CF426B.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 2_x_ × 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 2_x_) 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?

假设我们给定一个大小为 $x \times y$ 的矩阵 $b$，定义矩阵 $b$ 的镜像操作如下：矩阵 $b$ 的镜像是一个大小为 $2x \times y$ 的矩阵 $c$，满足以下性质：

• 矩阵 $c$ 的上半部分（即第 $1$ 行至第 $x$ 行）与 $b$ 完全相同；
• 矩阵 $c$ 的下半部分（即第 $x+1$ 行至第 $2x$ 行）与上半部分关于二者之间的分界线对称；该对称轴为位于中间的直线，即位于第 $x$ 行与第 $x+1$ 行之间的水平中线。

谢尔盖有一个 $n \times m$ 的矩阵 $a$。他希望找到一个矩阵 $b$，使得对 $b$ 执行若干次（可能为零次）镜像操作后可以得到矩阵 $a$。满足条件的矩阵 $b$ 所能具有的最小行数是多少？

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__i_1, _a__i_2, ..., a__im (0 ≤ a__ij ≤ 1) — the i-th row of the matrix a.

第一行包含两个整数 $n$ 和 $m$（$1 \leq n, m \leq 100$）。接下来的 $n$ 行每行包含 $m$ 个整数——即矩阵 $a$ 的元素。第 $i$ 行包含整数 $a_{i1},\ a_{i2},\ \dots,\ a_{im}$（$0 \leq a_{ij} \leq 1$）——即矩阵 $a$ 的第 $i$ 行。

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

在单行中输出问题的答案——矩阵 $b$ 的最小行数。

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

001
110

If we perform a mirroring operation with this matrix, we get the matrix a that is given in the input:

001
110
110
001

在第一个测试样例中，答案是一个 $2 \times 3$ 矩阵 $b$：

001  
110  

若对这个矩阵执行镜像操作，即可得到输入中给出的矩阵 $a$：

001  
110  
110  
001