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 main() {
  int a = 1023, b = 0, n, e;
  char op;
  cin >> n;
  while (n--) {
    cin >> op >> e;
    if (op == '|') {
      a |= e;
      b |= e;
    } else if (op == '&') {
      a &= e;
      b &= e;
    } else if (op == '^') {
      a ^= e;
      b ^= e;
    }
  }
  int ouxor = 0;
  int ou = 0;
  int exor = 0;
  e = 0;
  for (int i = 0; i < 10; i++) {
    int num = 1 << i;
    if ((a & num) && (b & num))
      ou |= num;
    else if ((b & num))
      exor |= num;
    else if (!(a & num) && !(b & num))
      ouxor |= num;
  }
  int count = 0;
  count += ouxor ? 2 : 0;
  count += ou ? 1 : 0;
  count += exor ? 1 : 0;
  cout << count << endl;
  if (ou) cout << "| " << ou << endl;
  if (ouxor) {
    cout << "| " << ouxor << endl;
    cout << "^ " << ouxor << endl;
  }
  if (exor) cout << "^ " << exor << endl;
}
