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:
n=int(input())
bits0=[0]*10
bits1=[1]*10
b0=0
b1=1023
fname=['&','|','^']
f=[[[0,0],[0,1]],[[0,1],[1,1]],[[0,1],[1,0]]]
for i in range(n):
    s=input()
    e=str(bin(int(s[2:])))
    d=int(s[2:])
    if s[0]=='^':
        b0=b0^d
        b1 = b1 ^ d
    elif s[0]=='|':
        b0=b0|d
        b1 = b1 | d
    elif s[0]=='&':
        b0=b0&d
        b1 = b1 & d
for j in range(10):
    bits0[9-j]=b0%2
    b0=b0//2
    bits1[9 - j] = b1 % 2
    b1 = b1 // 2
c=[[0]*10,[0]*10,[1]*10]
for j in range(10):
    if bits0[j]==bits1[j]:
        if bits0[j]==0:
            c[2][j]=0
        else:
            c[1][j]=1
    else:
        if bits0[j]==1:
            c[0][j]=1
print(3)
c0,c1,c2=[0,0,0]
for i in range(10):
    c0+=c[0][i]*(2**(9-i))
    c1 += c[1][i] * (2 ** (9 - i))
    c2 += c[2][i] * (2 ** (9 - i))
print("^ "+str(c0))
print("| "+str(c1))
print("& "+str(c2))