Design a combinational logic circuit that has three inputs $A,B,C$ and generates the output $F$ as

follows:

$F(A,B,C)={\displaystyle \underset{m}{\overset{?}{}}}(0,2,6,7)$

The combinational logic circuit should be constructed only using the following two

components:

One $3$ to $8$ decoder, and

the minimum number of two$-$input NAND gates. $($Note: If you solve the question

without meeting this condition, then you will lose $50\%$ of the total question grade$)$