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 MXN = 5e5 + 1;
int n;
pair<char, int> A[MXN];
int ans[3] = {0, 0, 1023};
int main() {
  cin >> n;
  for (int x = 0; x < n; x++) cin >> A[x].first >> A[x].second;
  for (int x = 0; x < n; x++) {
    if (A[x].first == '|') {
      ans[2] |= A[x].second;
      ans[1] = ans[1] & (~A[x].second);
      ans[0] |= A[x].second;
    } else if (A[x].first == '&') {
      ans[2] &= A[x].second;
      ans[1] &= (A[x].second);
      ans[0] &= A[x].second;
    } else {
      int not_used = ~ans[2] & A[x].second;
      int u = A[x].second & ans[0];
      A[x].second &= ~not_used & ~u;
      ans[1] ^= A[x].second;
      ans[2] = ans[2] & ~u;
      ans[2] |= not_used;
      ans[0] |= not_used;
      ans[0] &= ~u;
    }
  }
  cout << "3\n";
  cout << "| " << ans[0] << "\n";
  cout << "^ " << ans[1] << "\n";
  cout << "& " << ans[2] << "\n";
}
