A9372. Sereja and Mirroring

Let's assume that we are given a matrix $b$ of size $x×y$ , let's determine the operation of mirroring matrix $b$ . The mirroring of matrix $b$ is a $2x×y$ matrix $c$ which has the following properties:

- the upper half of matrix $c$ (rows with numbers from $1$ to $x$ ) exactly matches $b$ ;
- the lower half of matrix $c$ (rows with numbers from $x+1$ to $2x$ ) is symmetric to the upper one; the symmetry line is the line that separates two halves (the line that goes in the middle, between rows $x$ and $x+1$ ).

Sereja has an $n×m$ matrix $a$ . He wants to find such matrix $b$ , that it can be transformed into matrix $a$ , if we'll perform on it several (possibly zero) mirrorings. What minimum number of rows can such matrix contain?

The first line contains two integers, $n$ and $m$ $(1<=n,m<=100)$ . Each of the next $n$ lines contains $m$ integers — the elements of matrix $a$ . The $i$ -th line contains integers $a_{i1},a_{i2},...,a_{im}$ $(0<=a_{ij}<=1)$ — the $i$ -th row of the matrix $a$ .

In the single line, print the answer to the problem — the minimum number of rows of matrix $b$ .

In the first test sample the answer is a $2×3$ matrix $b$ :

<br></br>001<br></br>110<br></br>If we perform a mirroring operation with this matrix, we get the matrix $a$ that is given in the input:

<br></br>001<br></br>110<br></br>110<br></br>001<br></br>