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 JAVA):

Solution:
// CodeForces Round #879 C train

import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

public class ShortProgram {
	
	static class Command {
		char cmd;
		int x;
		
		public Command(char ca, int xa) {
			cmd = ca;
			x = xa;
		}
		
		int apply(int a) {
			int b;
			if (cmd=='&') {
				b = a & x;
			} else if (cmd=='|') {
				b = a | x;
			} else if (cmd=='^') {
				b = a ^ x;
			} else {
				throw new IllegalStateException("Illegal cmd: " + cmd);
			}
			return b;
		}
	}
	
	static class Program {
		List<Command> comms = new ArrayList<>();
		
		int apply(int a) {
			for (Command c : comms) {
				a = c.apply(a);
			}
			return a;			
		}
		
		void addCommand(char ca, int xa) {
			Command c = new Command(ca, xa);
			comms.add(c);			
		}
	}

	int n,k;
	Program inProg;
	Program outProg;

	private void readData(BufferedReader bin) throws IOException {
		String s = bin.readLine();
		String []ss = s.split(" ");
		n = Integer.parseInt(s);
		
		inProg = new Program();
		for (int i=0; i<n; i++) {
			s = bin.readLine();
			ss = s.split(" ");
			char ca = ss[0].charAt(0);
			int xa = Integer.parseInt(ss[1]);
			inProg.addCommand(ca, xa);
		}
	}

	void printRes() {
		System.out.println(outProg.comms.size());
		for (Command c : outProg.comms) {
			System.out.println(c.cmd + " " + c.x);
		}
	}	

	private void calculate() {
		int z = inProg.apply(0);
		int o = inProg.apply(1023);
		int xand=0,xor=0,xxor=0;
		for (int i=0; i<10; i++) {
			int r = 1<<i;
			int bz = z & r;
			int bo = o & r;
			if (bz==0 && bo==0) {
				// leave all 0
			} else if (bz==0 && bo!=0) {
				// bit stays the same, and<- 1, or, xor <- 0
				xand = xand | r;
			} else if (bz!=0 && bo==0) {
				// xor works, and<-1 or<-0 xor<-1
				xand = xand | r;
				xxor |= r;
			} else {
				// always 1, and<-1, xxor<-0, xor <-1
				xand |= r;
				xor |= r;
			}
		}
		outProg = new Program();
		outProg.addCommand('&', xand);
		outProg.addCommand('|', xor);
		outProg.addCommand('^', xxor);		
		// testing
		int zz = outProg.apply(0);
		int oo = outProg.apply(1023);
		// System.out.println("z o = " + z + " " + o + " ,zz oo = " + zz + " " + oo);
	}

	public static void main(String[] args) throws IOException {
		// BufferedReader bin = new BufferedReader(new FileReader("cactus.in"));
		BufferedReader bin = new BufferedReader(
				new InputStreamReader(System.in));
		ShortProgram l = new ShortProgram();
		l.readData(bin);
		l.calculate();
		l.printRes();
	}
}