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>
#pragma comment(linker, "/STACK:667177216")
using namespace std;
const long long MOD = 1000000000 + 7;
const long long MAXN = 100000 + 100;
int main() {
  int n;
  cin >> n;
  vector<pair<char, int>> ops(n);
  for (int(i) = 0; (i) < n; (i)++) cin >> ops[i].first >> ops[i].second;
  vector<char> ans;
  vector<int> orr, andd, xorr0, xorr1;
  for (int i = 0; (1 << i) <= 1023; ++i) {
    int res0 = 0, res1 = 1;
    int value = 0;
    for (int j = 0; j < ops.size(); ++j) {
      if (ops[j].first == '^') {
        value ^= ops[j].second;
      }
      if (ops[j].first == '&') {
        value &= ops[j].second;
      }
      if (ops[j].first == '|') {
        value |= ops[j].second;
      }
    }
    res0 = (value & (1 << i)) >> i;
    value = (1 << i);
    for (int j = 0; j < ops.size(); ++j) {
      if (ops[j].first == '^') {
        value ^= ops[j].second;
      }
      if (ops[j].first == '&') {
        value &= ops[j].second;
      }
      if (ops[j].first == '|') {
        value |= ops[j].second;
      }
    }
    res1 = (value & (1 << i)) >> i;
    if (res0 == 0 && res1 == 0) {
      andd.push_back(i);
    }
    if (res0 == 1 && res1 == 0) {
      xorr1.push_back(i);
    }
    if (res0 == 1 && res1 == 1) {
      orr.push_back(i);
    }
    if (res0 == 0 && res1 == 1) {
      xorr0.push_back(i);
    }
  }
  vector<pair<char, int>> answer;
  if (andd.size() > 0) {
    int value2 = 1023;
    for (int i = 0; i < andd.size(); ++i) {
      value2 ^= (1 << andd[i]);
    }
    answer.push_back(make_pair('&', value2));
  }
  if (orr.size() > 0) {
    int value2 = 0;
    for (int i = 0; i < orr.size(); ++i) {
      value2 ^= (1 << orr[i]);
    }
    answer.push_back(make_pair('|', value2));
  }
  if (xorr1.size() > 0) {
    int value2 = 0;
    for (int i = 0; i < xorr1.size(); ++i) {
      value2 ^= (1 << xorr1[i]);
    }
    answer.push_back(make_pair('^', value2));
  }
  cout << answer.size() << endl;
  for (int(i) = 0; (i) < answer.size(); (i)++) {
    cout << answer[i].first << " " << answer[i].second << endl;
  }
  return 0;
}
