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.
import sys
input=sys.stdin.readline
import copy
from math import *
n=int(input())
a=[-1 for i in range(10)]
for i in range(n):
    p,q=input().split()
    qq=(bin(int(q))[2:])
    q=list((10-len(qq))*"0"+qq)
    if p=='|':
        for i in range(9,-1,-1):
            if  q[i]=='1':
                a[i]=1
    if p=='&':
        for i in range(9,-1,-1):
            if  q[i]=='0':
                a[i]=0
    if p=='^':
        for i in range(9,-1,-1):
            if  q[i]=='1' and (a[i]==0 or a[i]==1):
                a[i]^=1
            elif q[i]=='1' :
                if a[i]==-1:
                    a[i]=-2
                else:
                    a[i]=-1
    #print(a)                
c=0
for i in range(10):
    if a[i]==-2:
        c+=(2**(10-i-1))
print(3)
print("^",c)
v=list("0"*10)
for i in range(10):
    if a[i]==1:
        v[i]='1'
print("|",int("".join(v),2))  
u=list("1"*10)
for i in range(10):
    if a[i]==0:
        u[i]='0'
print("&",int("".join(u),2))  