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≥ 3, there is no natural solution (except for x= 0 or y= 0) to the equation

For n= 2, by contrast, there are infinite non-trivial solutions. For instance, 3² + 4² = 5², 5² + 12² = 13², 6² + 8² = 10², ….

Write a program that, given four natural numbers a,b,c,d with a≤ b and c≤ d, prints a natural solution to the equation

such that a≤ x≤ b and c≤ y≤ d.

Input

Input consists of four natural numbers a, b, c, d such that a≤ b and c≤ d.

Output

Print a line following the format of the examples, with a natural solution to the equation

that fulfills a≤ x≤ b and c≤ y≤ 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!”.