import Control.Monad
import Data.Char
import Data.List
import System.Console.GetOpt
import System.Environment
import System.Exit
import System.IO
import Text.Printf


import System( getArgs )


main = do
  args <- getArgs
 -- print $ " The input args are :" ++ ( (  ((++ " ") . (show )  =<<) ) $ ( map read args ::[Int]) )
  printf $  nqueens $ ( map read args ::[Int])!!0 

qoer,noha,nova,nosea,noswa::(Integral n, Enum n ,Ord n)=> n -> [[n]] -- take size of board and return a list of clauses.

qoer  n = [ [ (n* (j-1) + i ) | i <- [1..n] ] ++ [0] | j <- [1..n] ]
noha  n = [ [ -1 *(n * ( j-1) + i )  , -1* (n * ( j-1) + k) , 0 ] |  j <- [1..n] , i <- [ 1.. (n-1)] , k <- [ (i+1)..n] ]
nova  n = [ [ -1 *(n * ( j-1) + i )  , -1*( n * ( k-1) + i) , 0 ] |  i <- [1..n] , j <- [ 1.. (n-1)] , k <- [ (j+1)..n] ]
nosea n = [ [ -1 *(n * ( j-1) + i )  , -1*( n * ( j-1 + k ) + i + k ) , 0 ] |  i <- [1..(n-1)] , j <- [ 1.. (n-1)] , k <- [1..(n*n)] , ( ( ( i+k) <= n ) && ( ( j+k) <=n ) ) ] -- bugs lurk here
noswa n = [ [ -1 *(n * ( j-1) + i )  , -1*( n * ( j-1 + k ) + i - k ) , 0 ] |  i <- [2..n] , j <- [ 1.. (n-1)] , k <- [1..(n*n)] , ( ( ( i-k) >= 1 ) && ( ( j+k) <=n ) ) ] -- bugs lurk here

generate::(Integral n, Enum n, Ord n) => n -> [[n]] --  -- take size of board and return a list of clauses.
generate n = ( qoer n) ++ (noha n) ++ (nova n) ++ (nosea n) ++ (noswa n)

printclause::(Integral n, Enum n, Ord n) => [n]->String
printclause l = (((++" ").show) =<< ( init l)) ++ (show ( last l) )

nqueens::(Integral n, Enum n, Ord n) => n -> String
nqueens nq = (header nv  nc )   ++  unlines ( map printclause clauses ) 
  where 
    clauses = generate nq
    nc      = genericLength clauses
    nv      = nq *nq 

header::(Integral n, Enum n, Ord n)=>n->n->String
header nv nc ="p cnf " ++ (show  nv )++ " " ++ ( show nc )++ "\n"