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;
long long n, x, full1 = 1023, full0 = 0;
char op;
int main() {
  scanf("%I64d", &n);
  for (int i = 0; i < n; i++) {
    getchar();
    scanf("%c %I64d", &op, &x);
    if (op == '|') {
      full0 = full0 | x;
      full1 = full1 | x;
    } else if (op == '&') {
      full0 = full0 & x;
      full1 = full1 & x;
    } else {
      full0 = full0 ^ x;
      full1 = full1 ^ x;
    }
  }
  int AND = 0, OR = 0, XOR = 0, base = 1;
  for (int i = 1; i <= 10; i++) {
    int num0 = full0 & 1;
    int num1 = full1 & 1;
    if (num0 == 0) {
      if (num1 == 0)
        ;
      else
        AND += base;
    } else {
      if (num1 == 1) {
        OR += base;
        AND += base;
      } else {
        XOR += base;
        AND += base;
      }
    }
    full0 >>= 1;
    full1 >>= 1;
    base <<= 1;
  }
  printf("3\n^ %d\n& %d\n| %d\n", XOR, AND, OR);
  return 0;
}