题目链接：GMOJ 2643。
题目
题目描述
棋盘是由许多个六边形构成的，共有 $n$ 种不同的六边形编号为 $1$ 到 $5$，棋盘的生成规则如下：
- 从中心的一个六边形开始，逆时针向外生成一个个六边形。
- 对于刚生成的一个六边形，我们要确定它的种类，它的种类必须满足与已生成的相邻的六边形不同。
- 如果有多个种类可以选，我们选择出现次数最少的种类。
- 情况3下还有多个种类可以选，我们选择数字编号最小的。
现在要你求第 $N$ 个生成的六边形的编号。
前 $14$ 个六边形生成图如下：
输入格式
第一行：$T$，表示数据组数。
接下来 $T$ 行，每行一个数：$N$，表示第 $N$ 个六边形。
输出格式
共 $T$ 行，每行一个数，表示第 $N$ 个数据的答案。
样例输入输出
#1
- Input:
4
1
4
10
100
- Output
1
4
5
5
数据范围
$100\%$ 数据满足 $1\leq T\leq 20,1\leq N\leq 10^4$。
$30\%$ 数据满足 $1\leq N\leq 10^2$。
题解
本题有多种写法，下面介绍几种比较简单的。
解法A
思路
我们将整个大的图形分为多个部分，每个部分都是由 $6\times k,k\in\mathbb{N _ +}$（中心为特殊情况）个正六边形构成的一个圈。
我们考虑第 $i$ 圈，第 $j$ 个六边形的相邻六边形。
- 内圈的（1个或者2个）。
- 相邻的（前面和后面）。
- 外圈的（3个或者4个）。
于是我们考虑简化一下情况，决定递推，于是我们只需要考虑最多三个相邻六边形：
- 内圈的（1个或者2个）。
- 相邻的（前面）。
另外的，根据相似三角形的相关知识，我们可以求出：
内圈的序数为 $\left\lceil j\times\frac{i-2}{i-1}\right\rceil$ 和 $\left\lfloor j\times\frac{i-2}{i-1}\right\rfloor$。
另外，当一圈即将结束时，这个六边形将会碰到圈首的那个六边形，这需要特殊考虑，我们按照题意模拟即可。
代码
#include<cstdio>
#include<cstring>
#define INF 789846556
const int MAXN=20000+5;
bool Can[9];
int T,n;
int Number[MAXN]={0,1,6},sum[MAXN]={0,1,7};
int color[MAXN];
int Times[9];
void Init(void);
int GetID(int,int);
int GetLast(int,int);
int main(void){
register int i,j;
scanf("%d",&T);
Init();
while(T--){
memset(color,0,sizeof(color));
memset(Times,0,sizeof(Times));
scanf("%d",&n);
for(i=j=1;GetID(i-1,j-1)<=n;++i){
for(j=1;j<=Number[i];++j){
//printf("%d (%d,%d)\n",GetID(i,j),i,j);
memset(Can,true,sizeof(Can));
Can[color[GetID(i,j)-1]]=false;
if(j*Number[i-1]%Number[i]==0){
if(j*Number[i-1]/Number[i]==0){
Can[color[GetID(i-1,Number[i-1])]]=false;
Can[color[GetID(i-1,1)]]=false;
}
else
Can[color[GetLast(i,j)]]=false;
}
else{
if(j*Number[i-1]/Number[i]==0){
Can[color[GetID(i-1,Number[i-1])]]=false;
Can[color[GetID(i-1,1)]]=false;
}
else{
Can[color[GetLast(i,j)]]=false;
Can[color[GetLast(i,j)+1]]=false;
}
}
if(j==Number[i])
Can[color[GetID(i,1)]]=false;
int c=0,times=INF;
for(int k=1;k<=5;++k)
if(Times[k]<times&&Can[k]){
c=k;
times=Times[k];
}
color[GetID(i,j)]=c;
++Times[c];
}
}
printf("%d\n",color[n]);
}
return 0;
}
void Init(void){
register int i;
for(i=3;sum[i-1]<20000;++i){
Number[i]=Number[i-1]+6;
sum[i]=sum[i-1]+Number[i];
//printf("Number[%d]=%d sum[%d]=%d\n",i,Number[i],i,sum[i]);
}
return;
}
int GetID(int i,int j){
return sum[i-1]+j;
}
int GetLast(int i,int j){
return GetID(i-1,j*Number[i-1]/Number[i]);
}
解法B
显然，每个六边形的周围都有六个与它相邻的六边形（因为它有六条边）。
那么我们开数组 $\text{Next} _ {i,x}$ 表示与第 $i$ 个六边形相邻的第 $x$ 个六边形的编号。
考虑初始化的情况后枚举即可。
代码略。
解法C
这是一种新奇的构造法。
我们将六边形压缩进入一个矩阵。
解法可见传送门
解法D
这是四种写法中最快速的一种，但它的前置技能是上述任意一种解法。
