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: