Gap Between the Clock Hands

Medium

An ordinary round analogue clock shows hours hours and minutes minutes. The hour hand moves smoothly: it covers 30° per hour, so it shifts by half a degree every minute. Return the smaller of the two angles between the hour hand and the minute hand, in degrees. Answers within 10⁻⁵ of the exact value are accepted.

Example 1

hours=9, minutes=0 → 90.0

The hour hand is exactly on 9 and the minute hand on 12: a quarter turn apart, 90°.

Example 2

hours=6, minutes=20 → 70.0

The minute hand points at 120°. In 20 minutes the hour hand has moved 10° past 180°, to 190°. The gap is 70°.

Example 3

hours=12, minutes=50 → 85.0

The minute hand is at 300° and the hour hand at 25°. That is 275° one way, but only 360 − 275 = 85° the other way.

Constraints

1 ≤ hours ≤ 12
0 ≤ minutes ≤ 59

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Topics

Math

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Input

hours=9, minutes=0

Expected

90.0

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