1. In a certain sports association, each team can choose at most $t$ distinctive colors for their team uniforms. For a set $S$ of teams, if each team in $S$ can be assigned one of their distinctive colors such that no team in $S$ is assigned any distinctive color of another team in $S$, then the set $S$ is called "color-identifiable." For all positive integers $n, t$, find the maximum value of the integer $g(n, t)$ such that in any sports association where all teams' distinctive colors consist of exactly $n$ different colors, there always exists a color-identifiable set of at least $g(n, t)$ teams.