这种解法无需详细的思路，十分显然，一看就懂，直接上代码。
#include<cstdio>
const int ans[]={0,1,2,3,4,5,2,3,1,4,5,1,2,3,1,4,3,5,4,2,5,2,1,3,4,5,3,1,2,4,5,1,2,4,3,1,5,3,2,4,5,2,4,1,3,1,2,5,3,4,5,1,2,3,4,5,1,2,4,3,1,5,3,5,2,4,1,3,2,4,5,2,3,1,4,5,1,2,3,4,5,1,2,3,4,5,1,3,2,4,2,1,5,4,3,5,2,3,4,1,5,1,3,4,5,2,3,1,2,4,5,1,2,3,4,5,3,1,2,1,4,5,2,4,3,5,3,2,1,2,5,4,1,4,5,1,3,2,3,4,5,1,2,3,4,5,3,1,2,1,4,5,4,2,3,1,2,5,3,4,5,1,2,3,5,1,4,2,4,3,5,3,1,2,5,2,1,4,3,4,5,1,2,3,4,5,3,1,2,1,4,5,3,4,5,2,1,2,3,4,5,2,3,1,4,5,1,2,3,4,5,1,2,3,5,1,2,4,3,4,5,3,1,4,5,2,1,2,5,3,4,3,1,2,1,4,2,5,3,4,5,1,2,5,3,1,4,3,4,5,2,1,3,4,5,2,3,1,2,4,5,1,2,3,4,5,1,2,3,4,5,1,2,5,3,4,2,3,1,4,5,2,3,1,4,5,1,2,3,4,5,1,3,4,2,5,1,2,3,4,1,5,2,3,5,1,2,4,3,4,5,1,2,3,4,5,3,1,2,4,5,1,4,2,3,2,5,1,5,3,4,3,1,4,2,5,1,4,2,3,1,3,5,4,2,5,1,2,3,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,1,5,2,3,4,5,1,2,3,4,5,3,1,2,1,4,5,3,5,2,4,2,3,1,4,5,1,2,3,4,5,1,2,3,5,1,4,2,3,5,4,2,4,1,3,1,5,3,2,4,5,1,2,3,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,5,4,1,4,2,3,2,5,1,5,3,4,1,2,3,4,5,1,2,4,3,5,1,3,4,2,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,5,2,4,1,4,3,1,5,3,2,4,5,1,2,3,4,5,3,1,2,1,4,5,4,3,2,3,5,1,2,4,1,5,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,1,4,2,4,5,1,3,4,2,3,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,5,2,4,3,1,4,2,1,5,3,1,4,5,4,2,3,1,2,5,3,4,5,1,2,5,4,1,2,3,4,3,5,2,3,1,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,1,2,4,3,4,5,1,4,2,3,5,1,2,3,4,5,1,2,5,3,4,3,1,2,1,5,4,5,2,3,1,2,5,4,3,1,4,2,4,5,3,1,2,3,4,5,2,3,1,4,5,1,2,3,4,1,5,3,4,2,5,1,2,3,4,5,2,1,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,5,3,4,2,1,4,1,3,5,4,2,3,2,5,1,3,4,5,1,2,3,4,2,1,3,4,5,2,5,1,3,1,5,4,2,3,5,1,4,2,3,4,5,1,3,4,5,2,3,1,2,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,2,1,3,4,5,1,2,3,4,5,3,1,2,1,4,5,4,2,3,2,5,1,5,3,4,2,3,1,4,5,1,3,2,5,4,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,3,2,5,1,4,3,2,4,5,2,3,1,5,4,1,2,3,5,4,1,2,3,4,5,1,2,3,4,5,3,1,2,4,5,1,2,3,4,5,1,3,2,1,4,5,4,2,3,1,5,2,5,3,4,3,1,2,1,4,2,5,3,4,5,1,2,3,4,5,1,2,3,4,5,1,3,4,2,5,1,2,4,5,3,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,2,3,1,5,4,1,2,3,5,4,1,2,3,4,5,3,1,2,1,4,5,3,5,2,4,3,1,2,1,4,5,4,3,5,2,1,2,3,4,5,2,1,3,4,5,1,2,3,4,5,1,3,4,2,5,1,2,3,4,5,1,2,3,4,5,1,2,4,5,1,3,4,2,3,5,1,2,4,3,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,4,2,3,1,5,2,3,1,5,4,5,2,3,2,4,1,5,3,4,1,2,3,4,5,1,2,4,3,5,1,2,3,4,5,1,2,5,4,1,3,4,3,5,2,1,3,4,2,5,1,2,3,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,4,2,3,5,1,2,4,3,5,1,2,3,4,5,1,2,5,3,4,3,1,2,1,4,5,