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;
const long long INF = 1e9 + 7;
const int N = 1e5 + 10;
char a[N];
int main() {
  string op;
  vector<int> v;
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    char o;
    int x;
    cin >> o >> x;
    op.push_back(o);
    v.push_back(x);
  }
  int x = 0, y = 0, z = 0;
  for (int i = 0; i < 10; i++) {
    int o = 1 << i;
    int a = 0, b = 1;
    for (int j = 0; j < n; j++) {
      if (op[j] == '&') {
        a &= (o & v[j]) >> i;
        b &= (o & v[j]) >> i;
      }
      if (op[j] == '|') {
        a |= (o & v[j]) >> i;
        b |= (o & v[j]) >> i;
      }
      if (op[j] == '^') {
        a ^= (o & v[j]) >> i;
        b ^= (o & v[j]) >> i;
      }
    }
    if (a == b) {
      z |= a << i;
    } else if (a == 0) {
      y |= 1 << i;
    } else {
      y |= 1 << i;
      z |= 1 << i;
    }
  }
  cout << 2 << endl;
  cout << "& " << y << endl;
  cout << "^ " << z << endl;
  return 0;
}