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 n;
int state[10];
int main() {
  cin >> n;
  for (int i = 0; i < 10; i++) {
    state[i] = 2;
  }
  for (int i = 0; i < n; i++) {
    char op;
    int x;
    cin >> op >> x;
    if (op == '&') {
      for (int j = 0; j < 10; j++) {
        if (!(x & (1 << j))) {
          state[j] = -1;
        }
      }
    } else if (op == '|') {
      for (int j = 0; j < 10; j++) {
        if (x & (1 << j)) {
          state[j] = 1;
        }
      }
    } else {
      for (int j = 0; j < 10; j++) {
        if (x & (1 << j)) {
          state[j] = -state[j];
        }
      }
    }
  }
  int andmask = 0, ormask = 0, xormask = 0;
  for (int i = 0; i < 10; i++) {
    if (state[i] == 1) {
      ormask |= 1 << i;
    } else if (state[i] == -1) {
      andmask |= 1 << i;
    } else if (state[i] == -2) {
      xormask |= 1 << i;
    }
  }
  andmask ^= (1 << 10) - 1;
  cout << "3\n& " << andmask << "\n| " << ormask << "\n^ " << xormask << '\n';
}