By Lucia Mutikani WASHINGTON(Reuters) -U.S. home sales unexpectedly increased in January, but investors paying in cash are squeezing out first-time buyers from the housing market amid record low inventory and higher prices. The surge in sales of previously owned homes last month reported by the National Association of Realtors on Friday likely reflected buyers rushing in to close on contracts in anticipation of mortgage rate rising further. Mortgage rates have climbed to levels not seen since 2019 as the Federal Reserve is expected to start increasing interest rates next month to tame soaring …