Fermat’s last theorem (1)

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!”.

Problem information

Author: Unknown
Translator: Carlos Molina

Generation: 2026-01-25T10:29:07.862Z