By Tim Kelly and Joseph CampbellTOKYO (Reuters) -Japan’s ruling party picks the country’s likely next prime minister on Saturday, aiming to regain public trust as voters reeling from rising prices turn to opposition groups promising big stimulus and clampdowns on foreigners. Also considered a contender is Chief Cabinet Secretary Yoshimasa Hayashi, 64, a centrist party veteran who has held the weighty foreign, defence and agriculture portfolios. But this is not assured as the party and its coalition partner lost their majorities in both houses in the past year. The rank-and-file vote share, however, drops to 47, favouring the candidate with the stronger backing among the parliamentary party. If selected, Koizumi would be a few months older than Hirobumi Ito when he became Japan’s first prime minister in 1885, under the nation’s prewar constitution.