The U.S. dollar stayed strong in the mid-161 yen zone early Tuesday in Tokyo after hitting a fresh 37-year high overnight, as rising U.S. Treasury yields reinforced prospects that the interest rate gap between the United States and Japan will remain wide. At 9 a.m., the dollar fetched 161.51-52 yen compared with 161.44-54 yen in New York after hitting 161.72 yen, its highest since December 1986, and 161.01-03 yen in Tokyo at 5 p.m. Monday. The euro was quoted at $1.0735-0739 and 173.38-46 yen against $1.0735-0745 and 173.40-50 yen in New York and $1.0754-0756 and 173.16-20 yen in Tokyo late Mo…