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.
n = int(raw_input())
l = []
for i in xrange(n):
    l.append(raw_input().split())
ll = [0,1,2,4,8,16,32,64,128,256,512]
ans = []
#lll = str(bin(11))[2:].zfill(10)
final = []
for i in [0,1023]:
    temp = i
    for j in range(n):
        if l[j][0] == '|':
            temp = temp|int(l[j][1])
        elif l[j][0] == '&':
            temp = temp&int(l[j][1])
        elif l[j][0] == '^':
            temp = temp^int(l[j][1])
    
    final.append(temp)
xxor = []
aand = []
oor = []
kk = [1 if ll[j]&final[1] else 0 for j in range(1,11)]
zz = [int(i) for i in str(bin(final[0]))[2:].zfill(10)]

for i in xrange(10):
    if zz[9-i] == 1 and kk[i] == 1:
        oor.append('1')
        aand.append('1')
        xxor.append('0')
    if (zz[9-i] == 0) and (kk[i] == 0):
        oor.append('0')
        aand.append('0')
        xxor.append('0')
    #if zz[i] and not kk[i]:
    #    and.append(i)
    if ( zz[9-i] == 1) and (kk[i])== 0:
        oor.append('0')
        aand.append('1')
        xxor.append('1')
    if ( zz[9-i] == 0) and (kk[i])== 1:
        oor.append('0')
        aand.append('1')
        xxor.append('0')

xxor = ''.join(xxor)[::-1]
oor = ''.join(oor)[::-1]
aand = ''.join(aand)[::-1]


print '3' #+ '\n'
print '| ' + str(int(oor,2)) #+ '\n'
print '^ ' + str(int(xxor,2)) #+ '\n'
print '& ' + str(int(aand,2)) #+ '\n'