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
n, m = map(int, input().split())
a = [list(map(int, input().split())) for _ in range(n)]

mod = 998244353

for i in range(n):
    for j in range(m):
        a[i][j] = a[i][j] % 2

# 掃き出し法
rank = 0
for i in range(n):
    target = -1
    for j in range(rank, m):
        if a[i][j]:
            target = j
            break

    if target == -1:
        continue

    if target != rank:
        for k in range(rank, n):
            a[k][rank], a[k][target] = a[k][target], a[k][rank]

    for k in range(i+1, n):
        if a[k][rank]:
            for j in range(m):
                a[k][j] ^= a[i][j]

    rank += 1


def modpow(a, n, mod=mod):
    res = 1
    while n > 0:
        if n & 1:
            res = res * a % mod
        a = a * a % mod
        n >>= 1
    return res

print(modpow(2, m-1) * (modpow(2, n) - modpow(2, n-rank)) % mod)
