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 main() {
  int n;
  cin >> n;
  char c;
  int x, zero = 0, one = 1023;
  for (int i = 0; i < n; i++) {
    cin >> c >> x;
    if (c == '&') {
      zero = zero & x;
      one = one & x;
    }
    if (c == '|') {
      zero = zero | x;
      one = one | x;
    }
    if (c == '^') {
      zero = zero ^ x;
      one = one ^ x;
    }
  }
  int bitmask = 0, bitmask1 = 0;
  int it = 1;
  pair<int, int> matrix[2][2] = {{make_pair(1, 1), make_pair(0, 0)},
                                 {make_pair(0, 1), make_pair(1, 0)}};
  for (int i = 0; i < 10; i++) {
    bitmask = bitmask | (matrix[(zero & it) > 0][(one & it) > 0].first * it);
    bitmask1 = bitmask1 | (matrix[(zero & it) > 0][(one & it) > 0].second * it);
    it <<= 1;
  }
  cout << 2 << "\n| " << bitmask << "\n^ " << bitmask1;
}