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.
#!/usr/local/bin/python3

import sys

n = int(sys.stdin.readline())

zero_result = 0
ones_result = 1023

while (n > 0) :
	[op, val] = sys.stdin.readline().split(" ")
	val = int(val)
	n -= 1
	if (op == '&') :
		zero_result = zero_result & val
		ones_result = ones_result & val
	elif (op == '|') :
		zero_result = zero_result | val
		ones_result = ones_result | val
	elif (op == '^') :
		zero_result = zero_result ^ val
		ones_result = ones_result ^ val
	else:
		pass

and_bin = [1 for i in range(10)]
or_bin = [0 for i in range(10)]
xor_bin = [0 for i in range(10)]

for i in range(10) :
	j = 9 - i 
	zero_digit = zero_result >> j 
	ones_digit = ones_result >> j
	zero_result = zero_result - zero_digit*(2**j)
	ones_result = ones_result - ones_digit*(2**j)
	if ((zero_digit == 0) and (ones_digit == 0)) :
		and_bin[j] = 0
	elif ((zero_digit == 1) and (ones_digit == 0)) :
		xor_bin[j] = 1
	elif ((zero_digit == 1) and (ones_digit == 1)) :
		or_bin[j] = 1

and_int = 0
xor_int = 0
or_int = 0

for i in range(10):
	and_int += and_bin[i]*(2**i)
	or_int += or_bin[i]*(2**i)
	xor_int += xor_bin[i]*(2**i)

print(3)
print('&', and_int)
print('|', or_int)
print('^', xor_int)


