0 \equiv \sum_{i=1}^{n}{\left[ (x_{i+1}-x_{i})^2+(y_{i+1}-y_{i})^2 \right]}~(mod~2)=\sum_{i=1}^{n}{|A_{i}A_{i+1}|^2} \equiv \sum_{i=1}^{n}{|A_{i}A_{i+1}|}~(mod~2)