VTMO 2017 — Grade 8 — final Question 2

Real $a , b , c , d$ satisfy $\left(a + b\right) \left(c + d\right) = 2 , \left(a + c\right) \left(b + d\right) = 3 , \left(a + d\right) \left(b + c\right) = 4$. Find the minimum sum of their squares.