Sereja and Mirroring

题意翻译

给一个n*m的矩阵，它是由一个小矩阵进行几次镜像而来， 一次镜像代表把原来矩阵上下颠倒，再放在原来矩阵下面。 问这个矩阵镜像前至少有多少行。

题目描述

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?

输入输出格式

输入格式

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 $ .

输出格式

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

输入输出样例

输入样例 #1

4 3
0 0 1
1 1 0
1 1 0
0 0 1

输出样例 #1

2

输入样例 #2

3 3
0 0 0
0 0 0
0 0 0

输出样例 #2

3

输入样例 #3

8 1
0
1
1
0
0
1
1
0

输出样例 #3

2

说明

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>`