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 a[27];
void AND(int d) {
  for (int i = 0; i < 10; i++) {
    if (d & (1 << i)) continue;
    a[i] = 0;
  }
}
void OR(int d) {
  for (int i = 0; i < 10; i++) {
    if (d & (1 << i)) a[i] = 1;
  }
}
void XOR(int d) {
  for (int i = 0; i < 10; i++) {
    if (d & (1 << i)) a[i] ^= 1;
  }
}
int main() {
  for (int i = 0; i <= 10; i++) a[i] = 3;
  int n;
  scanf("%d", &n);
  while (n--) {
    char c;
    int d;
    scanf(" %c", &c);
    scanf("%d", &d);
    if (c == '&') AND(d);
    if (c == '|') OR(d);
    if (c == '^') XOR(d);
  }
  int A = 0, O = 0, X = 0;
  for (int i = 0; i < 10; i++) {
    if (a[i] == 1) {
      A |= 1 << i;
      O |= 1 << i;
    }
    if (a[i] == 2) {
      A |= 1 << i;
      X |= 1 << i;
    }
    if (a[i] == 3) {
      A |= 1 << i;
    }
  }
  cout << 3 << endl;
  cout << "& " << A << endl;
  cout << "^ " << X << endl;
  cout << "| " << O << endl;
  return 0;
}