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 PYTHON3):

Solution:
from math import gcd
from itertools import product

def egcd(a, b):
    if a == 0:
        return b, 0, 1
    else:
        gcd, x, y = egcd(b % a, a)
        return gcd, y - (b // a) * x, x

def make_muls(o, A):
    s = bin(A)
    s = s[2:][::-1]
    i = len(s)
    r = []
    it = 0
    while i > 0:
        i -= 1
        if s[i] == "1":
            r.append(str(o * it) + " + " + str(o))
            it += 1
        r.append(str(o * it) + " + " + str(o * it))
        it *= 2
    return r[1:]

#import random
#for x in range(1000):
inp = int(input())
#inp = random.randint(1,1000000)
if inp%2 == 0:
    inp += 1
#print (inp)
ops = []
A = 0
B = 0
for z in range(1,10000000):
    if ((inp*z) ^ inp) % 2 == 1 and gcd(inp, (inp*z) ^ (inp)) == 1:
        A = 1
        B = z
        break
#print(A,B)

ops = make_muls(inp, A)
ops += make_muls(inp, B)
ops += [str(inp*A) + " ^ " + str(inp*B)]

X = inp*A
Y = (inp*B) ^ (inp*A)

# x and y are both odd

_,C,D = egcd(X, Y)
C,D = abs(C),abs(D)
if max(X*C, Y*D) % 2 == 0:
    C += Y
    D += X
ops += make_muls(X, C)
ops += make_muls(Y, D)
ops += [str(X * C) + " ^ " + str(Y * D)]

print (len(ops))
for o in ops:
    print (o)
#print (ops[-1])
#assert eval(ops[-1]) == 1
#print()