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;
string second;
void Or(int num) {
  int i = 9;
  while (num) {
    int ch = num % 2;
    num /= 2;
    if (ch == 1) second[i] = '1';
    i--;
  }
}
void And(int num) {
  int i = 9;
  while (i >= 0) {
    int ch = num % 2;
    num /= 2;
    if (ch == 0) second[i] = '0';
    i--;
  }
}
void Xor(int num) {
  int i = 9;
  while (num) {
    int ch = num % 2;
    num /= 2;
    if (ch == 1) {
      if (second[i] == '0')
        second[i] = '1';
      else if (second[i] == '1')
        second[i] = '0';
      else if (second[i] == 't')
        second[i] = 'x';
      else
        second[i] = 't';
    }
    i--;
  }
}
int main() {
  {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
  };
  int n;
  cin >> n;
  for (int i = 0; i < 9; i++) {
    second.push_back('x');
  }
  for (int i = 0; i < n; i++) {
    string s2;
    int num;
    cin >> s2 >> num;
    if (s2[0] == '|')
      Or(num);
    else if (s2[0] == '&')
      And(num);
    else
      Xor(num);
  }
  cout << 2 << endl;
  cout << '|' << ' ';
  int ans = 0, two = 1;
  for (int i = 9; i >= 0; i--) {
    if (second[i] == '0' || second[i] == '1') ans += two;
    two *= 2;
  }
  cout << ans << endl;
  cout << '^' << ' ';
  ans = 0, two = 1;
  for (int i = 9; i >= 0; i--) {
    if (second[i] == 't' || second[i] == '0') ans += two;
    two *= 2;
  }
  cout << ans << endl;
}
