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:
x = int(input())
X = x
ans = []
t = x
st = set()
while x & t != 1:
    #ans.append((t, '+', x))
    #st.add(t + x)
    t += x
# print(t)
ans.append((t, '+', x))
ans.append((t, '^', x))
ans.append((t + x, '+', t ^ x))
ans.append((t ^ x, '+', t ^ x))
ans.append((t + x + (t ^ x), '^', t + x + (t ^ x) - 2))
# st.add(t + x)
# st.add(t ^ x)
# st.add(t + x + (t ^ x))
# st.add((t ^ x) * 2)
# st.add((t + x + (t ^ x)) ^ (t + x + (t ^ x) - 2))
p = 2
while x > 1:
    if x & p:
        ans.append((p, '^', x))
        x ^= p
    ans.append((p, '+', p))
    p += p
ans1 = []
q = t // X - 1
tmp = X
re = X
while q > 0:
    if q & 1:
        ans1.append((re, '+', tmp))
        #st.add(re + tmp)
        re += tmp
    ans1.append((tmp, '+', tmp))
    #st.add(tmp + tmp)
    tmp += tmp
    q >>= 1
ans = ans1 + ans
print(len(ans))
for row in ans:
    print(*row)