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>
namespace {
using i64 = long long;
using ui64 = unsigned long long;
using ui32 = unsigned int;
}  // namespace
int main() {
  int N;
  std::cin >> N;
  std::vector<std::pair<char, int>> arr(N);
  for (auto& el : arr) {
    std::cin >> el.first >> el.second;
  }
  std::pair<char, int> digs[10];
  ui32 a = 0;
  ui32 o = 0;
  ui32 x = 0;
  for (size_t i = 0; i < 10; ++i) {
    int flag = 0x01 << i;
    std::pair<char, int> cur(' ', -1);
    for (size_t i = 0; i < arr.size(); ++i) {
      if (arr[i].first == '&') {
        if ((arr[i].second & flag) != 0) {
          continue;
        }
        cur = arr[i];
      } else if (arr[i].first == '|') {
        if ((arr[i].second & flag) == 0) {
          continue;
        }
        cur = arr[i];
      } else {
        if ((arr[i].second & flag) == 0) {
          continue;
        }
        if (cur.first == '^') {
          cur.first = ' ';
        } else if (cur.first == '&') {
          cur.first = '|';
        } else if (cur.first == '|') {
          cur.first = '&';
        } else {
          cur.first = '^';
        }
      }
    }
    if (cur.first == '&') {
      a = a | flag;
    } else if (cur.first == '|') {
      o = o | flag;
    } else if (cur.first == '^') {
      x = x | flag;
    }
  }
  int count = 0;
  if (a != 0) ++count;
  if (o != 0) ++count;
  if (x != 0) ++count;
  std::cout << count << std::endl;
  if (a != 0) std::cout << "& " << (~a & 0x3FF) << std::endl;
  if (o != 0) std::cout << "| " << o << std::endl;
  if (x != 0) std::cout << "^ " << x << std::endl;
  return 0;
}