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:
N = int(raw_input())

a = 1023
b = 0
for i in range(N):
    arr = raw_input().split(" ")
    num = int(arr[1])
    if arr[0] == "&":
        a = a & num
        b = b & num
    elif arr[0] == "|":
        a = a | num
        b = b | num
    else:
        a = a ^ num
        b = b ^ num

a1 = a | b
a2 = a & b
a3 = (a ^ 1023) & (b ^ 0)
count = 0
if a1 != 1023:
    count += 1
if a2 != 0:
    count += 1
if a3 != 0:
    count += 1
print count
if a1 != 1023:
    print "& ", a1
if a2 != 0:
    print "| ", a2
if a3 != 0:
    print "^ ", a3