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Fermat's last theorem (2) P18203

Statement

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This is another exercise about Fermat’s last theorem. (See the exercise ‍.)

Write a program such that, given a sequence of lines, each one with four natural numbers a, b, c, d with a≤ b and c≤ d, prints the first natural solution to the equation

x³ + y³ = z³

that fulfills the restrictions of a line: a≤ x≤ b and c≤ y≤ d.

Input

Input has several lines, each one with 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

x³ + y³ = z³

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!”.

Public test cases

Input

2 5 4 13

Output

No solution!

Input

1 1 1 1
0 1 0 1
1 100 1 100

Output

0^3 + 0^3 = 0^3

Information

Author: Salvador Roura
Language: English
Translator: Carlos Molina
Original language: Catalan
Other languages: Catalan
Official solutions: C++ Java Python
User solutions: C C++ Python