THE DRUNK JAILER (数论)

最新推荐文章于 2019-05-14 15:01:00 发布

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在一座拥有n间相连牢房的监狱里，狱卒通过饮酒和解锁、上锁的方式，试图让囚犯们陷入混乱。然而，经过多次循环后，一部分囚犯发现了他们的牢房被解开的秘密，并成功逃狱。本文详细解析了这一过程，揭示了囚犯们如何利用规律找到逃狱的机会。

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Description

A certain prison contains a long hall of n cells,

 each right next to each other. Each cell has a prisoner in it, and each cell is locked. 
One night, the jailer gets bored and decides to play a game.

 For round 1 of the game, he takes a drink of whiskey,

and then runs down the hall unlocking each cell. For round 2,

he takes a drink of whiskey, and then runs down the 
hall locking every other cell (cells 2, 4, 6, ?). For round 3,

he takes a drink of whiskey, and then runs down the hall.

 He visits every third cell (cells 3, 6, 9, ?). If the cell is locked, he unlocks it;

if it is unlocked, he locks it. He 
repeats this for n rounds, takes a final drink, and passes out. 
Some number of prisoners, possibly zero, realizes that their cells

 are unlocked and the jailer is incapacitated. They immediately escape. 
Given the number of cells, determine how many prisoners escape jail.

Input

The first line of input contains a single positive integer.

This is the number of lines that follow. Each of the following lines contains

 a single integer between 5 and 100, inclusive, which is the number of cells n.

Output

For each line, you must print out the number of prisoners that escape

when the prison has n cells.

Sample Input

2
5
100

Sample Output

2
10

代码

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