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 A[500005], ctos, ceros, unos;
char Q[500005];
char R[20];
int P[20];
int main() {
  ios::sync_with_stdio(false);
  cin >> ctos;
  for (int i = 1; i <= ctos; i++) {
    cin >> Q[i] >> A[i];
  }
  ceros = 0;
  unos = 1023;
  for (int i = 1; i <= ctos; i++) {
    if (Q[i] == '&') {
      ceros &= A[i];
      unos &= A[i];
    } else if (Q[i] == '|') {
      ceros |= A[i];
      unos |= A[i];
    } else {
      ceros ^= A[i];
      unos ^= A[i];
    }
  }
  for (int i = 0; i < 10; i++) {
    if ((ceros & (1 << i)) == 0) {
      if ((unos & (1 << i)) == 0) {
        R[i] = '&';
      } else
        R[i] = 'n';
    } else {
      if ((unos & (1 << i)) == 0) {
        R[i] = '^';
      } else {
        R[i] = '|';
      }
    }
  }
  cout << "3\n";
  int por = 0;
  for (int i = 0; i < 10; i++) {
    if (R[i] != '&') {
      por += (1 << i);
    }
  }
  cout << "& " << por << "\n";
  por = 0;
  for (int i = 0; i < 10; i++) {
    if (R[i] == '^') {
      por += (1 << i);
    }
  }
  cout << "^ " << por << "\n";
  por = 0;
  for (int i = 0; i < 10; i++) {
    if (R[i] == '|') {
      por += (1 << i);
    }
  }
  cout << "| " << por << "\n";
  return 0;
}