Inverse

Prime number $n$ is given. The inverse number to $i(1\le i<n)$ is such number $j$ that $i\ast j=1(modn)$. It's possible to prove that for each $i$ exists only one inverse.

For all possible values of $i$ find the inverse numbers.

Input

One prime number $n(2\le n\le 10^6)$.

Output

Print $n-1$ numbers. The $i$-th printed number should be the inverse to $i$.

Examples