Time Limit: 2 sec / Memory Limit: 1024 MB

Problem Statement

There is a grid with $H$ rows and $W$ columns. Let $(i,j)$ denote the cell at the $i-th$ row from the top $(1≤i≤H)$ and the $j-th$ column from the left $(1≤j≤W)$.

Cell $(i,j) (1≤i≤H,1≤j≤W)$ has a non-negative integer $A_{i,j}$ written on it.

Let us place zero or more dominoes on the grid. $A$ domino covers two adjacent cells, namely one of the following pairs:

1、cells $(i,j)$ and $(i,j+1)$ for $1≤i≤H,1≤j<W$;

2、cells $(i,j)$ and $(i+1,j)$ for $1≤i<H,1≤j≤W$.

No cell may be covered by more than one domino.

For a placement of dominoes, define its score as the bitwise $XOR$ of all integers written in cells not covered by any domino.

Find the maximum possible score.

What is bitwise $XOR$?

For non-negative integers $A$ and $B$, their bitwise $XOR A⊕B$ is defined as follows:

In binary, the $2_k$ bit $(k≥0)$ of $A⊕B$ is $1$ if exactly one of $A$ and $B$ has $1$ in that bit, and $0$ otherwise. For example, $3⊕5=6$ (in binary, $011⊕101=110$). For $k$ non-negative integers $p_1 ,p_2 ,p_3 ,…,p_k$ , their bitwise $XOR$ is $(…((p_1⊕p_2 )⊕p_3)⊕...⊕p_k )$, which can be proved to be independent of the order of the operands.

Constraints

$1≤H$

$1≤W$

$HW≤20$

$0≤A_{i,j} <2^{60} (1≤i≤H, 1≤j≤W)$

All input values are integers.

Input

The input is given from Standard Input in the following format:

$H W$

$A_{1,1}A_{1,2}… A_{1,W}$

$A_{2,1}A_{2,2}… A_{2,W}$

$…$

$A_{H,1}A_{H,2}… A_{H,W}$

Output

Output the answer.

Sample Input 1

3 4
1 2 3 8
4 0 7 10
5 2 4 2

Sample Output 1

15

The grid is as follows:

For example, the placement below yields a score of 15.

No placement achieves a score of 16 or higher, so output 15.

Sample Input 2

1 11
1 2 4 8 16 32 64 128 256 512 1024

Sample Output 2

2047

You may also choose to place no dominoes.

Sample Input 3

4 5
74832 16944 58683 32965 97236
52995 43262 51959 40883 58715
13846 24919 65627 11492 63264
29966 98452 75577 40415 77202

Sample Output 3

131067