Cycles

题意翻译

## 题目描述 构造一个无向图（没有自环），使这个无向图恰好有 $m$ 个三元环，输出这个无向图的 $01$ 矩阵。 $($无向图的顶点数不超过 $100,1 \leq m \leq 10^5)$ ## 输入输出格式 **输入格式：** 一行一个整数 $m$ 。 **输出格式：** 第一行为无向图的顶点数 $n$，接下来 $n$ 行为这个无向图的 $01$ 矩阵，不需要输出空格。

题目描述

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.

输入输出格式

输入格式

A single line contains an integer $ k $ ( $ 1<=k<=10^{5} $ ) — the number of cycles of length $ 3 $ in the required graph.

输出格式

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 $ .

输入输出样例

输入样例 #1

1

输出样例 #1

3
011
101
110

输入样例 #2

10

输出样例 #2

5
01111
10111
11011
11101
11110