Description

Input an array with $n$ rows and $m$ columns, and output its transpose. Specifically,
the number in the $i$-th row and $j$-th column of the output should be the number in the $j$-th row and $i$-th column of the input.
$1 \le n \le 20000; 1 \le m \le 20000; 1 \le n * m \le 20000; 1 \le a[i][j] \le 1000$
Note: You cannot declare a two-dimensional array with both dimensions of size $20000$ (arrays cannot be too large, and the size of a two-dimensional array is the product of its dimensions).
A two-dimensional array is essentially equivalent to a one-dimensional array, so you only need a one-dimensional array of size $20000$.

Input Format

First line contains two integers $n$ and $m$ representing the number of rows and columns of the array.
Next $n$ lines, each containing $m$ integers representing the array contents.

Output Format

First line outputs $m$ and $n$. Then output the transpose, consisting of $m$ rows and $n$ columns. The number in the $i$-th row and $j$-th column should be the number in the $j$-th row and $i$-th column of the input.

Sample

3 2
1 2
3 4
5 6

2 3
1 3 5
2 4 6