Problem Statement

You are given $N$ length-$M$ sequences, where each element is $0$ or $1$. The $i$-th sequence is $A_i = (A_{i, 1}, A_{i, 2}, \dots, A_{i, M})$.

For integers $i, j \ (1 \leq i, j \leq N)$, define $f(i, j)$ as follows:

• $f(i, j) :=$ The smallest non-negative integer $x$ such that $A_i$ and $A_j$ become identical after performing the following operation $x$ times, or $0$ if such $x$ does not exist.
• For all integers $k \ (1 \leq k \leq M)$ simultaneously, replace $A_{i, k}$ with $\displaystyle \left (\sum_{l=1}^{k} A_{i, l} \right ) \bmod 2$.

Find $\displaystyle \sum_{i=1}^{N} \sum_{j=i}^{N} f(i, j)$, modulo $998244353$.

Constraints

• $1 \leq N \times M \leq 10^6$
• $A_{i, j} \in \{0, 1\}$

Input

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

N M
A_{1, 1} A_{1, 2} \cdots A_{1, M}
A_{2, 1} A_{2, 2} \cdots A_{2, M}
\vdots
A_{N, 1} A_{N, 2} \cdots A_{N, M}

Output

Print the answer in one line.