Distantland

In the Republic of Distantland, people celebrate their independence day every year. However, since it happened a very long time ago, nobody remembers the exact date. The only thing known is that today, the number of days elapsed since their independence ($D$) is a perfect square, and it is the largest possible number that can be written as the product of distinct numbers less than or equal to $n$.

Since a year in Distantland has $1000000007$ days, the citizens only need to find $D$ modulo $1000000007$. Note that they are interested in the largest $D$, not the largest $D$ modulo $1000000007$.