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.
def fun (n1,o,n2):
    if o=="|":
        return n1|n2
    elif o=="&":
        return n1&n2
    else:
        return n1^n2
def fun2(n):
    l=[0 for i in range(10)]
    for i in range(9,-1,-1):
        if 1<<i <=n:
            l[i]=1
            n-=1<<i
    return l
n=int(input())
a=0
b=1023
for i in range(n):
    o,n2=input().split()
    n2=int(n2)
    a=fun(a,o,n2)
    b=fun(b,o,n2)
l1=fun2(a)
l2=fun2(b)
a=0
b=0
for i in range(10):
    if l1[i]==1 and l2[i]==1:
        a+=1<<i
    elif l1[i]==0 and l2[i]==0:
        a+=1<<i
        b+=1<<i
    elif l1[i]==1 and l2[i]==0:
        b+=1<<i
print(2)
print("|",a)
print("^",b)
    
    
            
