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:
# -*- coding: utf-8 -*-

import math
import collections
import bisect
import heapq
import time
import random
import itertools
import sys

"""
created by shhuan at 2017/11/5 16:54

"""

N = int(input())

P = []
for i in range(N):
    P.append(input().split())


N = 2
S = [0, 1023]
T = [v for v in S]
for i in range(N):
    for p, v in P:
        v = int(v)
        if p == '^':
            T[i] ^= v
        elif p == '|':
            T[i] |= v
        else:
            T[i] &= v

a, b, c = 0, 0, 0
for i in range(10, -1, -1):
    a <<= 1
    b <<= 1
    c <<= 1
    c |= 1
    if all([(v>>i) & 1 == 1for v in T]):
        b |= 1
    elif all([(v>>i) & 1 == 0 for v in T]):
        c >>= 1
        c <<= 1
    elif all([(S[j]>>i)&1 != (T[j]>>i)&1 for j in range(N)]):
        a |= 1


print(3)
print('^', a)
print('|', b)
print('&', c)