Hadamard matrix. The n-by-n Hadamard matrix H(n) is a boolean matrix with the remarkable p...

Hadamard matrix. The n-by-n Hadamard matrix H(n) is a boolean matrix with the remarkable property that any two rows differ in exactly n / 2 values. (This property makes it useful for designing error-correcting codes.) H(1) is a 1-by-1 matrix with the single element true, and for n > 1, H(2n) is obtained by aligning four copies of H(n) in a large square, and then inverting all of the values in the lower right n-by-n copy, as shown in the following examples (with T representing true and F representing false, as usual).

Write a program that takes an integer command-line argument n and prints H(n). Assume that n is a power of 2.