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;
struct fuck {
  int a;
  int x;
};
fuck a[500000];
int n;
void get_it(int &x) {
  for (int i = 0; i < n; ++i) {
    if (a[i].a == 0) x |= a[i].x;
    if (a[i].a == 1) x &= a[i].x;
    if (a[i].a == 2) x ^= a[i].x;
  }
}
int main() {
  string str;
  cin >> n;
  int x;
  for (int i = 0; i < n; ++i) {
    cin >> str >> x;
    if (str == "|") {
      a[i].a = 0;
    }
    if (str == "&") {
      a[i].a = 1;
    }
    if (str == "^") {
      a[i].a = 2;
    }
    a[i].x = x;
  }
  int zero = 0;
  int one = 0;
  for (int i = 0; i < 10; ++i) one += (1 << i);
  int ans2 = one;
  get_it(zero);
  get_it(one);
  int ans1 = 0, ans3 = 0;
  for (int i = 0; i < 10; ++i) {
    if (((1 << i) & one) == 0 && ((1 << i) & zero) == 0) {
      ans2 ^= (1 << i);
    }
    if (((1 << i) & one) != 0 && ((1 << i) & zero) == 0) {
    }
    if (((1 << i) & one) == 0 && ((1 << i) & zero) != 0) {
      ans3 |= (1 << i);
    }
    if (((1 << i) & one) != 0 && ((1 << i) & zero) != 0) {
      ans1 |= (1 << i);
    }
  }
  cout << 3 << endl;
  cout << "| " << ans1 << endl;
  cout << "& " << ans2 << endl;
  cout << "^ " << ans3 << endl;
  return 0;
}