Ivan is reading a book about tournaments. He knows that a tournament is an oriented graph with exactly one oriented edge between each pair of vertices. The score of a vertex is the number of edges going outside this vertex.

Yesterday Ivan learned Landau's criterion: there is tournament with scores $*d*_{1} ≤ *d*_{2} ≤ ... ≤ *d*_{*n*}$ if and only if for all $1 ≤ *k* < *n*$ and .

Now, Ivan wanna solve following problem: given a set of numbers $*S* = {*a*_{1}, *a*_{2}, ..., *a*_{*m*}}$, is there a tournament with given set of scores? I.e. is there tournament with sequence of scores $*d*_{1}, *d*_{2}, ..., *d*_{*n*}$ such that if we remove duplicates in scores, we obtain the required set ${*a*_{1}, *a*_{2}, ..., *a*_{*m*}}$?

Find a tournament with minimum possible number of vertices.

Input

The first line contains a single integer $*m*$ ($1 ≤ *m* ≤ 31$).

The next line contains $*m*$ distinct integers $*a*_{1}, *a*_{2}, ..., *a*_{*m*}$ ($0 ≤ *a*_{*i*} ≤ 30$) — elements of the set $*S*$. It is guaranteed that all elements of the set are distinct.

Output

If there are no such tournaments, print string "=(" (without quotes).

Otherwise, print an integer $*n*$ — the number of vertices in the tournament.

Then print $*n*$ lines with $*n*$ characters — matrix of the tournament. The $*j*$-th element in the $*i*$-th row should be $1$ if the edge between the $*i*$-th and the $*j*$-th vertices is oriented towards the $*j*$-th vertex, and $0$ otherwise. The main diagonal should contain only zeros.