[USACO解题报告]The Castle (castle)

第一次写解题报告。好多USACO的程序写完后都放在学校了，没拿回来，所以没能写结题报告。刚才做了一道，叫The Castle，现在把解题报告放上去。

原题：

The Castle
IOI’94 – Day 1

In a stroke of luck almost beyond imagination, Farmer John was sent a ticket to the Irish Sweepstakes (really a lottery) for his birthday. This ticket turned out to have only the winning number for the lottery! Farmer John won a fabulous castle in the Irish countryside.

Bragging rights being what they are in Wisconsin, Farmer John wished to tell his cows all about the castle. He wanted to know how many rooms it has and how big the largest room was. In fact, he wants to take out a single wall to make an even bigger room.

Your task is to help Farmer John know the exact room count and sizes.

The castle floorplan is divided into M (wide) by N (1 <=M,N<=50) square modules. Each such module can have between zero and four walls. Castles always have walls on their “outer edges” to keep out the wind and rain.

Consider this annotated floorplan of a castle:

     1   2   3   4   5   6   7
   #############################
 1 #   |   #   |   #   |   |   #
   #####---#####---#---#####---#
 2 #   #   |   #   #   #   #   #
   #---#####---#####---#####---#
 3 #   |   |   #   #   #   #   #
   #---#########---#####---#---#
 4 # ->#   |   |   |   |   #   #
   ############################# 
#  = Wall     -,|  = No wall
-> = Points to the wall to remove to
     make the largest possible new room

By way of example, this castle sits on a 7 x 4 base. A “room” includes any set of connected “squares” in the floor plan. This floorplan contains five rooms (whose sizes are 9, 7, 3, 1, and 8 in no particular order).

Removing the wall marked by the arrow merges a pair of rooms to make the largest possible room that can be made by removing a single wall.

The castle always has at least two rooms and always has a wall that can be removed.

PROGRAM NAME: castle

INPUT FORMAT

The map is stored in the form of numbers, one number for each module, M numbers on each of N lines to describe the floorplan. The input order corresponds to the numbering in the example diagram above.

Each module number tells how many of the four walls exist and is the sum of up to four integers:

1: wall to the west
2: wall to the north
4: wall to the east
8: wall to the south

Inner walls are defined twice; a wall to the south in module 1,1 is also indicated as a wall to the north in module 2,1.

Line 1:

Two space-separated integers: M and N

Line 2..:

M x N integers, several per line.

SAMPLE INPUT (file castle.in)

7 4

11 6 11 6 3 10 6
7 9 6 13 5 15 5
1 10 12 7 13 7 5
13 11 10 8 10 12 13

OUTPUT FORMAT

The output contains several lines:

Line 1:

The number of rooms the castle has.

Line 2:

The size of the largest room

Line 3:

The size of the largest room creatable by removing one wall

Line 4:

The single wall to remove to make the largest room possible

Choose the optimal wall to remove from the set of optimal walls by choosing the wall farthest to the west (and then, if still tied, farthest to the south). Name that wall by naming the module that borders it on either the west or south, along with a direction of N or E giving the location of the wall with respect to the module.

SAMPLE OUTPUT (file castle.out)

我的非正式的USACO题目翻译，翻译得不好，欢迎大家指正。

城堡

IOI’94 – Day 1

以我们憨厚的USACO主人公农夫约翰(Farmer John) 无法想象的运气, 我们的农夫约翰在他生日那天收到了一份特别的礼物：一张“幸运爱尔兰”（一种彩票）。结果这张彩票让我们的农夫约翰获得了这次比赛唯一的奖品——坐落于爱尔兰郊外的一座梦幻般的城堡！（Sinya：真是傻人有傻福啊……然后他应该就在爱尔兰养牛吧……然后还产生了那么多关于奶牛和牛奶的数学问题……）

喜欢HP的农夫约翰立刻回到有着HP传统的威斯康辛老家开始HP了（Sinya：关于HP是什么见旧文新电脑（图））, 农夫约翰想要告诉他的奶牛们关于他的城堡的一切（Sinya：又关奶牛什么事……）。他需要做一些HP的准备工作：比如说知道城堡有多少个房间，每个房间有多大。而且农夫约翰想要把一个单独的墙（Sinya：指两个单位间的墙）给拆掉以获得一个更大的房间（Sinya：个人觉得还是小房间舒适。更能保护隐私……当然有个大房间可以HP……）