4,2,3,2,5,1,4,3,5,2,3,1,4,5,2,1,4,5,3,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,1,4,2,3,4,5,1,2,3,4,1,5,2,4,5,1,2,3,4,5,1,3,4,2,3,5,1,2,3,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,2,3,4,5,1,4,2,3,2,5,1,4,1,3,5,3,2,4,2,5,1,5,3,4,3,1,4,2,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,3,4,2,5,1,3,4,2,1,2,5,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,4,1,5,2,3,4,5,1,2,3,4,5,1,4,2,3,5,1,2,3,4,5,3,1,2,1,4,5,4,3,2,3,5,1,2,1,4,5,4,2,3,2,5,3,1,4,5,1,2,3,5,4,1,2,4,3,5,1,2,3,4,5,1,2,3,5,1,4,2,3,4,5,1,2,3,4,5,1,2,3,4,1,2,5,4,5,1,3,4,2,5,1,3,4,3,1,2,5,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,5,4,1,4,2,3,2,5,1,5,3,4,2,1,4,1,3,5,4,2,3,1,2,5,3,4,5,1,2,5,4,1,2,3,4,3,5,1,2,3,4,5,1,2,4,5,3,1,2,3,4,1,2,5,3,5,1,4,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,4,5,1,2,3,4,1,2,3,4,5,1,5,3,2,4,5,1,2,3,4,1,5,2,3,4,5,1,2,3,4,5,3,1,2,1,4,5,4,2,3,2,5,1,4,3,5,3,1,2,1,4,5,4,2,1,3,5,2,3,4,5,1,2,3,4,5,1,3,2,5,4,1,2,3,4,5,2,3,1,4,5,1,2,3,4,1,5,3,4,2,5,1,2,3,4,5,1,2,3,4,5,1,2,4,3,5,1,2,3,4,1,2,3,5,1,4,5,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,2,1,5,3,1,4,5,4,2,3,2,1,5,1,3,4,5,4,2,3,1,2,5,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,4,5,2,1,3,4,5,1,2,3,4,5,1,2,4,5,3,1,2,3,4,5,1,3,4,5,2,3,1,2,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,2,3,4,5,1,2,4,3,5,1,2,3,4,5,1,2,3,1,4,5,2,3,4,5,1,2,5,3,4,3,1,2,1,5,4,5,2,3,4,3,1,2,1,4,5,4,2,3,2,5,3,1,5,1,4,2,4,5,3,1,2,3,4,5,3,2,4,5,1,2,1,3,4,5,2,3,1,4,5,1,2,3,4,5,1,2,3,4,1,2,5,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,4,3,5,1,2,3,4,5,1,2,3,4,5,3,1,2,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,4,2,3,2,5,1,5,4,3,4,1,2,3,2,5,1,4,3,1,3,5,2,1,4,5,3,4,2,5,1,2,3,4,2,1,3,4,5,1,5,2,3,4,5,1,2,3,4,5,1,2,4,5,3,2,3,1,5,1,4,2,3,4,5,1,2,4,3,1,2,5,3,4,5,1,3,4,5,2,3,1,2,4,5,1,2,3,4,5,1,2,3,4,1,5,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,4,3,5,1,2,3,4,5,3,1,2,1,4,5,3,5,2,4,3,1,2,1,4,5,4,3,2,3,5,1,2,1,4,5,2,3,4,5,1,2,3,1,5,2,3,4,5,4,1,2,3,5,4,2,1,3,4,5,1,2,4,5,3,1,2,3,4,5,1,3,2,5,1,4,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,4,5,2,3,4,3,1,5,1,2,3,4,5,1,2,3,4,1,5,2,3,4,5,1,2,3,4,5,3,1,2,4,5,1,2,3,4,5,1,2,3,4,1,5,2,3,4,5,1,2,3,1,4,5,4,2,3,2,5,1,5,3,4,3,1,2,1,4,5,3,2,4,2,5,1,5,3,4,1,2,3,4,5,1,2,4,3,5,1,2,3,4,5,1,2,5,4,1,2,3,4,3,5,1,2,3,4,5,1,2,3,4,5,2,1,4,5,3,1,2,3,4,1,2,5,3,4,5,1,2,3,5,1,2,4,5,3,4,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,1,5,2,3,4,5,3,1,2,1,4,5,3,5,2,4,3,1,2,1,4,5,4,2,3,2,1,5,1,3,4,5,4,2,5,3,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