Tournament Construction

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 ≤ ... ≤ dn if and only if for all 1 ≤ k < n and .

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

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, ..., am (0 ≤ ai ≤ 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

2 1 2

Output

4 0011 1001 0100 0010

Input

2 0 3

Output

6 000111 100011 110001 011001 001101 000000

inputFormat

Input

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

The next line contains m distinct integers a1, a2, ..., am (0 ≤ ai ≤ 30) — elements of the set S. It is guaranteed that all elements of the set are distinct.

outputFormat

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

2 1 2

Output

4 0011 1001 0100 0010

Input

2 0 3

Output

6 000111 100011 110001 011001 001101 000000

样例

2
0 3

6
000000
101100
100110
100011
110001
111000

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