When we see an arithmetic expression:

6 * 9 = 42

We usually think of it as a wrong expression. This is because we usually use the decimal system(Base₁₀).

In fact, this expression is correct in Base₁₃:

6₁₃ * 9₁₃ = 42₁₃

Because:

6₁₃ == 6₁₀

9₁₃ == 9₁₀

42₁₃ == 54₁₀

Task

You are given a string exp that represents a arithmetic expression, such as a + b = c, a - b = c or a * b = c. Your task is to determine the possible base of it. the range of base is 2-32. If more than one base are valid, return the smallest base. If no valid base found, return -1.

Example

For exp = "1 + 1 = 2", The output should be 3.

For exp = "1 + fe = ff", The output should be 16.

For exp = "1 + a = b", The output should be 12.

For exp = "1 * a = a", The output should be 11.

For exp = "1 + 1 = 10", The output should be 2.

For exp = "a + b = c", The output should be -1.

Note

• string exp contains only digits and lowercase letters.

• Happy Coding ^_^