Clear Symmetry
题意翻译
【问题描述】
给你一个整数 x,表示有 x 个 1,现在你要创造一个 n × n 的矩阵,把这 x 个 1 填到矩阵里,每两个 1 之间不能相邻,且构成的矩阵关于横方向和纵方向对称,问所需矩阵最短边长为多少。
【输入描述】
输入一个整数 x,表示矩阵中 1 的个数。
【输出描述】
输出矩阵的最小边长。
1<= x <=100
题目描述
Consider some square matrix $ A $ with side $ n $ consisting of zeros and ones. There are $ n $ rows numbered from $ 1 $ to $ n $ from top to bottom and $ n $ columns numbered from $ 1 $ to $ n $ from left to right in this matrix. We'll denote the element of the matrix which is located at the intersection of the $ i $ -row and the $ j $ -th column as $ A_{i,j} $ .
Let's call matrix $ A $ clear if no two cells containing ones have a common side.
Let's call matrix $ A $ symmetrical if it matches the matrices formed from it by a horizontal and/or a vertical reflection. Formally, for each pair $ (i,j) $ $ (1<=i,j<=n) $ both of the following conditions must be met: $ A_{i,j}=A_{n-i+1,j} $ and $ A_{i,j}=A_{i,n-j+1} $ .
Let's define the sharpness of matrix $ A $ as the number of ones in it.
Given integer $ x $ , your task is to find the smallest positive integer $ n $ such that there exists a clear symmetrical matrix $ A $ with side $ n $ and sharpness $ x $ .
输入输出格式
输入格式
The only line contains a single integer $ x $ ( $ 1<=x<=100 $ ) — the required sharpness of the matrix.
输出格式
Print a single number — the sought value of $ n $ .
输入输出样例
输入样例 #1
4
输出样例 #1
3
输入样例 #2
9
输出样例 #2
5
说明
The figure below shows the matrices that correspond to the samples:
![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF201A/4a353f15397909088e2fcb0cff23c93ecb30c822.png)