你的工作就是帮农夫约翰做HP的准备，算出房间数与房间的大小。

城堡的平面图被划分成M*N（M是宽度）个正方形的单位，一个这样的单位可以有0到4面墙环绕。城堡周围一定有外墙环绕以遮风挡雨。（Sinya：就是说平面图的四周一定是墙。咦，难道是说我们中国伟大的防火墙？！难道我们的女友W是一个城堡？！）

请仔细研究下面这个有注解的城堡平面图：

     1   2   3   4   5   6   7
   #############################
 1 #   |   #   |   #   |   |   #
   #####---#####---#---#####---#
 2 #   #   |   #   #   #   #   #
   #---#####---#####---#####---#
 3 #   |   |   #   #   #   #   #
   #---#########---#####---#---#
 4 # ->#   |   |   |   |   #   #
   ############################# 
#  = 墙     -,|  = 没有墙
-> = 指向一面墙，这面墙推掉的话我们就有一间最大的新房间

友情提示，这个城堡的平面图是7×4个单位的。一个“房间”指的是平面图中一个连通的“正方形单位”的集合。比如说这个样例就有5个房间。（大小分别为9、7、3、1、8个单位（排名不分先后））

移去箭头所指的那面墙，可以使2个房间合为一个“移掉一面单独的墙可以形成的最大的新房间”。（Sinya：翻译这句话后我有理由相信英语比普通话科学。原文远比译文容易理解。原文为：Removing the wall marked by the arrow merges a pair of rooms to make the largest possible room that can be made by removing a single wall. ）

我们很人道的USACO向我们保证城堡至少有2个房间，而且一定有一面墙可以被移走。

程序名（Sinya：就是提交程序写在抬头处的）: castle

输入格式

城堡的平面图用一个由数字组成的矩阵表示，一个数字表示一个单位，矩阵有N行M列。输入与样例的图一致。

每一个单位的数字告诉我们这个单位的东西南北是否有墙存在。每个数字是由以下四个整数的某个或某几个或一个都没有加起来的。

1: 这个单位的西边有墙
2: 这个单位的北边有墙
4: 这个单位的东边有墙
8: 这个单位的南边有墙

城堡内部的墙会被规定两次。比如说（1，1）南面的墙，亦会被标记为（2，1）北面的墙。

第一行:两个由空格分隔的整数： M 还有 N

第二行:M*N个整数，一行有M个

样例输入 (输入文件 castle.in)

7 4

11 6 11 6 3 10 6
7 9 6 13 5 15 5
1 10 12 7 13 7 5
13 11 10 8 10 12 13

输出格式

输出文件有以下数行:

第1行:城堡拥有的房间数

第2行:最大的房间的大小

第3行:
“推倒 ”（Sinya：不要想歪了）一面墙可以创造出来的最大的房间的大小。

第4行:要造出第三行那么大的大房间所要推倒的一面墙。

选择最佳的墙来推倒。有多解时选最西边的（还是有多解时选最南的）。用这面墙南边或西边的单位，还有这面墙在那个单位的方位（”N”（北）或者”E”（东））来表示这面墙。

样例输出 (输出文件 castle.out)

翻译翻译了好久，一定要把这篇文章标记为原创精品，不然就太对不起自己了。

我的解题思路

这道题很简单，就是调用两次USACO所谓的flood fill，应该就是我们的图的遍历。问题一分为二，首先是遍历出房间个数与每个房间的大小与每个单元格属于哪个房间。便解决了一、二行的输出。

这部分时间复杂度为O(nm).

然后两层for语句便可以找出要拆除的墙。

这部分时间复杂度也是O(nm).

输入的处理方法: 把每个单元格的数字转换为二进制,若个位为1则西面有墙,2位为1则北面有墙,依此类推

详见下面的程序还有注解。

{

ID: Sinya1

PROG: castle

LANG: PASCAL

}

{WELCOME TO MY WEBSITE: HTTP://SINYA.YO2.CN/}

{I love my hometown, Swatow, China!!!!!}

{Anyway,I Love You, Kekyang!!!!!}

Program castle;

Var

{}a:array[1..50,1..50]of byte; {输入}

{}i,j,n,m,nn,mm,h:integer; {h为房间数}

{}l:array[1..2500]of integer; {每个房间的大小}

{}s:array[1..50,1..50]of integer; {每个单元格属于哪一个房间}

{}r1,r2,r:integer;

{}c:char;

procedure tswe; {找一个没有被遍历到的点,坐标存在nn与mm}

begin

{}nn:=1;

{}while nn<=n do begin

{}{}mm:=1;

{{}}while mm<=m do begin

{}{{}}if s[nn,mm]=0 then

{}{}{}{}exit;

{}{{}}inc(mm)

{}{}end;

