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 maxn = 1e5 + 20;
const int maxb = 10;
int b[maxb][2];
int and_, or_, xor_;
int main() {
  for (int i = 0; i < maxb; i++)
    for (int j = 0; j < 2; j++) b[i][j] = j;
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    char ch;
    int x;
    cin >> ch >> x;
    for (int i = 0; i < maxb; i++) {
      if (ch == '|') {
        if ((((x) >> (i)) & 1)) b[i][0] = b[i][1] = 1;
      }
      if (ch == '&') {
        if (!(((x) >> (i)) & 1)) b[i][0] = b[i][1] = 0;
      }
      if (ch == '^') {
        if ((((x) >> (i)) & 1)) b[i][0] = !b[i][0], b[i][1] = !b[i][1];
      }
    }
  }
  for (int i = maxb - 1; i >= 0; i--) {
    and_ *= 2;
    or_ *= 2;
    xor_ *= 2;
    if (b[i][0] == 0 && b[i][1] == 0) {
      continue;
    }
    if (b[i][0] == 0 && b[i][1] == 1) {
      and_++;
    }
    if (b[i][0] == 1 && b[i][1] == 0) {
      and_++;
      xor_++;
    }
    if (b[i][0] == 1 && b[i][1] == 1) {
      or_++;
      and_++;
    }
  }
  cout << 3 << endl;
  cout << "| " << or_ << endl;
  cout << "& " << and_ << endl;
  cout << "^ " << xor_ << endl;
}