D. Tournament Construction
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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.

Examples
Input
21 2
Output
40011100101000010
Input
20 3
Output
6000111100011110001011001001101000000