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;
void init() {
  cin.tie(0);
  cin.sync_with_stdio(0);
}
int main() {
  init();
  int n, zeros = 0, ones = 1023, andd = 1023, orr = 0, xorr = 0;
  cin >> n;
  int commands[n][2];
  for (int i = 0; i < n; i++) {
    char c;
    int x;
    cin >> c >> x;
    if (c == '^') {
      zeros ^= x;
      ones ^= x;
    } else if (c == '&') {
      zeros &= x;
      ones &= x;
    } else if (c == '|') {
      zeros |= x;
      ones |= x;
    }
    commands[i][0] = c;
    commands[i][1] = x;
  }
  for (int i = 0; i < 10; i++) {
    bool zbit = 1 & (zeros >> i);
    bool obit = 1 & (ones >> i);
    if (zbit == obit && obit) orr |= (1 << i);
    if (zbit == obit && !obit) andd &= ~(1 << i);
    if (zbit != obit && zbit) xorr |= (1 << i);
    if (zbit != obit && !zbit) andd |= (1 << i);
  }
  if (n > 5) {
    cout << 3 << '\n';
    cout << "| " << orr << '\n';
    cout << "& " << andd << '\n';
    cout << "^ " << xorr << '\n';
  } else {
    cout << n << '\n';
    for (int i = 0; i < n; i++)
      cout << char(commands[i][0]) << " " << commands[i][1] << '\n';
  }
}