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.
#include <bits/stdc++.h>
using namespace std;
int n;
int main() {
  cin >> n;
  int v[10];
  for (int i = 0; i < 10; i++) {
    v[i] = 2;
  }
  while (n--) {
    char c[2];
    int t;
    scanf("%s %d", c, &t);
    if (c[0] == '|') {
      for (int i = 0; i < 10; i++) {
        if (t & (1 << i)) v[i] = 1;
      }
    }
    if (c[0] == '&') {
      for (int i = 0; i < 10; i++) {
        if (!(t & (1 << i))) v[i] = 0;
      }
    }
    if (c[0] == '^') {
      for (int i = 0; i < 10; i++) {
        if (t & (1 << i)) v[i] ^= 1;
      }
    }
  }
  int v1 = 0, v2 = 0, v3 = 0;
  for (int i = 0; i < 10; i++) {
    if (v[i] == 0) v1 |= (1 << i);
    if (v[i] == 1) v2 |= (1 << i);
    if (v[i] == 3) v3 |= (1 << i);
  }
  printf("3\n| %d\n& %d\n^ %d", v2, 1023 ^ v1, v3);
  cout << endl;
  return 0;
}
