prithivMLmods/Coder-Stat

1 2<H1>3Fermat's Last Theorem4</H1>5 6<p>7In the 17th century, Fermat wrote that he proved for any integer $n \geq 3$,8there exist no positive integers $x$, $y$, $z$ such that9$x^n + y^n = z^n$.10However he never disclosed the proof.  Later, this claim was named11Fermat's Last Theorem or Fermat's Conjecture.12</p>13 14<p>15If Fermat's Last Theorem holds in case of $n$, then it also holds16in case of any multiple of $n$.17Thus it suffices to prove cases where $n$ is a prime number18and the special case $n$ = 4.19</p>20 21<p>22A proof for the case $n$ = 4 was found in Fermat's own memorandum.23The case $n$ = 3 was proved by Euler in the 18th century.24After that, many mathematicians attacked Fermat's Last Theorem.25Some of them proved some part of the theorem, which was a26partial success.27Many others obtained nothing.28It was a long history.29Finally, Wiles proved Fermat's Last Theorem in 1994.30</p>31 32<p>33Fermat's Last Theorem implies that for any integers $n \geq 3$34and $z > 1$, it always holds that35<br/>36$z^n > $ max { $x^n + y^n | x > 0, y > 0, x^n + y^n \leq z^n$ }.37<br/>38</p>39<p>40Your mission is to write a program that verifies this in the case41$n$ = 3 for a given $z$.  Your program should read in42integer numbers greater than 1, and, corresponding to each input43$z$, it should output the following:44<br/>45$z^3 - $ max { $x^3 + y^3 | x > 0, y > 0, x^3 + y^3 \leq z^3$ }.46<br/>47</p>48 49<H2>Input</H2>50<p>51The input is a sequence of lines each containing one positive integer52number followed by a line containing a zero.  You may assume that all of53the input integers are greater than 1 and less than 1111.54</p>55 56<H2>Output</H2>57<p>58The output should consist of lines each containing a single59integer number.  Each output integer should be60 61<br/>62$z^3 - $ max { $x^3 + y^3 | x > 0, y > 0, x^3 + y^3 \leq z^3$ }.63<br/>64 65<p>66for the corresponding input integer <I>z</I>.67No other characters should appear in any output line.68</p>69<H2>Sample Input</H2>70<pre>71672473274075</pre>76<H2>Output for the Sample Input</H2>77<pre>7827791080681</pre>82 83