For a given $n$ calculate the value of $G$, where $$ G = \sum_{i=1}^{n-1} \sum_{j=i+1}^{n} GCD(i,j) $$ Here $GCD(i, j)$ means the greatest common divisor of integers $i$ and $j$. For those who have trouble understanding summation notation, the meaning of $G$ is given in the following code: \begin{center} \begin{lstlisting}[language=C++] g = 0; for (i = 1; i < n; i++) for (j = i + 1; j <= n; j++) g += gcd(i, j); \end{lstlisting} \end{center} \InputFile Consists of no more than $20000$ lines. Each line contains one integer $n~(1 < n \le 4 \cdot 10^6)$. Input is terminated by a line containing a single zero and should not be processed. \OutputFile For each input number $n$ print in a separate line the corresponding value of $G$. The value of $G$ fits in a $64$-bit signed integer.