Problem: You have a blackboard and initially only an odd number x is written on it. Your goal is to write the number 1 on the blackboard.

You may write new numbers on the blackboard with the following two operations. 

  * You may take two numbers (not necessarily distinct) already on the blackboard and write their sum on the blackboard. The two numbers you have chosen remain on the blackboard. 
  * You may take two numbers (not necessarily distinct) already on the blackboard and write their [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) on the blackboard. The two numbers you have chosen remain on the blackboard. 

Perform a sequence of operations such that at the end the number 1 is on the blackboard.

Input

The single line of the input contains the odd integer x (3 ≤ x ≤ 999,999).

Output

Print on the first line the number q of operations you perform. Then q lines should follow, each describing one operation. 

  * The "sum" operation is described by the line "a + b", where a, b must be integers already present on the blackboard. 
  * The "xor" operation is described by the line "a ^ b", where a, b must be integers already present on the blackboard. 

The operation symbol (+ or ^) must be separated from a, b by a whitespace.

You can perform at most 100,000 operations (that is, q≤ 100,000) and all numbers written on the blackboard must be in the range [0, 5⋅10^{18}]. It can be proven that under such restrictions the required sequence of operations exists. You can output any suitable sequence of operations.

Examples

Input


3


Output


5
3 + 3
3 ^ 6
3 + 5
3 + 6
8 ^ 9


Input


123


Output


10
123 + 123
123 ^ 246
141 + 123
246 + 123
264 ^ 369
121 + 246
367 ^ 369
30 + 30
60 + 60
120 ^ 121

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
 
public class Main{
	static int ttl = 0;
	static long old_r, old_s, old_t;
	public static void main(String[] args) throws IOException{
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		long k = pint(in);
		StringBuilder sb = new StringBuilder();
		xor(sb,k,k);
		long kh = k;
		for(long i = 1; i < Long.highestOneBit(k); i <<= 1) {
			add(sb,kh,kh);
			kh <<= 1;
		}
		xor(sb,kh,k);
		long kp = (k * Long.highestOneBit(k)) ^ k;
		xgcd(k,kp);
		old_s = Math.abs(old_s);
		old_t = Math.abs(old_t);
		if(Math.max(old_s * k, old_t * kp) % 2 == 0) {
			old_s += kp;
			old_t += k;
		}
		
		mul(sb, k, old_s);
		mul(sb, kp, old_t);
		xor(sb, k * old_s, kp * old_t);
		ret(sb);
		return;
	
	}
	static void mul(StringBuilder sb, long a, long b) {
		long p = 0;
		long k = a;
		for(long i = 1; i <= b; i *= 2) {
			if((b & i) > 0) {
				add(sb,p,k);
				p += k;
			}
			add(sb,k,k);
			k <<= 1;
		}
	}
	static void xgcd(long a, long b) {
		old_r = a; long r = b;
		old_s = 1; long s = 0;
		old_t = 0; long t = 1;
		while(r != 0) {
			long q = old_r / r;
			long temp;
			temp = r;
			r = old_r - q * r;
			old_r = temp;
			
			temp = s;
			s = old_s - q * s;
			old_s = temp;
			
			temp = t;
			t = old_t - q * t;
			old_t = temp;
		}
	}
	static long gcd(long a, long b) {
		if(a == 0) {return b;}
		return gcd(b % a, a);
	}
	static void ret(StringBuilder sb) {
		System.out.println(ttl);
		System.out.print(sb);
	}
	static void add(StringBuilder sb, long x, long y) {
		sb.append(x);
		sb.append(' ');
		sb.append('+');
		sb.append(' ');
		sb.append(y);
		sb.append('\n');
		ttl++;
	}
	static void xor(StringBuilder sb, long x, long y) {
		sb.append(x);
		sb.append(' ');
		sb.append('^');
		sb.append(' ');
		sb.append(y);
		sb.append('\n');
		ttl++;
	}
    static int pint(BufferedReader in) throws IOException {return Integer.parseInt(in.readLine());}
    static int pint(StringTokenizer st) {return Integer.parseInt(st.nextToken());}
}