,4,3,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,1,4,2,3,4,5,1,2,3,4,1,5,3,4,2,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,4,3,5,1,2,3,4,1,5,2,3,4,5,1,2,3,4,5,1,2,5,3,4,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,4,5,1,4,2,3,2,5,1,5,3,4,3,1,2,1,4,5,4,2,3,2,5,1,5,3,4,1,4,2,3,1,2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,2,3,5,1,4,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,4,5,2,1,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,4,3,5,1,2,3,4,5,1,4,2,3,2,5,1,5,3,4,3,1,2,1,4,5,4,2,3,1,5,2,5,3,4,3,1,2,1,4,5,4,2,3,2,5,1,5,3,4,3,1,2,1,4,5,4,3,2,3,5,1,4,2,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,1,4,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,2,1,4,5,3,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,5,1,4,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,3,1,2,1,4,5,4,2,3,2,5,1,4,3,5,3,1,2,1,4,5,4,2,3,1,5,2,5,3,4,3,1,2,1,4,5,4,2,3,2,5,1,5,4,3,4,1,2,3,2,5,3,1,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,2,1,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,5,4,1,2,3,4,3,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,1,2,5,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,1,2,5,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,4,3,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,4,5,1,4,2,3,2,5,1,5,3,4,3,1,2,1,4,5,4,2,3,2,5,1,5,3,4,3,1,2,1,5,4,5,2,3,4,3,1,2,1,4,5,4,3,2,3,5,1,2,1,4,2,5,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2
,3,4,5,1,2,3,4,5,2,1,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,1,5,2,3,4,5,4,1,2,4,5,3,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,3,4,2,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,1,5,3,4,2,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,1,5,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,1,5,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,4,3,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,3,1,2,1,4,5,4,3,2,3,5,1,2,1,4,5,4,3,2,3,5,1,2,1,4,5,4,2,3,2,5,1,4,3,5,3,1,2,1,4,5,4,2,3,5,3,1,2,1,4,5,4,2,5,3,2,3,1,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,2,1,3,4,5,1,5,2,3,4,5,1,2,5,4,1,2,3,4,3,5,1,3,4,2,5,1,2,3,4,5,1,2,3,4,1,2,5,3,4,5,1,2,3,4,5,1,3,4,2,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,2,1,4,5,3,1,2,3,4,5,1,2,4,3,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,1,5,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,1,5,2,3,4,5,1,2,3,4,5,1,4,2,3,2,5,1,5,3,4,3,1,2,1,4,5,3,2,4,2,5,1,5,3,4,3,1,2,1,4,5,4,2,3,2,5,1,5,3,4,3,1,2,1,4,5,4,2,3,2,5,1