Simple division

Integer division between a dividend $n$ and a divisor $d$ yields a quotient $q$ and a remainder $r$. $q$ is the integer which maximizes $q\cdot d$ such that $q\cdot d\le n$ and $r=n-q\cdot d$.

For any set of integers there is an integer $d$ such that each of the given integers when divided by $d$ leaves the same remainder.

Input

Each line contains a sequence of nonzero $32$-bit signed integers separated by space. The last number on each line is $0$ and this number does not belong to the sequence. There will be at least $2$ and no more than $1000$ numbers in a sequence; not all numbers occurring in a sequence are equal. The last line contains a single $0$ and should not be processed.

Output

For each input line, print the largest integer which when divided into each of the input integers leaves the same remainder.

Examples