On the origins of the Turkic directive suffixes -jar(y) and -sar(y)

This study is devoted to the problem of the interrelationship between Turkic syŋar ‘direction’ and jak ~ jan ‘side’ on the one hand, and the Khakas, Shor and Oyrot directive suffixes -jar(y) ~ -sar(y) ~ -sāra, and so on, on the other. The paper seeks to answer four questions: (1) Are jak ‘side’ and jan id. two derivatives ultimately of the same root *√ja?; (2) How do jak ‘side’ and sak id. compare?; (3) If it is true that jar, sar < *jagar, *sagar, how, then, should the final vowel in jary, sara, etc. be explained?; (4) How do Old Tkc. syŋar ‘direction’ (also used as a directive postposition) and sar ~ jar compare?