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;
const int N = (int)1e6 + 5;
const int mod = 1000000007;
int main() {
  int anda = 1023;
  int xora = 0;
  int ora = 0;
  int n;
  scanf("%d", &n);
  int min = 0;
  int max = 1023;
  while (n--) {
    char c;
    int x;
    cin >> c >> x;
    if (c == '|')
      min |= x, max |= x;
    else if (c == '&')
      min &= x, max &= x;
    else
      min ^= x, max ^= x;
  }
  for (int i = 0; i < 10; i++) {
    int l = 0, r = 0;
    if ((1 << i) & min) l = 1;
    if ((1 << i) & max) r = 1;
    if (l + r == 2) ora |= (1 << i);
    if (l + r == 0) anda ^= (1 << i);
    if (l && !r) xora ^= (1 << i);
  }
  cout << 3 << endl
       << "| " << ora << endl
       << "& " << anda << endl
       << "^ " << xora << endl;
  return 0;
}