{}{}inc(nn);

{}end;

end;

procedure tsingsyu(x,y:integer); {深度优先遍历}

begin

{}inc(l[h]);

{}s[x,y]:=h;

{}if((a[x,y]and 1)=0)and {若北面无墙}

{}{}((s[x,y-1]=0))then {且北面的单元格没被遍历过}

{}{}tsingsyu(x,y-1); {对北面的单元格进行深搜}

{}if((a[x,y]and 2)=0)and

{}{}((s[x-1,y]=0))then

{}{}tsingsyu(x-1,y);

{}if((a[x,y]and 4)=0)and

{}{}((s[x,y+1]=0))then

{}{}tsingsyu(x,y+1);

{}if((a[x,y]and 8)=0)and

{}{}((s[x+1,y]=0))then

{}{}tsingsyu(x+1,y);

end;

Begin

{}Assign(input, ‘castle.in’); Reset(input);

{}Assign(output, ‘castle.out’); Rewrite(output);

{}readln(m,n);

{}for i:=1 to n do

{}for j:=1 to m do

{}read(a[i,j]);

{读入}

{}fillchar(l,sizeof(l),0);

{}fillchar(s,sizeof(s),0);

{}h:=0;

{}{清空}

{}tswe; {找到一个没有被遍历到的点}

{}while nn<=n do begin {直到所有点都找到为止}

{}{}inc(h); {房间数加1}

{}{}tsingsyu(nn,mm); {深度搜索那个点}

{}{}tswe; {再找一个点}

{}end;

{}writeln(h);

{}{输出房间数}

{}j:=0;

{}for i:=1 to h do

{}{}if l[i]>j then

{}{}{}j:=l[i];

{}writeln(j);

{输出最大的房间的大小}

{下面是第二部分问题}

{}r:=0; {最优解清零}

{}for j:=1 to m do

{}{}for i:=n downto 1 do begin{从西往东,从南往北搜索}

{}{}{}if(i>1) {若不在第一行}

{}{}{}{}and((a[i,j]and 2)>0) {且北面有墙}{这一行似乎可以省略，若下面那一句为TRUE，那么这一句也应为TRUE，当然要第一部分正确}

{}{}{}{}and(s[i,j]<>s[i-1,j]) {且背面的墙两边是不一样的房间}

{}{}{}{}and(l[s[i,j]]+l[s[i-1,j]]>r)then begin {且推掉这面墙形成的新房间比最优解大}

{}{}{}{}r:=l[s[i,j]]+l[s[i-1,j]]; {记录最优解}

{}{}{}{}r1:=i;

{}{}{}{}r2:=j;

{}{}{}{}c:=’N’;

{}{}{}end;

{}{}{}if(j<m)

{}{}{}{}and((a[i,j]and 4)>0)

{}{}{}{}and(s[i,j]<>s[i,j+1])

{}{}{}{}and(l[s[i,j]]+l[s[i,j+1]]>r)then begin

{}{}{}{}r:=l[s[i,j]]+l[s[i,j+1]];

{}{}{}{}r1:=i;

{}{}{}{}r2:=j;

{}{}{}{}c:=’E’;

{}{}{}end

{}{}end;

{}writeln(r);

{}writeln(r1,’ ‘,r2,’ ‘,c);

{}{输出最优解}

{}Close(input);

{}Close(output);

End.

天哪,原来写解题报告这么麻烦.

结果&测试数据

USER: Sinya Lee [sinya1]

TASK: castle

LANG: PASCAL
NEW GRADER -- report problems!

Java users: CPU no longer includes JAVA startup time

Java users: Some syscalls incorrectly cause failures -- please email kolstad (Comment below) if you see this


Compiling...

Compile: OK


Executing...

   Test 1: TEST OK [0.011 secs, 216 KB]

   Test 2: TEST OK [0.000 secs, 220 KB]

   Test 3: TEST OK [0.000 secs, 220 KB]

   Test 4: TEST OK [0.000 secs, 216 KB]

   Test 5: TEST OK [0.000 secs, 220 KB]

   Test 6: TEST OK [0.000 secs, 220 KB]

   Test 7: TEST OK [0.065 secs, 216 KB]

   Test 8: TEST OK [0.011 secs, 220 KB]


All tests OK.

YOUR PROGRAM ('castle') WORKED FIRST TIME!  That's fantastic

-- and a rare thing.  Please accept these special automated

congratulations.

