for the n queens problem:

how can i verify if a given configuration is avalid solution to the n queens problem. i am trying to check if a queen can attack another queen can attack another queen using haskell.

using the signature:

queens:: [Int] -> Bool

Strategies: A configuaration is a valid solution to the n-queen problem is all of the following:

All n queens are at the valid positions- that is row and column number they are at must be between 1 to n

No two queens are in the same column- this condition automatically satisfied since we can only put one number in each position of the list

No two queens are in the same row- this means making sure no two queens having the same row number

No two queens are on the same diagnol- this mean making sure:

no two queens having the same (row + column) value;and

no two queens have the same (row - column) value

If condition are met then the function should return true otherwise false.