You must be bored of this Algo Cup and thats why you have opened this challenge problem. So, I wouldn't bore you more.

You need to make a magical square of side n which have digits $1 \le m$. All digits i which are $1 \le i \le m$ must appear once in the magical square.

A magic square is a square which has equal sum value of all rows and columns $i.e$ if we add all the integers in a row/column it must be equal to sum of integers in any other row/column.

For a given m, you need to construct a magic square such that $1 \le n \le 10^3$.

For a correct magic square you will get a total score = $n^4*SumValueOfARow$.

INPUT CONSTRAINTS

$1 \le m \le 1000$

INPUT FORMAT

Input contains a single integer m.

OUTPUT

Print a single integer n on the first line of output.After that print n lines each containing n space separated integers, denoting your magic square.