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.
def doOr(num):
  for i in xrange(10):
    if num[i]=='1':
      arr[i]=2

def doAnd(num):
  for i in xrange(10):
    if num[i]=='0':
      arr[i]=1

def doXor(num):
  for i in xrange(10):
    if num[i]=='1':
      arr[i]^=3

arr = [0]*10
for i in xrange(input()):
  op, num = raw_input().strip().split()
  num = bin(int(num))[2:].zfill(10)
  if op=='|':
    doOr(num)
  elif op=='&':
    doAnd(num)
  elif op=='^':
    doXor(num)

ansor = 0
ansand = 0
ansxor = 0
for i in arr:
  ansor*=2
  ansand*=2
  ansxor*=2
  ansand+=1
  if i==1:
  	ansand-=1
  elif i==2:
  	ansor+=1
  elif i==3:
  	ansxor+=1
ans = int(ansor!=0)+int(ansand!=1023)+int(ansxor!=0)
print ans
if ansor!=0:
	print "|", ansor
if ansand!=1023:
	print "&", ansand
if ansxor!=0:
	print "^", ansxor