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 execute(prg, n):
	for op, x in prg:
		if op == "|":
			n |= x
		elif op == "&":
			n &= x
		elif op == "^":
			n ^= x
	return n
n = int(input())
prg = []
for i in range(n):
	op, x = map(str, input().split())
	x = int(x)
	prg.append((op, x))
zeroes = execute(prg, 0)
ones = execute(prg, 1023)
orx, andx, xorx = 0, 0, 0
for i in range(10):
	bit = 1 << i
	if zeroes & bit == 0 and ones & bit == 0:
		pass
	elif zeroes & bit == 0 and ones & bit != 0:
		andx |= bit
	elif zeroes & bit != 0 and ones & bit == 0:
		xorx |= bit
		andx |= bit
	elif zeroes & bit != 0 and ones & bit != 0:
		orx |= bit
		andx |= bit
print(3)
print("|", orx)
print("&", andx)
print("^", xorx)