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:
#!/usr/bin/env pypy3

from sys import stdin, stdout
 
def input():
    return stdin.readline().strip()

def run_program(n, program):
    for op, a in program:
        assert(op in "&|^")
        if op == '&': n = n & a
        if op == '|': n = n | a
        if op == '^': n = n ^ a
    return n

N = int(input())

q = 1023
r = 0

original_program = []
for _ in range(N):
    op, s = input().split(' ')
    s = int(s)

    original_program += [(op, s)]

    if op == '&':
        q = q & s
        r = r & s
    elif op == '^':
        r = r ^ s
    elif op == '|':
        q, r = (q ^ (q&s)), (r ^ s ^ (r&s))
    else:
        assert(False)

final_program = [('&', q), ('^', r)]

print(2)
print(f"& {q}")
print(f"^ {r}")