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 ≤ 5·10^5) — 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 x_{i} 0 ≤ x_{i} ≤ 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
& 1
& 3
& 5

Output
1
& 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.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import io, os\ninput = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline\n# input = io.StringIO(os.read(0, os.fstat(0).st_size).decode()).readline\nii=lambda:int(input())\nkk=lambda:map(int, input().split())\nll=lambda:list(kk())\n\n\n# xor + 0 --> unchanged(2)\n# xor + 1 --> flip(3)\n# or + 0 --> unchanged(2)\n# or + 1 --> 1(1)\n# and + 0 --> 0(0)\n# and + 1 --> unchanged(2)\narr = [2]*10\nfor _ in range(ii()):\n\ts,v=input().split()\n\tv = int(v)\n\tif s == b"|":\n\t\tfor i in range(10):\n\t\t\tif v&(2**i):\n\t\t\t\tarr[i]= 1\n\telif s == b"^":\n\t\tfor i in range(10):\n\t\t\tif v&(2**i):\n\t\t\t\tarr[i]^=1\n\telif s == b"&":\n\t\tfor i in range(10):\n\t\t\tif not (v&(2**i)):\n\t\t\t\tarr[i]=0\n\telse:\n\t    print(s)\nprint(3)\nx=o=a= 0\nfor i in range(10):\n\tif arr[i]==3: x += 2**i\n\telif arr[i]==0: a+=2**i\n\telif arr[i]==1:o+=2**i\nprint(\'|\',o)\nprint(\'^\',x)\nprint(\'&\',2**10 - a - 1)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: