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:
#!/usr/bin/env python3

def simu(P,i):
    for c,x in P:
        if c=='&':
            i &= x
        elif c=='|':
            i |= x
        else:
            i ^= x
    return i

def simpl(P):
    out0,out1 = simu(P,0),simu(P,1023)
    A,O,X = 1023,0,0
    for i in range(10):
        B01 = (out0>>i)&1,(out1>>i)&1
        if B01==(0,0):
            A ^= 1<<i
        elif B01==(1,0):
            X |= 1<<i
        elif B01==(1,1):
            O |= 1<<i
    return A,O,X

def main():
    n = int(input())
    P = []
    for _ in range(n):
        c,x = input().split()
        P.append((c,int(x)))
    A,O,X = simpl(P)
    print(3)
    print('&',A)
    print('|',O)
    print('^',X)

main()