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 main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  unsigned long long a = 0, b = (1 << 10) - 1;
  unsigned long long a1 = a, b1 = b;
  for (int i = 0; i < n; ++i) {
    char s;
    int x;
    cin >> s;
    if (s == '&') {
      cin >> x;
      a &= x, b &= x;
    } else if (s == '^') {
      cin >> x;
      a ^= x, b ^= x;
    } else {
      cin >> x;
      a |= x, b |= x;
    }
  }
  for (int x = 0; x < 1024; ++x) {
    for (int y = 0; y < 1024; ++y) {
      for (int z = 0; z < 1024; ++z) {
        if ((a1 & x ^ y | z) == a && (b1 & x ^ y | z) == b) {
          cout << 3 << '\n';
          cout << "& " << x << '\n';
          cout << "^ " << y << '\n';
          cout << "| " << z << '\n';
          return 0;
        }
      }
    }
  }
  return 0;
}