XOR maximum-minimum matrices

Chef has an integer matrix $A$ of $N$ rows and $M$ columns, and an integer $X$. A **submatrix** is defined as a rectangle of values inside $A$. More formally, given two intervals $[l, r]$ and $[L, R]$, the corresponding submatrix consists of the values $a_{ij}$ such that $l\le i\le r$ and $L\le j\le R$. Two submatrices are considered different if one of the ranges $[l,r]$ or $[L,R]$ differs.