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>
int main() {
  int n;
  scanf("%d", &n);
  int one = 1023, zero = 0;
  for (int i = 0; i < n; i++) {
    char otr;
    int ord;
    scanf(" %c %d", &otr, &ord);
    if (otr == '&') {
      one &= ord;
      zero &= ord;
    } else if (otr == '|') {
      one |= ord;
      zero |= ord;
    } else {
      one ^= ord;
      zero ^= ord;
    }
  }
  int _xor = 0, _and = 0, _or = 0;
  for (int i = 1; i < 1023; i *= 2) {
    if ((one & i) && (zero & i))
      _or |= i;
    else if ((one & i) && !(zero & i))
      _and |= i;
    else if (!(one & i) && (zero & i)) {
      _and |= i;
      _xor |= i;
    }
  }
  printf("3\n& %d\n^ %d\n| %d\n", _and, _xor, _or);
  return 0;
}