
	if(ans_x!=0):
		print '^ ' + str(ans_x)
		# val_1^=ans_x
def e():
	global val_1
	if(ans_a!=-1):
		# val_1&=ans_a
		print '& ' + str(ans_a)
if(first=='|'):
	q()
elif(first=='&'):
	e()
elif(first=='^'):
	w()
if(second=='|'):
	q()
elif(second=='&'):
	e()
elif(second=='^'):
	w()
if(third=='|'):
	q()
elif(third=='&'):
	e()
elif(third=='^'):
	w()

if(val_1!=val):
	k = val_1^val
	print '^ ' + str(k) 
# print val, val_1