,5,3,4,1,2,3,4,5,1,2,5,4,1,2,3,4,3,5,1,2,5,4,1,2,3,4,3,5,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,4,1,2,5,3,4,5,1,2,3,4,1,2,5,4,5,3,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,3,2,5,1,4,2,3,4,5,1,2,3,4,1,5,3,4,2,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,2,3,4,1,5,2,3,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,4,3,5,1,2,3,4,5,1,2,4,3,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,3,5,2,4,3,1,2,1,4,5,4,2,3,2,5,1,5,3,4,3,1,2,5,4,1,4,2,3,2,5,1,5,3,4,3,1,2,1,4,5,4,2,3,2,1,5,1,3,4,5,4,2,3,2,5,3,1,4,5,1,2,3,4,5,1,2,3,4,5,1,2,4,3,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,1,5,3,4,2,5,1,2,3,4,1,5,3,4,2,5,1,2,3,4,5,1,2,3,4,1,2,5,3,4,5,1,2,3,4,5,2,3,1,4,5,1,2,3,4,5,1,2,3,4,1,2,4,5,3,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,2,3,4,1,5,2,3,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,4,3,5,1,4,2,3,2,5,1,5,4,3,4,1,2,3,2,5,1,5,3,4,3,1,2,1,4,5,4,3,2,3,5,1,2,1,4,5,4,2,3,2,5,1,5,3,4,3,1,2,1,4,5,4,2,3,2,5,1,4,3,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,1,5,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,3,2,4,5,1,2,1,3,4,5,1,2,4,5,3,1,2,3,4,5,1,2,3,4,5,1,2,3,5,1,4,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,2,3,4,1,5,2,3,4,5,1,2,3,4,5,2,1,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,4,3,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,4,5,1,3,2,4,5,3,1,2,1,4,5,4,3,2,3,5,1,2,1,4,5,4,2,3,2,1,5,1,3,4,5,4,2,3,2,5,1,3,1,4,5,4,2,3,2,5,1,5,3,4,3,1,2,1,4,5,3,2,4,2,5,3,1,4,5,1,2,3,1,5,2,3,4,5,4,1,2,3,4,5,1,2,3,4,5,1,2,5,4,1,2,3,4,3,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,1,4,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,2,3,1,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,4,3,1,2,5,3,4,5,1,2,3,4,5,1,2,4,3,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,3,2,4,5,1,2,3,4,5,1,2,3,4,1,5,2,3,4,5,1,2,3,4,5,2,1,3,4,5,1,2,3,1,4,5,4,2,3,2,5,1,5,4,3,4,1,2,3,2,5,1,5,3,4,3,1,2,1,4,5,4,2,3,2,5,1,5,3,4,3,1,2,1,5,4,5,2,3,4,3,1,2,1,4,5,4,3,2,1,2,5,3,4,5,1,2,5,4,1,2,3,4,3,5,1,2,3,4,5,3,2,4,5,1,2,1,3,4,5,1,2,4,5,3,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,4,3,5,1,2,4,5,3,1,2,3,4,5,2,1,4,5,3,1,2,3,4,5,1,2,3,4,5,1,2,3,4,1,5,3,4,2,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,2,1,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,1,5,2,3,4,5,1,2,3,4,5,1,2,4,3,5,1,2,3,4,5,1,2,3,4,5,1,2,3,5,4};
int T,n;
int main(void){
scanf("%d",&T);
while(T--){
scanf("%d",&n);
printf("%d\n",ans[n]);
}
return 0;
}
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