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 = "from sys import stdin\n\nBITCOUNT = 10\nxONES = (1 << 10) - 1\nxZEROS = 0\nn = int(stdin.readline())\n\nfor i in range(n):\n    op, num = stdin.readline().split()\n    num = int(num)\n    if op == '&':\n        xONES &= num\n        xZEROS &= num\n    elif op == '|':\n        xONES |= num\n        xZEROS |= num\n    else:\n        xONES ^= num\n        xZEROS ^= num\n\nandmask = 0\nxormask = 0\nmask = 1\nfor i in range(BITCOUNT):\n    ONESbit = (xONES >> i) & 1\n    ZEROSbit = (xZEROS >> i) & 1\n    if (ONESbit == 1) and (ZEROSbit == 0):\n        andmask += mask\n    elif (ONESbit == 0) and (ZEROSbit == 1):\n        andmask += mask\n        xormask += mask\n    elif (ONESbit == 1) and (ZEROSbit == 1):\n        xormask += mask\n    mask *= 2\n\nprint(2)\nprint('& {}'.format(andmask))\nprint('^ {}'.format(xormask))"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13409