Equal Slices of a Round Cake

Easy

A round cake is cut with straight cuts, and every cut must pass through the center. A cut can be one of two kinds: - a **full** cut, from edge to edge through the center (along a diameter); - a **radial** cut, from the center to a single point on the edge. Given an integer slices, return the smallest number of cuts after which the cake is divided into exactly slices identical pieces.

Example 1

slices=6 → 3

Three cuts through the center, 60° apart, give six equal pieces.

Example 2

slices=5 → 5

An odd number of pieces cannot come from full cuts, so you need five radial cuts from the center to the edge.

Example 3

slices=1 → 0

The cake is already one piece, so no cuts are needed.

Constraints

1 ≤ slices ≤ 100

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Topics

Geometry Math

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Input

slices=6

Expected

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