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:
z = 0
o = 1023
n = int(input())
for i in range(n):
    a,b = input().split()
    b = int(b)
    if(a == "&"):
        z = z&b
        o = o&b
    if (a == "^"):
        z = z ^ b
        o = o ^ b
    if (a == "|"):
        z = z | b
        o = o | b
z = '{:010b}'.format(z)
o = '{:010b}'.format(o)
an = 0
r = 0
xo = 0
pw = 512
for i in range(10):
    an+=pw
    if(o[i]=='0' and z[i] == '0'): an-=pw
    if (o[i] == '1' and z[i] == '1'): r+=pw
    if (o[i] == '0' and z[i] == '1'): xo+=pw
    pw//=2
print(3)
print("&",an)
print("|",r)
print("^",xo)