The U.S. dollar remained a steady rate against the yen Tuesday morning in Tokyo, keeping its gains in New York overnight on a hopeful beginning to the grand holiday shopping season in the United States. At noon, the dollar traded at 78.16-21 yen against 77.95-78.05 yen in New York and 77.71-72 yen in Tokyo at 5 p.m. Monday. The euro changed hands at 1.3316-3321 dollars and 104.07-10 yen compared with 1.3315-3325 dollars and 103.79-89 yen in New York and 1.3295-3296 dollars and 103.32-36 yen in Tokyo late Monday afternoon.