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())
import operator
s1 = 1023
s2 = 0
operations = {'&': operator.and_, '|': operator.or_, '^':operator.xor}
for i in range(n):
    a, b = raw_input().split(' ')
    s1 = operations[a](s1, int(b))
    s2 = operations[a](s2, int(b))
s1 = format(s1, '010b')
s2 = format(s2, '010b')
ops = {'&': ['1' for i in range(10)],'^':['0' for i in range(10)],'|':['0' for i in range(10)]}
for i in range(10):
    if s1[i] == s2[i]:
        if s1[i] == '1':
            ops['|'][i] = '1'
        else:
            ops['&'][i] = '0'
    else:
        if s1[i] == '0': 
            ops['^'][i] = '1'
a, b, c = ''.join( ops['&'] ), ''.join( ops['^'] ),''.join( ops['|'] )
a = int(a,2)
b = int(b,2)
c = int(c,2)
print 3
print '&' + ' ' + str(a)
print '^' + ' ' + str(b)
print '|' + ' ' + str(c)