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 queue

def readTuple():
    return input().split()
def readInts():
    return tuple(map(int, readTuple()))


def to_int(x):
    x=x[::-1]
    res = 0
    for i in x:
        res <<= 1
        res |= i
    return res

def solve():
    res = ['X']*10
    n, = readInts()
    a,b = 0, 1023
    for _ in range(n):
        char, num = readTuple()
        num = int(num)
        if char == '|':
            a |= num
            b |= num
        if char == '&':
            a &= num
            b &= num
        if char == '^':
            a ^= num
            b ^= num

    XOR, OR = [],[]
    for i in range(10):
        b1 = a&(1<<i)
        b2 = b&(1<<i)
        if b1 and b2:
            OR.append(1)
            XOR.append(0)
        if not b1 and not b2:
            OR.append(1)
            XOR.append(1)
        if b1 and not b2:
            OR.append(0)
            XOR.append(1)
        if not b1 and b2:
            OR.append(0)
            XOR.append(0)

    print(2)
    print(f"| {to_int(OR)}")
    print(f"^ {to_int(XOR)}")

if __name__ == '__main__':
    solve()

