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?

Input

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 $*a*$.

Output

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

Note

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