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;
pair<char, int> arr[500009];
int n;
char last;
int ans[20];
int get_bit(int pos, int val) { return ((1 << pos) & val); }
int calc(int pos, int start) {
  int ret = (start << pos);
  for (int i = 0; i < n; i++) {
    if (arr[i].first == '|') {
      ret |= (get_bit(pos, arr[i].second));
    } else if (arr[i].first == '^') {
      ret ^= (get_bit(pos, arr[i].second));
    } else {
      ret &= (get_bit(pos, arr[i].second));
    }
  }
  return ret;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf(" %c %d", &arr[i].first, &arr[i].second);
  }
  for (int i = 0; i < 10; i++) {
    int satu = calc(i, 1);
    int nol = calc(i, 0);
    if (!satu && !nol)
      ans[i] = 0;
    else if (satu && nol)
      ans[i] = 1;
    else if (satu && !nol)
      ans[i] = 2;
    else
      ans[i] = 3;
  }
  int dan = 1023, atau = 0, balik = 0;
  for (int i = 0; i < 10; i++) {
    if (ans[i] == 0) {
      dan ^= (1 << i);
    } else if (ans[i] == 1) {
      atau |= (1 << i);
    } else if (ans[i] == 3) {
      balik |= (1 << i);
    }
  }
  printf("3\n");
  printf("& %d\n", dan);
  printf("| %d\n", atau);
  printf("^ %d\n", balik);
}
