Which numbers can be written as the sum of two squares?

Input

Two integers \(m, n \in \mathbb{N}\), where \(m \leq n\).

Output

Each sum of squares (\(x^2 + y^2\) where \(x \leq y\)) that results in a value from the interval \([m, n]\). The output is a list of line that are formatted as

x ** 2 + y ** 2 = z

Note

Some numbers can be written as a sum of two squares in multiple ways. The output must contain all of them.

Example

Input:

48
52

Output:

0 ** 2 + 7 ** 2 = 49
1 ** 2 + 7 ** 2 = 50
4 ** 2 + 6 ** 2 = 52
5 ** 2 + 5 ** 2 = 50