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())
stat = [0] * 10 # 0: stay, 1: flip, 2: on, 3: off

for i in range(n):
    op, arg = sys.stdin.readline().split()
    arg = int(arg)

    if op == '&':
        for j in range(10):
            if arg & (1 << j) == 0:
                stat[j] = 3
    elif op == '|':
        for j in range(10):
            if arg & (1 << j) > 0:
                stat[j] = 2
    else:
        for j in range(10):
            if arg & (1 << j) > 0:
                stat[j] ^= 1

print('3')
orarg = 0
for i in range(10):
    if stat[i] == 2:
        orarg |= (1 << i)
print('| ' + str(orarg))

andarg = (1 << 10) - 1
for i in range(10):
    if stat[i] == 3:
        andarg ^= (1 << i)
print('& ' + str(andarg))

xorarg = 0
for i in range(10):
    if stat[i] == 1:
        xorarg += (1 << i)
print('^ ' + str(xorarg))