Description
在太平洋的一个小岛上，岛民想要建立一个环岛的堤坝，我们可以将小岛简化为一个二维平面，你需要使用K条边（这些边要么是水平或者垂直长度为1的边，要么是45度倾斜的长度为√2的边）围成一个多边形，多边形的顶点必须位于整点，然后要让围成的多边形面积最大，你需要求出最大面积是多少。
Input
输入包含多个测试实例，每组实例给出一个数K。（3≤K≤2000000000）
Output
每一行对应一个要求的答案。（保留一位小数）
Sample Input
3
4
5
6
Sample Output
0.5
2.0
2.5
4.0
可以画图推导公式。首先无论拼出来的是什么多边形都可以划分成三角形，最基本的元（3条边构成的三角形）的面积是1*1*0.5=0.5。随着边数增加，有以下规律：
边数k 3 4 5 6 7 8三角形个数 1 4 5 8 9 12
(k-3)/2=a……b（b为余数）
- 若b=0，则面积S=（1+4a)0.5
- 若b!=0，则面积S=（1+4a+3)0.5
<code class="hljs perl has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">#include <stdio.h></span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> main(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> argc, char <span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">*argv</span>[]){ <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> k = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;<span class="hljs-regexp" style="color: rgb(0, 136, 0); box-sizing: border-box;">//</span>边数 <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> a = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;<span class="hljs-regexp" style="color: rgb(0, 136, 0); box-sizing: border-box;">//</span>商 <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> b = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;<span class="hljs-regexp" style="color: rgb(0, 136, 0); box-sizing: border-box;">//</span>余数 float <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">s</span> = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;<span class="hljs-regexp" style="color: rgb(0, 136, 0); box-sizing: border-box;">//</span>面积 <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">while</span>(scanf(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"<span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">%d</span>"</span>, &k) != EOF){ <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(k<<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span> || k><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2000000000</span>) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">continue</span>; a = (k-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>)/<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>; b = (k-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>)<span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">%2</span>; <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(b == <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>) <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">s</span> = (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>+a<span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">*4</span>)<span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">*0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>; <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">s</span> = (<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span><span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">*a</span>+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>)<span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">*0</span>.<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>; <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">printf</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"<span class="hljs-variable" style="color: rgb(102, 0, 102); box-sizing: border-box;">%0</span>.1f\n"</span>, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">s</span>); } <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li></ul>这是我的一个解决办法，公式并未经过严格证明。若有错误请指正，谢谢！
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