Accidentally_Coder, a renowned coder from CSEland, is in a dilemma – she wants to give her friend, The_Author, a special gift. After thinking for a while, she went to her favorite shop at Zindabazar and bought an empty matrix $$$A$$$ of size $$$n \times n$$$. She knows that her friend loves numbers which are power of $$$2$$$. So she decided to fill the matrix in a way that the following conditions hold:

• For each $$$1 \leq i \leq n$$$, $$$1 \leq j \leq n$$$, $$$A_{i,j}$$$ is an integer and $$$1 \leq A_{i,j} \leq 10^9$$$ holds

• The sum of numbers in each row is a power of $$$2$$$ (that is, $$${\sum_{j=1}^n A_{i,j}}$$$ should be a power of $$$2$$$ for each $$$1 \leq i \leq n$$$)

• The sum of numbers in each column is a power of $$$2$$$ (that is, $$${\sum_{i=1}^n A_{i,j}}$$$ should be a power of $$$2$$$ for each $$$1 \leq j \leq n$$$)

• The sum of numbers in each of the primary and secondary diagonals is a power of $$$2$$$ (that is, $$${\sum_{i=1}^n A_{i,i}}$$$ should be a power of $$$2$$$ and $$${\sum_{i=1}^n A_{i,n + 1 - i}}$$$ should be a power of $$$2$$$)

A number $$$P$$$ is considered a power of $$$2$$$, if there is some integer $$$i$$$$$$(0 \leq i)$$$, for which $$$P = 2^i$$$

Your task is to find any matrix of size $$$n \times n$$$ satisfying these conditions or report that no such matrix exists.