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 n, a = 1023, b = 0, x, aa[11], bb[11], op1, op2, op3;
char op, what[12];
int main() {
  cin >> n;
  while (n > 0) {
    cin >> op >> x;
    if (op == '&') {
      a = a & x;
      b = b & x;
    }
    if (op == '^') {
      a = a ^ x;
      b = b ^ x;
    }
    if (op == '|') {
      a = a | x;
      b = b | x;
    }
    n = n - 1;
  }
  for (int i = 0; i <= 9; i++) aa[i] = bb[i] = 0;
  int n1 = 0, n2 = 0;
  while (a) {
    aa[n1] = a % 2;
    a = a / 2;
    n1 = n1 + 1;
  }
  while (b) {
    bb[n2] = b % 2;
    b = b / 2;
    n2 = n2 + 1;
  }
  for (int i = 0; i <= 9; i++) {
    if (aa[i] == 0 and bb[i] == 0) what[i] = '&', op1 = 1;
    if (aa[i] == 1 and bb[i] == 1) what[i] = '|', op2 = 1;
    if (aa[i] == 1 and bb[i] == 0) what[i] = '0';
    if (aa[i] == 0 and bb[i] == 1) what[i] = '^', op3 = 1;
  }
  cout << op1 + op2 + op3 << "\n";
  if (op1 == 1) {
    x = 0;
    n = 1;
    for (int i = 0; i <= 9; i++) {
      if (what[i] != '&') x = x + n;
      n = n * 2;
    }
    cout << "& " << x << "\n";
  }
  if (op2 == 1) {
    x = 0;
    n = 1;
    for (int i = 0; i <= 9; i++) {
      if (what[i] == '|') x = x + n;
      n = n * 2;
    }
    cout << "| " << x << "\n";
  }
  if (op3 == 1) {
    x = 0;
    n = 1;
    for (int i = 0; i <= 9; i++) {
      if (what[i] == '^') x = x + n;
      n = n * 2;
    }
    cout << "^ " << x << "\n";
  }
  return 0;
}