WUSTOJ 1327: Lucky Numbers（Java）

题目链接：1327: Lucky Numbers

Description

A lucky number is made by the following rules:

Given a positive integer sequence {x | 1 <= x <= n}. From the first number, delete the last one in every 2 numbers. Select the minimum that has not been unused from the rest numbers. This number is xi. Then delete the last number in every xi numbers.

幸运数字由以下规则制定：

给定正整数序列{x | 1 <= x <= n}。 从第一个数字中删除每2个数字中的最后一个。 从剩余数字中选择尚未使用的最小值。 这个数字是xi。 然后删除每个xi编号中的最后一个数字。

Input

There are several test cases, ended by the end of file.

Each test case has a positive integer n.(3<=n<=10000)

Output

Output the number of lucky numbers in one line.

在一行输出幸运数字的个数。

Sample Input

20
30

Sample Output

6
8

HINT

eg.1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

For the first time, delete the last number in every two numbers. The sequence become 1 3 5 7 9 11 13 15 17 19

For the second time, the minimum number that has never been used is 3. Delete the last number in every 3 numbers. The sequence become 1 3 7 9 13 15 19

For the third time, the minimum number that has never been used is 7. Delete the last number in every 7 numbers. The sequence becomes 1 3 7 9 13 15.

Then you cannot delete any numbers. There are 6 numbers left over. So the answer is 6.

例如：1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

显然不能每 1 个数删除 1 个，那就无意义了。

第一次，删除每 2 个数字中的最后一个数字。 序列变为1 3 5 7 9 11 13 15 17 19

第二次，删除每 3 个数字中的最后一个数字。 序列变为1 3 7 9 13 15 19

第三次，删除每 7 个数字中的最后一个数字。 序列变为1 3 7 9 13 15。

分析