Harmony Analysis

题意翻译

给定 $k$，求 $2^k$ 个 $2^k$ 维向量满足每个向量的坐标表示中任意一维都为 $1$ 或 $-1$，且这些向量两两点积为 $0$。 $0\leq k\leq 9$。

题目描述

The semester is already ending, so Danil made an effort and decided to visit a lesson on harmony analysis to know how does the professor look like, at least. Danil was very bored on this lesson until the teacher gave the group a simple task: find $ 4 $ vectors in $ 4 $ -dimensional space, such that every coordinate of every vector is $ 1 $ or $ -1 $ and any two vectors are orthogonal. Just as a reminder, two vectors in $ n $ -dimensional space are considered to be orthogonal if and only if their scalar product is equal to zero, that is: .Danil quickly managed to come up with the solution for this problem and the teacher noticed that the problem can be solved in a more general case for $ 2^{k} $ vectors in $ 2^{k} $ -dimensinoal space. When Danil came home, he quickly came up with the solution for this problem. Can you cope with it?

输入输出格式

输入格式

The only line of the input contains a single integer $ k $ ( $ 0<=k<=9 $ ).

输出格式

Print $ 2^{k} $ lines consisting of $ 2^{k} $ characters each. The $ j $ -th character of the $ i $ -th line must be equal to ' $ * $ ' if the $ j $ -th coordinate of the $ i $ -th vector is equal to $ -1 $ , and must be equal to ' $ + $ ' if it's equal to $ +1 $ . It's guaranteed that the answer always exists. If there are many correct answers, print any.

输入输出样例

输入样例 #1

2

输出样例 #1

++**
+*+*
++++
+**+

说明

Consider all scalar products in example: - Vectors $ 1 $ and $ 2 $ : $ (+1)·(+1)+(+1)·(-1)+(-1)·(+1)+(-1)·(-1)=0 $ - Vectors $ 1 $ and $ 3 $ : $ (+1)·(+1)+(+1)·(+1)+(-1)·(+1)+(-1)·(+1)=0 $ - Vectors $ 1 $ and $ 4 $ : $ (+1)·(+1)+(+1)·(-1)+(-1)·(-1)+(-1)·(+1)=0 $ - Vectors $ 2 $ and $ 3 $ : $ (+1)·(+1)+(-1)·(+1)+(+1)·(+1)+(-1)·(+1)=0 $ - Vectors $ 2 $ and $ 4 $ : $ (+1)·(+1)+(-1)·(-1)+(+1)·(-1)+(-1)·(+1)=0 $ - Vectors $ 3 $ and $ 4 $ : $ (+1)·(+1)+(+1)·(-1)+(+1)·(-1)+(+1)·(+1)=0 $