Jailing

Bobo has a matrix of size $n \times m$ filled with integers. It is guaranteed that all cells which contain the same value are $4$-side connected.

Let's define a jailing $J\_x$ of a connected component with value $x$ as minimum-area rectangle (with sides parallel to the matrix sides) that covers all cells of the component.

For each jailing $B\_x$, Jessica would like to find the value of

$s(B\_x)=\sum\_{B\_y \in A \setminus \\{x\\}} f(B\_x, B\_y) \cdot y$

where $A$ is the set of all integers in the matrix and

$f(B\_x,B\_y)=\begin{cases} 0 & \text{ the area of intersection of } B\_x \text{ and } B\_y \text{ is } 0 \\\ 0 & B\_x \text{ is completely inside } B\_y \text{ or vice versa} \\\ 1 & \text{Otherwise} \end{cases}$

The input consists of several test cases terminated by end-of-file. For each test case:

The first line contains two integers $n$ and $m$ -- the size of the matrix.

The second line contains $n \cdot m$ integers $a\_{1,1}, a\_{1,2}, \ldots, a\_{1, m}$, $a\_{2,1}, a\_{2,2}, \ldots, a\_{2, m}$, $\ldots$, $a\_{n, 1}, a\_{n, 2}, \ldots, a\_{n,m}$, where $a\_{i,j}$ is the value in the $i$-th row and the $j$-th column.

For each test case, output an integer denoting the value of $\sum\_{x \in A} s(x) \oplus x$, where $\oplus$ denotes the exclusive-or (XOR) operator.

• $1 \leq n \cdot m \leq 10^6$
• $1 \leq a\_{i,j} \leq nm$
• It is guaranteed that all cells which contain the same value are $4$-side connected.
• It is guaranteed that the sum of $n \cdot m$ in all test cases does not exceed $10^7$.