Given a multiset (elements may be duplicates), $K$ of integers $ \ge 2$, the sum of remainders function associated with $K, S_K$ , defined on non-negative integers, $n$, is given by:

$S_K(n) = \sum(k\ in\ K\ |\ n \bmod k)$

For instance, if $K = \{2, 5, 5, 11\}$,

$S_K(23) = 23 \bmod 2 + 23 \bmod 5 + 23 \bmod 5 + 23 \bmod 11 = 1 + 3 + 3 + 1 = 8$.

Note that $S_K(0) = 0$ for any $K$.

For this problem you will write a program which takes as input the values of $S_K (n)$ for $n$ from $1$ to $N$ for some unknown multiset $K$. The program will output the number of integers in $K$ followed by the integers in $K$ in non-decreasing order.

Input consists of multiple lines. The first line contains a single decimal integer $N, (1 ≤ N ≤ 100)$, which is the number of values of $S_K (n), (1 \le n \le N)$, that follow. The following lines contain the $N$ values as space separated decimal integers, $10$ values per line (except perhaps for the last line).

There is one line of output containing a space separated sequence of decimal integers. The first value is the number, $m$, of integers in the multiset $K$. This is followed by the $m$ integers of the multiset $K$ in non-decreasing order. Note: if a value is a member multiple times, it should appear in the list that many times.