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 sys
import io, os
input = sys.stdin.readline

n = int(input())

X = [-1]*10
# 0: 0
# 1: 1
# -1: -
# 2: ~
for i in range(n):
    c, x = map(str, input().split())
    x = int(x)
    if c == '&':
        for j in range(10):
            if not (x & (1 << j)):
                X[j] = 0
    elif c == '|':
        for j in range(10):
            if x & (1 << j):
                X[j] = 1
    else:
        for j in range(10):
            if x & (1 << j):
                if X[j] == -1:
                    X[j] = 2
                elif X[j] == 2:
                    X[j] = -1
                elif X[j] == 1:
                    X[j] = 0
                else:
                    X[j] = 1
a, b, c = 0, 0, 0
for i in range(10):
    if X[i] == -1:
        a |= (1<<i)
    elif X[i] == 2:
        a |= (1<<i)
        c |= (1<<i)
    elif X[i] == 1:
        b |= (1<<i)
print(3)
print('&', a)
print('|', b)
print('^', c)
