Problem: 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.

Solution (in PYTHON3):

Solution:
import sys
n = int(sys.stdin.readline())
zero_model, one_model = 0, (1<<10)-1
commands = []
for i in range(n):
	c, k = sys.stdin.readline()[:-1].split()
	k = int(k)
	commands.append((c,k))

def process(n,commands):
	for comm in commands:
		c, k = comm
		if c=='|':
			n |= k
		elif c=='^':
			n ^= k
		elif c=='&':
			n &= k
	return n

zero_model = process(0,commands)
one_model = process((1<<10)-1,commands)

set_zero = (1<<10)-1
flip = 0
set_one = 0
for i in range(10):
	bz = zero_model&(1<<i)
	bo = one_model&(1<<i)
	if bz >= 1 and bo==0:
		flip |= 1<<i
	elif bz >= 1 and bo >= 1:
		set_one |= 1<<i
	elif bz==0 and bo==0:
		set_zero &= ~(1<<i)
ans = [("&",set_zero),("^",flip),("|",set_one)]

print(len(ans))
for comm in ans:
	print(*comm)

# for i in range(1<<10):
# 	if process(i,commands) != process(i,ans):
# 		print(bin(process(i,commands)),"vs",bin(process(i,ans)))