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
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≤ b and c≤ d, prints a natural solution to the equation
x^{2} + y^{2} = z^{2} |
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
x^{2} + y^{2} = z^{2} |
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!”.
Input
2 5 4 13
Output
3^2 + 4^2 = 5^2
Input
1 1 1 1
Output
No solution!