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:
n = int(input())
import random

out = []
b2 = [n]
for i in range(41):
    out.append('{0} + {0}'.format(b2[-1]))
    b2.append(2*b2[-1])
b2 = b2[::-1]


basis = []
for j in range(1000):
    i = random.randint(1, n * n + 50)
    want = n * i
    for v in basis:
        if want ^ v < want:
            want = want ^ v
    if want > 0:
        add = []
        w2 = n * i
        for v in b2:
            if v <= w2:
                w2 -= v
                add.append(v)
        while len(add) > 1:
            u, v = add.pop(), add.pop()
            out.append('{1} + {0}'.format(u,v))
            add.append(u+v)

        assert(add[0] == n * i)

        w2 = n * i
        for v in basis:
            if w2 ^ v < w2:
                out.append('{1} ^ {0}'.format(w2,v))
                w2 = w2 ^ v
        
        basis.append(want)
        basis.sort(reverse = True)

print(len(out))
print('\n'.join(out))