Odd Subrectangles

There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.

Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:

• The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.

Constraints

• 1 \leq N,M \leq 300
• 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M a_{11} ... a_{1M} : a_{N1} ... a_{NM}

Output

Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.

Examples

Input

2 2 0 1 1 0

Output

6

Input

2 3 0 0 0 0 1 0

Output

8

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N M a_{11} ... a_{1M} : a_{N1} ... a_{NM}

outputFormat

Output

Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.

Examples

Input

2 2 0 1 1 0

Output

6

Input

2 3 0 0 0 0 1 0

Output

8

样例

2 2
0 1
1 0

6