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;
int main() {
  int n;
  scanf("%d", &n);
  vector<int> ans(10);
  vector<bool> fix(10);
  while (n--) {
    char ch;
    int a;
    cin >> ch;
    scanf("%d", &a);
    int i = 0;
    while (i < 10) {
      int bpos = a & 1;
      if (ch == '|') {
        if (bpos == 1) {
          ans[i] = bpos;
          fix[i] = true;
        }
      } else if (ch == '&') {
        if (bpos == 0) {
          ans[i] = bpos;
          fix[i] = true;
        }
      } else {
        if (bpos == 1) ans[i] = 1 - ans[i];
      }
      i++;
      a = a >> 1;
    }
  }
  int xorval = 0, andval = 1023, orval = 0, num = 1;
  for (int i = 0; i < 10; i++) {
    if (fix[i] == true) {
      if (ans[i] == 1)
        orval += num;
      else
        andval -= num;
    } else {
      if (ans[i] == 1) xorval += num;
    }
    num = num << 1;
  }
  printf("%d\n", 3);
  printf("%c %d\n", '&', andval);
  printf("%c %d\n", '|', orval);
  printf("%c %d\n", '^', xorval);
}