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.
n = int(raw_input())
bits = [[0 for x in range(10)] for x in range(2)]
bits[1] = [1 for x in range(10)]
for i in range(n):
  a,b = raw_input().split()
  b = int(b)
  temp = [0 for x in range(10)]
  cur = 0
  while b:
    temp[cur] = b%2
    b /= 2
    cur += 1
  if a=='|':
    for j in range(10):
      if temp[j]:
        bits[0][j] = 1
        bits[1][j] = 1
  elif a=='^':
    for j in range(10):
      bits[0][j] ^= temp[j]
      bits[1][j] ^= temp[j]
  else:
    for j in range(10):
      bits[0][j] &= temp[j]
      bits[1][j] &= temp[j]
ans = [0,1023,0]
val = [0,0,0]
pr = '|&^'
for i in range(10):
  if bits[0][i] and bits[1][i]:
    ans[0] |= (1<<i)
    val[0] = 1
  elif not bits[1][i] and not bits[0][i]:
    ans[1] ^= (1<<i)
    val[1] = 1
  elif bits[0][i] and not bits[1][i]:
    ans[2] |= (1<<i)
    val[2] = 1
print sum(val)
for i in range(3):
  if val[i]:
    print pr[i],ans[i]