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
import heapq
import math
from enum import Enum

class Status:
    UNTOUCHED = 1
    FLIPPED = 2
    ONE = 3
    ZERO = 4

bits = [Status.UNTOUCHED]*10
lines = sys.stdin.read().splitlines()

n = int(lines[0])

andNum = 1023
orNum = 0
xorNum = 0
for i in range(1, n+1):
    # print(andNum)
    # print(orNum)
    # print(xorNum)

    operation, num = lines[i].split(' ')
    num = int(num)
    # print(num)
    # print('----')
    if operation == '|':
        andNum=andNum|num
        orNum=orNum|num
        xorNum=xorNum&(orNum^1023)
    elif operation == '&':
        andNum=andNum&num
        orNum=orNum&num
        xorNum=xorNum&num
    else:
        # Flip all ones to zeroes and flip untouched
        # All bits that were set to 1 in OR mask and 1 in num, should be set to 0 in AND mask
        # All bits that were set to 0 in AND mask and 1 in num, should be set to 1 in OR mask
        # All those bits that were not set to 0 in AND mask and not set to 1 in OR mask should be set to 1 in xor MASK
        oldAndNum=andNum
        oldOrNum=orNum
        andNum=andNum^((orNum|(andNum^1023))&num)
        orNum=orNum^(((oldAndNum^1023)|(orNum))&num)
        xorNum=xorNum^(oldAndNum&(oldOrNum^1023)&num)

# OR
print(3)
print('& '+str(andNum))
print('| '+str(orNum))
print('^ '+str(xorNum))