How to prove this relation between Ramsey Numbers: $R(s,t)≤R(s,t−1)+R(s−1,t)-1$ for $s,t>2$ when $R(s,t-1)$ and $R(s-1,t)$ are even.

Question

I am beginner in combinatorics and have been following this book PRINCIPLE AND TECHNIQUES IN COMBINATORICS by CHEN CHUAN-CHONG. In this book the authors improves the relation $R(s,t)≤R(s,t−1)+R(s−1,t)$ for $s,t>2$ to above relation by making a constraint that $R(s,t-1)$ and $R(s-1,t)$ are both even.

I am unable to follow through the author's reasoning for this proof.

Please help.