Design a XOR2 by 4 NAND2

Design a XOR2 gate with 4 NOR2 gates. The most nearby answer is to use 5 XOR2 gates as the following fomula.

O = A & !B + !A & B = !(!(A&!B)&!(!A&B))

According to the formula above, it takes 3 NAND2 for three “&” symbol locations, and !A and !B need another two, so the total is 5.

There is a solution existing. The trick part is to have A&!A and B&!B to combine with other terms.

O = A & !B + !A & B = A&!A + A&!B + !A&B + B&!B  = A&(!(A&B) + B&!(A&B) = !(!(A&(!(A&B))) & !(B&!(A&B))))