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.
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e6 + 2;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int i, j, n, ans, andd = 0, orr = 0, xorr = 0;
  char bit[100];
  memset(bit, 'x', sizeof(bit));
  cin >> n;
  for (i = 0; i < n; ++i) {
    char ch;
    long long int first;
    cin >> ch >> first;
    if (ch == '|') {
      for (j = 11; j >= 0; --j) {
        if ((1 << j) & first) bit[j] = '1';
      }
    }
    if (ch == '&') {
      for (j = 11; j >= 0; --j) {
        if ((1 << j) & first) continue;
        bit[j] = '0';
      }
    }
    if (ch == '^') {
      for (j = 11; j >= 0; --j) {
        if ((1 << j) & first) {
          if (bit[j] == 'x')
            bit[j] = 'y';
          else if (bit[j] == 'y')
            bit[j] = 'x';
          else if (bit[j] == '1')
            bit[j] = '0';
          else
            bit[j] = '1';
        }
      }
    }
  }
  for (i = 0; i <= 9; ++i) {
    if (bit[i] == '1') orr += (1 << i);
    if (bit[i] == 'y') xorr += (1 << i);
    if (bit[i] != '0') andd += (1 << i);
  }
  cout << 3 << "\n";
  cout << "| " << orr << "\n";
  cout << "& " << andd << "\n";
  cout << "^ " << xorr << "\n";
}
