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>
int main(void) {
  int n;
  scanf("%d", &n);
  int a = 0, b = 1023;
  for (int i = 1; i <= n; ++i) {
    char ch[2];
    int x;
    scanf("%s%d", ch, &x);
    if (ch[0] == '&') {
      a &= x;
      b &= x;
    } else if (ch[0] == '|') {
      a |= x;
      b |= x;
    } else if (ch[0] == '^') {
      a ^= x;
      b ^= x;
    }
  }
  int ans1 = 0, ans2 = 0;
  for (int T = 0; T < 10; T++) {
    int flag1 = (b & (1 << T));
    int flag2 = (a & (1 << T));
    if (flag1 && flag2) {
      ans1 |= (1 << T);
    } else if (!flag1 && flag2) {
      ans2 ^= (1 << T);
    } else if (!flag1 && !flag2) {
      ans1 |= (1 << T);
      ans2 ^= (1 << T);
    }
  }
  printf("2\n| %d\n^ %d\n", ans1, ans2);
  return 0;
}