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:
import sys
input = sys.stdin.readline

n = int(input())
com = []

for _ in range(n):
    l = input().split()
    com.append((l[0], int(l[1])))

AND, OR, XOR = [], [], []

for i in range(10):
    res1 = 0
    res2 = 1
    
    for s, n in com:
        b = (n>>i)&1
        
        if s=='&':
            res1 &= b
            res2 &= b
        elif s=='|':
            res1 |= b
            res2 |= b
        elif s=='^':
            res1 ^= b
            res2 ^= b
        
    if (res1, res2)==(0, 0):
        AND.append(i)
    elif (res1, res2)==(1, 1):
        OR.append(i)
    elif (res1, res2)==(1, 0):
        XOR.append(i)

AND_n = 0

for i in range(10):
    if i not in AND:
        AND_n += 2**i

OR_n = 0

for i in OR:
    OR_n += 2**i

XOR_n = 0

for i in XOR:
    XOR_n += 2**i

print(3)
print('&', AND_n)
print('|', OR_n)
print('^', XOR_n)

"""
for i in range(1024):
    res1 = i
    
    for s, n in com:
        if s=='&':
            res1 &= n
        elif s=='|':
            res1 |= n
        elif s=='^':
            res1 ^= n
    
    res2 = i
    res2 &= AND_n
    res2 |= OR_n
    res2 ^= XOR_n
    
    if res1!=res2:
        1/0
"""