Fermat's last theorem (2) P18203

This is another exercise about Fermat’s last theorem. (See the exercise problem://problemsjutge.org:problems/p1/roura/fermat-1.pbm.)

Write a program such that, given a sequence of lines, each one with four natural numbers $a, b, c, d$ with $a\le b$ and $c\le d$, prints the first natural solution to the equation $$x^3 + y^3 = z^3$$ that fulfills the restrictions of a line: $a\le x\le b$ and $c\le y\le d$.

Input

Input has several lines, each one with four natural numbers $a,b,c,d$ such that $a\le b$ and $c\le d$.

Output

Print a line following the format of the examples, with a natural solution to the equation $$x^3 + y^3 = z^3$$ that fulfills the restrictions of a line. If there are two or more lines with solution, print the first found. If there are several solutions for the same line, print the one with the smallest $x$. If there is a tie in $x$, print the solution with the smallest $y$. If there are no lines with solution, print “No solution!”.