Problem Statement

Snuke received two matrices ~A~ and ~B~ as birthday presents. Each of the matrices is an ~N~ by ~N~ matrix that consists of only ~0~ and ~1~ .

Then he computed the product of the two matrices, ~C = AB~ . Since he performed all computations in modulo two, ~C~ was also an ~N~ by ~N~ matrix that consists of only ~0~ and ~1~ . For each ~1 ≤ i, j ≤ N~ , you are given ~c_{i, j}~ , the ~(i, j)~ -element of the matrix ~C~ .

However, Snuke accidentally ate the two matrices ~A~ and ~B~ , and now he only knows ~C~ . Compute the number of possible (ordered) pairs of the two matrices ~A~ and ~B~ , modulo ~10^9+7~ .

Constraints

• ~1 ≤ N ≤ 300~
• ~c_{i, j}~ is either ~0~ or ~1~ .

Input

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

~N~

~c_{1, 1}~ ~...~ ~c_{1, N}~

~c_{N, 1}~ ~...~ ~c_{N, N}~

Output

Print the number of possible (ordered) pairs of two matrices ~A~ and ~B~ (modulo ~10^9+7~ ).

Sample Input 1

2
0 1
1 0

Sample Output 1

6

Sample Input 2

10
1 0 0 1 1 1 0 0 1 0
0 0 0 1 1 0 0 0 1 0
0 0 1 1 1 1 1 1 1 1
0 1 0 1 0 0 0 1 1 0
0 0 1 0 1 1 1 1 1 1
1 0 0 0 0 1 0 0 0 0
1 1 1 0 1 0 0 0 0 1
0 0 0 1 0 0 1 0 1 0
0 0 0 1 1 1 0 0 0 0
1 0 1 0 0 1 1 1 1 1

Sample Output 2

741992411