Let $N^2$ be the total inhabitants such that: $N^2 + 100 = x^2+1$ (i); $N^2 + 200 = y^2$ (ii). Subtracting (i) from (ii) yields $100 = y^2-x^2-1 \Rightarrow 101= y^2-x^2 = (y+x)(y-x)$ (iii). SInce $101$ is a prime, we have: $101 = y+x$ (iv); $1 =y-x$ (v) which yields $x=50, y = 51$. Substitution of $x$ and $y$ respectively into (i) and (ii) respectively yields $N^2 = 7^4 =$$\fbox{ 2401}$.