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.
import sys

def readS(): return raw_input()
def readN(): return int(readS())
def readLS(): return raw_input().split()
def readLN(): return [int(x) for x in readLS()]
def matrix(height, width): return [[None for i in xrange(width)] for j in xrange(height)]

s = [3 for i in xrange(10)]

n_lines = readN()
lines = sys.stdin.readlines()
for line in lines:
	op, n = line.split()
	n = int(n)
	if op == '|':
		pos = 0
		while n > 0:
			if n & 1:
				s[pos] = 1
			n = n >> 1
			pos += 1
	elif op == '&':
		for pos in xrange(10):
			if not (n >> pos) & 1:
				s[pos] = 0
	else:
		pos = 0
		while n > 0:
			if n & 1:
				if s[pos] == 3: s[pos] = 2
				elif s[pos] == 2: s[pos] = 3
				elif s[pos] == 0: s[pos] = 1
				elif s[pos] == 1: s[pos] = 0
			n = n >> 1
			pos += 1

print 3 # foo

n = 0
for pos in xrange(10):
	if s[9 - pos] == 0:
		n = n * 2
	else:
		n = n * 2 + 1
print '&', n

n = 0
for pos in xrange(10):
	if s[9 - pos] == 1:
		n = n * 2 + 1
	else:
		n = n * 2
print '|', n

n = 0
for pos in xrange(10):
	if s[9 - pos] == 2:
		n = n * 2 + 1
	else:
		n = n * 2
print '^', n