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 = '#!/usr/bin/env pypy3\n\nfrom sys import stdin, stdout\n \ndef input():\n    return stdin.readline().strip()\n\ndef run_program(n, program):\n    for op, a in program:\n        assert(op in "&|^")\n        if op == \'&\': n = n & a\n        if op == \'|\': n = n | a\n        if op == \'^\': n = n ^ a\n    return n\n\nN = int(input())\n\nq = 1023\nr = 0\n\noriginal_program = []\nfor _ in range(N):\n    op, s = input().split(\' \')\n    s = int(s)\n\n    original_program += [(op, s)]\n\n    if op == \'&\':\n        q = q & s\n        r = r & s\n    elif op == \'^\':\n        r = r ^ s\n    elif op == \'|\':\n        q, r = (q ^ (q&s)), (r ^ s ^ (r&s))\n    else:\n        assert(False)\n\nfinal_program = [(\'&\', q), (\'^\', r)]\n\nprint(2)\nprint(f"& {q}")\nprint(f"^ {r}")'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13735