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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int n, stare[100];
int main() {
  int i, j, x, bit;
  char c;
  cin >> n;
  for (i = 0; i < 20; ++i) stare[i] = 2;
  while (n--) {
    cin >> c >> x;
    if (c == '|') {
      for (bit = 0; bit < 20; ++bit)
        if ((1 << bit) & x) stare[bit] = 1;
    } else if (c == '^') {
      for (bit = 0; bit < 20; ++bit)
        if ((1 << bit) & x) {
          if (stare[bit] <= 1)
            stare[bit] ^= 1;
          else
            stare[bit] = 5 - stare[bit];
        }
    } else {
      for (bit = 0; bit < 20; ++bit)
        if (((1 << bit) & x) == 0) stare[bit] = 0;
    }
  }
  int val_or = 0;
  for (i = 0; i < 10; ++i)
    if (stare[i] == 1) val_or += (1 << i);
  int val_and = 0;
  for (i = 0; i < 10; ++i)
    if (stare[i]) val_and += (1 << i);
  int val_xor = 0;
  for (i = 0; i < 10; ++i)
    if (stare[i] == 3) val_xor += (1 << i);
  cout << "3\n";
  cout << "| " << val_or << "\n";
  cout << "& " << val_and << "\n";
  cout << "^ " << val_xor << "\n";
  return 0;
}