Fermat's last theorem (1) P36430

A famous theorem of the mathematician Pierre de Fermat, proved after more than 300 years, states that, for any natural number $n\ge 3$, there is no natural solution (except for $x= 0$ or $y= 0$) to the equation $$x^{n} + y^{n} = z^{n} .$$ For $n= 2$, by contrast, there are infinite non-trivial solutions. For instance, $3^2 + 4^2 = 5^2$, $5^2 + 12^2 = 13^2$, $6^2 + 8^2 = 10^2$, ….

Write a program that, given four natural numbers $a,b,c,d$ with $a\le b$ and $c\le d$, prints a natural solution to the equation $$x^2 + y^2 = z^2$$ such that $a\le x\le b$ and $c\le y\le d$.

Input

Input consists of 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 $$x^2 + y^2 = z^2$$ that fulfills $a\le x\le b$ and $c\le y\le d$. If there is more than one solution, 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 solutions, print “No solution!”.