Heath is driving his car to Miami. Heath reached a point where he was confused and couldn't decide which road he should take. Lucky Heath's friend Hary was with him who decided to help Heath.

Hary: How many gallons of gas left in your tank?

Heath: why?

Hary: Because depending on how much is remaining I will decide which road we should take.

If the number of gallons is greater than 50 then Hary will ask about the length of the 2 roads (in Km)

(It is known that each gallon can go as far as 1.5 km) Choose the road which the car can go through with the current amount of gas. If both roads can be taken, choose the shortest one.

Any other case you should decide to turn back and take neither of the two roads.

• Output A if road 1 is chosen.
• Output B if road 2 is chosen.
• Output X otherwise.

Input

G .. number of gallons (Integer), 0 < G < 10,000.

R1 .. length of road number 1 (Float), R1 > 0.0.

R2 .. length of road number 2 (Float), R2 > 0.0.

Output

One line with either A or B or X.

Example

Input:
60 90 100

Output:
A

Input:
30

Output:
X