Little Ben had just learned different bases in math. He learned very quickly how to add and subtract in multiple bases, so his teacher provided him with a worksheet to work on. Each section provided a different base and gave an example.

Unfortunately, Little Ben's teacher forgot to write what base each question was in! Please help Little Ben do his homework; he'll be very grateful!

Input

The first line of input contains an integer n (1 ≤ n < 36) that indicates the amount of sections (test cases). Each test case is as follows:

A - B = C
I
X1 op Y1 =
X2 op Y2 =
...
XI op YI =

where A - B = C is the correct example, I (1 ≤ I ≤ 1000) is the number of questions in that section, Xi and Yi are the operands of each problem (Xi = |Xi|, Yi = |Yi|), and op is either + or -, denoting addition or subtraction.

Output

Your program should output in the following format:

SECTION 1 (BASE b)
  X1 op Y1 = Z1
  X2 op Y2 = Z2
  ...
  Xi op Yi = Zi
SECTION 2 (BASE b)
  X1 op Y1 = Z1
  X2 op Y2 = Z2
  ...
  Xi op Yi = Zi
...
SECTION N (BASE b)
  X1 op Y1 = Z1
  X2 op Y2 = Z2
  ...
  Xi op Yi = Zi

where Zi is the solution to Xi op Yi, and b is the base used. (2 ≤ b ≤ 36). If the base is ambiguous, use the smallest base for which the example is correct and the questions are valid. You may assume all solutions fit inside a 64-bit integer and that each base will appear at most once.

Example

Input:

4
110 - 101 = 1
2
1111111 + 1 =
100 - 1 =
177 + 1 = 200
2
7712347 + 7 =
11111 + 7777 =
ZAP + DZ = ZOO
1
E + PI =
10 + 1 = 11
1
5 + 5 =

Output:

SECTION 1 (BASE 2)
  1111111 + 1 = 10000000
  100 - 1 = 11
SECTION 2 (BASE 8)
  7712347 + 7 = 7712356
  11111 + 7777 = 21110
SECTION 3 (BASE 36)
  E + PI = PW
SECTION 4 (BASE 6)
  5 + 5 = 14

Notes:

• large input/output data, be careful with certain languages
• Tricky input/output; please read problem statement carefully