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 PYTHON):

Solution:
# -*- coding: utf-8 -*-
def writeline(l): print " ".join(map(str, l))
def readline(): return map(int, raw_input().split())
def readint(): return int(raw_input(), 10)


def inv(x): return 1023 ^ x

def main():
    n = readint()
    zeros, ones = 0, 1023
    for __ in xrange(n):
        command, raw_value = raw_input().split()
        value = int(raw_value)
        if command == '|':
            zeros, ones = zeros | value, ones | value
        elif command == '&':
            zeros, ones = zeros & value, ones & value
        elif command == '^':
            zeros, ones = zeros ^ value, ones ^ value
        else:
            raise Exception("unrecognized command")

    set_one = zeros & ones
    set_zero = inv(zeros) & inv(ones)
    #set_id = inv(zeros) & ones
    set_not = zeros & inv(ones)

    commands = list()
    if set_one:
        commands.append("| {}".format(set_one))

    if set_zero:
        commands.append("& {}".format(inv(set_zero)))

    if set_not:
        commands.append("^ {}".format(set_not))

    print len(commands)
    for command in commands:
        print command


main()