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 MAX = 500005;
int v[MAX];
char c[MAX];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> c[i] >> v[i];
  int a = 0, o = 0, x = 0;
  for (int b = 0; b < 10; b++) {
    int r0 = 0, r1 = 1;
    for (int i = 0; i < n; i++) {
      int val = ((v[i] >> b) & 1);
      if (c[i] == '&') r0 &= val;
      if (c[i] == '|') r0 |= val;
      if (c[i] == '^') r0 ^= val;
    }
    for (int i = 0; i < n; i++) {
      int val = ((v[i] >> b) & 1);
      if (c[i] == '&') r1 &= val;
      if (c[i] == '|') r1 |= val;
      if (c[i] == '^') r1 ^= val;
    }
    if (r0 == r1) {
      if (r0 == 0)
        continue;
      else
        o |= (1 << b);
    } else {
      a |= (1 << b);
      if (r0 == 0)
        continue;
      else
        x |= (1 << b);
    }
  }
  cout << "3\n^ " << x << "\n& " << a << "\n| " << o << "\n";
  return 0;
}