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;
long long op(long long x, pair<char, long long> o) {
  if (o.first == '|') return (x | o.second);
  if (o.first == '&') return (x & o.second);
  return (x ^ o.second);
}
signed main() {
  long long n;
  cin >> n;
  vector<pair<char, long long>> v(n);
  for (long long i = 0; i < n; ++i) cin >> v[i].first >> v[i].second;
  vector<long long> v0(11, 0), v1(11, 1);
  for (long long i = 0; i < n; ++i)
    for (long long j = 0; j < 11; ++j) {
      v0[j] = (op(v0[j] << j, v[i]) >> j) & 1;
      v1[j] = (op(v1[j] << j, v[i]) >> j) & 1;
    }
  long long or_number = 0;
  long long xor_number = 0;
  for (long long j = 9; j >= 0; --j) {
    or_number = (or_number << 1) + (v0[j] == v1[j]);
    xor_number = (xor_number << 1) + (v1[j] == 0);
  }
  cout << 2 << '\n';
  cout << "| " << or_number << '\n';
  cout << "^ " << xor_number << '\n';
}
