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;
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int n;
  cin >> n;
  long long int a = 0, b = 1023;
  for (long long int i = 0; i < n; i++) {
    char c;
    cin >> c;
    long long int x;
    cin >> x;
    if (c == '&') {
      a = a & x;
      b = b & x;
    } else if (c == '|') {
      a = a | x;
      b = b | x;
    } else if (c == '^') {
      a = a ^ x;
      b = b ^ x;
    }
  }
  vector<long long int> v1, v2, v3;
  for (long long int i = 0; i < 10; i++) {
    long long int x = (a >> i) & 1, y = (b >> i) & 1;
    if (x == 1 && y == 1) {
      v1.push_back(1);
      v2.push_back(1);
      v3.push_back(0);
    } else if (x == 1 && y == 0) {
      v1.push_back(0);
      v2.push_back(1);
      v3.push_back(1);
    } else if (x == 0 && y == 0) {
      v1.push_back(0);
      v2.push_back(0);
      v3.push_back(0);
    } else {
      v1.push_back(0);
      v2.push_back(1);
      v3.push_back(0);
    }
  }
  long long int pw = 1, a1 = 0, a2 = 0, a3 = 0;
  for (long long int i = 0; i < v1.size(); i++) {
    a1 += v1[i] * pw;
    a2 += v2[i] * pw;
    a3 += v3[i] * pw;
    pw *= 2;
  }
  cout << "3 \n";
  cout << "| " << a1 << endl;
  cout << "& " << a2 << endl;
  cout << "^ " << a3 << endl;
  return 0;
}
