Prove that the following languages are not context-free:

a) {0ⁿ1ⁿ0ⁿ1ⁿ : n 0} over S = {0, 1}

b) {w₁#w₂#...#w_n : n 2; w_i {0, 1}^*; some w_j = w_k; j k; 2 j, k n} over S = {0, 1, #}

c) {w : w has same number of 1s as 2s and same number of 3s as 4s} over S = {1, 2, 3, 4}