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 main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  int bitPos[10][2];
  int action[n], var[n];
  for (int i = 0; i < n; i++) {
    char c;
    cin >> c >> var[i];
    action[i] = c;
  }
  for (int i = 0; i < 10; i++) {
    for (int bit = 0; bit < 2; bit++) {
      int v = (bit) << i;
      for (int k = 0; k < n; k++) {
        if (action[k] == '^') {
          v = v ^ (var[k] & (1 << i));
        } else if (action[k] == '|') {
          v = v | (var[k] & (1 << i));
        } else {
          v = v & (var[k] & (1 << i));
        }
      }
      bitPos[i][bit] = v >> i;
    }
  }
  int AND = (1 << 10) - 1, OR = 0, XOR = 0;
  for (int i = 0; i < 10; i++) {
    if (bitPos[i][0] == 0 && bitPos[i][1] == 0) AND = AND & (~(1 << i));
    if (bitPos[i][0] == 1 && bitPos[i][1] == 1) OR = OR | ((1 << i));
    if (bitPos[i][0] == 1 && bitPos[i][1] == 0) XOR = XOR | ((1 << i));
  }
  cout << 3 << endl << "& " << AND << endl << "| " << OR << endl << "^ " << XOR;
  return 0;
}