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;
inline void Boost() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
}
const int NMax = 30;
int state[NMax];
int main() {
  Boost();
  int n;
  cin >> n;
  for (int i = 0; i < 12; ++i) state[i] = 2;
  while (n--) {
    char op;
    int val;
    cin >> op >> val;
    if (op == '|') {
      for (int bit = 0; bit < 10; ++bit) {
        if ((1 << bit) & val) {
          state[bit] = 1;
        }
      }
    }
    if (op == '&') {
      for (int bit = 0; bit < 10; ++bit) {
        if (((1 << bit) & val) == 0) {
          state[bit] = 0;
        }
      }
    }
    if (op == '^') {
      for (int bit = 0; bit < 10; ++bit) {
        if ((1 << bit) & val) {
          if (state[bit] <= 1) {
            state[bit] ^= 1;
          } else {
            state[bit] = 5 - state[bit];
          }
        }
      }
    }
  }
  int vand, vor, vxor;
  vand = vor = vxor = 0;
  for (int bit = 0; bit < 10; ++bit) {
    if (state[bit] == 1) {
      vor |= (1 << bit);
    }
  }
  for (int bit = 0; bit < 10; ++bit) {
    if (state[bit]) {
      vand |= (1 << bit);
    }
  }
  for (int bit = 0; bit < 10; ++bit) {
    if (state[bit] == 3) {
      vxor |= (1 << bit);
    }
  }
  cout << "3\n"
       << "& " << vand << "\n| " << vor << "\n^ " << vxor;
  return 0;
}
