Tournament Construction

2000ms

524288K

Description:

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 d₁ ≤ d₂ ≤ ... ≤ d_n if and only if $\text{[math]}$ for all 1 ≤ k < n and $\text{[math]}$ .

Now, Ivan wanna solve following problem: given a set of numbers S = {a₁, a₂, ..., a_m}, is there a tournament with given set of scores? I.e. is there tournament with sequence of scores d₁, d₂, ..., d_n such that if we remove duplicates in scores, we obtain the required set {a₁, a₂, ..., 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 a₁, a₂, ..., 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.

Sample Input:

2
1 2

Sample Output:

Sample Input:

2
0 3

Sample Output:

Informação

Provedor Codeforces

Código CF850D