TH-TMO 2021 Problem 6

The cheering team of Ubon Ratchathani University sits on the amphitheater that has $441$ seats arranged into a $21\times 21$ grid. Every seat is occupied by exactly one person, and each person has a blue sign and a yellow sign.

Count the number of ways for each person to raise one sign so that each row and column has an odd number of people raising a blue sign.