If $N = n \cdot a $ where $a$ is an integer, show that the variance $V_{SY}(\hat{t}_\pi)$ given by $$ V_{SY}(\hat{t}_\pi) = N^2 \dfrac{1}{a} \sum_{r=1}^{a} \left( \bar{y}_{Sr} - \bar{y}_U\right)^2 $$ with $\bar{y}_U = \sum_U y_k/N$ which is the population mean, can be written as $$ V_{SY}(\hat{t}_\pi) = \dfrac{1}{2} \sum_{r=1}^{a} \sum_{r^{\prime}=1}^{a} \left( t_{Sr} - t_{Sr^{\prime}}\right)^2$$ where $t_{Sr} = \sum_{Sr} y_k $
Would someone be so kind of giving me a Hint?, I think I'm overthinking it and it's more simple than it looks, the exercise is from Model Assited Survey Sampling-Snärdal,ex 3.24