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B. Sereja and Mirroring

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLet'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*_{i1}, *a*_{i2}, ..., *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*.

Examples

Input

4 3

0 0 1

1 1 0

1 1 0

0 0 1

Output

2

Input

3 3

0 0 0

0 0 0

0 0 0

Output

3

Input

8 1

0

1

1

0

0

1

1

0

Output

2

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

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

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