Tokyo, Oct. 27 (Jiji Press)--Japan's benchmark Nikkei 225 stock average closed above 50,000 for the first time ever on Monday, amid hopes for new Japanese Prime Minister Sanae Takaichi's policies. The Nikkei index finished at 50,512.32, up 1,212.67 points, or 2.45 pct, from Friday. The broader TOPIX index climbed 55.60 points, or 1.70 pct, to 3,325.05, also hitting a new record high. "Me...