Consider a list of integers $L$. Initially $L$ contains the integers $1$ through $n$, each of them exactly once (but it may contain multiple copies of some integers later). The order of elements in $L$ is not important. You should perform the following operation $n − 1$ times: \begin{itemize} \item Choose two elements of the list, let's denote them by $x$ and $y$. These two elements may be equal. \item Erase the chosen elements from $L$. \item Append the number $x + y + x \cdot y$ to $L$. \end{itemize} At the end, $L$ contains exactly one integer. Find the maximum possible value of this integer. Since the answer may be large, compute it modulo $10^9 + 7$. \InputFile The first line contains the number of test cases $t$. Each of the next $t$ lines contains a single integer $n~(1 \le n \le 10^6)$. \OutputFile For each test case, print a single line containing one integer --- the maximum possible value of the final number in the list modulo $10^9 + 7$.