CF232A.Cycles

John Doe started thinking about graphs. After some thought he decided that he wants to paint an undirected graph, containing exactly k cycles of length 3.

A cycle of length 3 is an unordered group of three distinct graph vertices a, b and c, such that each pair of them is connected by a graph edge.

John has been painting for long, but he has not been a success. Help him find such graph. Note that the number of vertices there shouldn't exceed 100, or else John will have problems painting it.

约翰·多伊（John Doe）开始思考图论问题。经过一番思考，他决定绘制一个恰好包含 $k$ 个长度为 3 的环的无向图。

长度为 3 的环是指三个互不相同的图顶点 $a$、$b$ 和 $c$ 组成的无序三元组，且其中每一对顶点之间都由一条图的边相连。

约翰已经尝试绘制很久了，但一直未成功。请帮他找出这样一个图。注意：图中顶点数不得超过 100 个，否则约翰将难以完成绘制。

A single line contains an integer k (1 ≤ k ≤ 105) — the number of cycles of length 3 in the required graph.

一行包含一个整数 $k$（$1 \leq k \leq 10^5$）——即所求图中长度为 3 的环的个数。

In the first line print integer n (3 ≤ n ≤ 100) — the number of vertices in the found graph. In each of next n lines print n characters "0" and "1": the i-th character of the j-th line should equal "0", if vertices i and j do not have an edge between them, otherwise it should equal "1". Note that as the required graph is undirected, the i-th character of the j-th line must equal the j-th character of the i-th line. The graph shouldn't contain self-loops, so the i-th character of the i-th line must equal "0" for all i.

第一行输出一个整数 $n$（$3 \leq n \leq 100$），表示所构造图的顶点数。接下来的 $n$ 行中，每行输出 $n$ 个字符，每个字符为 "0" 或 "1"：第 $j$ 行的第 $i$ 个字符应为 "0"，当且仅当顶点 $i$ 与顶点 $j$ 之间没有边；否则应为 "1"。注意，由于所要求的图是无向图，因此第 $j$ 行的第 $i$ 个字符必须等于第 $i$ 行的第 $j$ 个字符。该图不应包含自环，因此对所有 $i$，第 $i$ 行的第 $i$ 个字符必须为 "0"。