Here are the test data inputs:

------- test 1 -------

7 4

11 6 11 6 3 10 6

7 9 6 13 5 15 5

1 10 12 7 13 7 5

13 11 10 8 10 12 13

------- test 2 -------

2 1

15 15

------- test 3 -------

5 5

3 2 6 3 6

1 8 4 1 4

13 7 13 9 4

3 0 2 6 5

9 8 8 12 13

------- test 4 -------

15 14

11 14 3 6 3 6 3 6 3 6 3 6 11 2 6

3 10 12 9 12 9 12 9 12 9 12 9 6 1 4

13 7 11 10 10 10 10 10 10 14 11 6 5 1 4

11 4 3 10 10 10 10 10 10 10 6 5 13 1 4

7 13 5 7 11 10 2 10 14 7 5 13 7 9 12

1 14 5 1 10 14 5 11 10 4 9 6 1 10 6

13 7 5 5 3 10 8 10 6 5 3 12 9 10 12

11 4 5 13 5 3 10 6 5 13 5 3 10 10 6

7 13 1 10 4 1 10 4 1 10 4 5 3 10 12

1 14 5 7 5 9 10 12 5 7 5 5 9 10 6

13 7 13 5 9 10 2 10 12 13 13 5 3 10 12

7 5 15 9 10 14 5 11 14 11 14 5 9 10 6

5 13 7 7 11 10 8 10 14 7 3 12 3 10 12

13 15 13 13 11 10 14 11 10 12 9 10 8 10 14

------- test 5 -------

10 10

11 10 10 14 7 3 10 2 2 6

3 2 2 6 5 1 2 0 0 4

1 0 0 4 5 1 0 0 0 4

1 0 0 4 13 9 8 8 8 4

1 0 0 4 7 11 10 10 14 13

1 0 0 4 5 7 3 2 2 6

1 0 0 4 5 5 1 0 0 4

1 0 0 4 13 5 1 0 0 4

1 0 0 4 7 5 1 0 0 4

9 8 8 12 13 13 9 8 8 12

------- test 6 -------

32 32

3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 6 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 6

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

9 8 8 8 8 8 8 8 8 8 8 8 8 8 8 12 9 8 8 8 8 8 8 8 8 8 8 8 8 8 8 12

------- test 7 -------

50 50

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

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15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

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15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

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15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

------- test 8 -------

50 50

7 15 7 3 14 11 10 10 14 3 2 2 6 15 7 7 7 7 11 2 6 3 10 2 6 15 3 14 3 10 10 10 6 11 10 2 14 7 7 11 14 3 14 7 7 15 11 14 15 7

1 14 9 0 10 14 15 7 7 13 9 8 8 2 0 12 9 0 2 4 13 1 14 5 9 6 9 14 13 7 15 7 13 3 10 0 2 4 13 15 11 4 15 13 13 11 10 10 6 5

13 15 11 8 14 11 6 5 13 3 6 15 11 12 1 14 15 1 12 9 6 1 6 1 10 4 11 6 3 8 2 4 7 13 3 12 13 13 3 6 15 9 2 6 3 14 7 7 1 12

7 3 14 7 3 14 5 1 2 0 4 15 11 14 13 11 2 0 14 11 12 1 0 8 6 1 2 12 5 15 5 1 8 14 13 11 2 2 4 1 6 11 12 13 1 14 9 12 5 7

9 0 14 1 8 2 8 0 4 1 4 3 2 14 7 7 5 13 11 14 3 12 9 10 4 9 0 14 1 2 0 0 10 6 11 10 4 1 4 9 0 14 15 15 9 10 10 10 0 12

7 9 6 13 3 12 15 9 4 5 13 1 4 15 1 8 4 3 2 2 0 6 7 15 5 15 9 2 12 1 12 5 11 4 7 7 1 8 8 6 5 11 10 6 15 15 11 14 5 7

13 7 5 15 13 7 11 6 5 13 15 13 1 2 12 15 5 9 8 12 5 1 0 2 8 10 10 4 15 5 15 13 11 4 5 1 12 15 3 12 9 2 6 9 14 7 3 6 5 13

11 8 0 6 15 9 2 8 12 11 6 3 12 9 2 2 4 11 6 15 9 8 4 1 14 7 15 5 15 1 6 11 2 0 8 0 14 15 5 15 7 13 5 15 15 9 8 0 12 7

7 7 13 13 3 6 13 11 2 2 12 9 14 11 8 0 4 11 8 14 3 14 1 4 3 12 3 4 3 4 9 10 0 12 7 5 7 11 12 15 1 10 8 10 14 7 11 8 2 4

9 8 2 2 8 8 2 14 9 4 15 7 3 6 11 8 8 6 15 15 5 7 9 4 13 7 5 5 9 0 10 10 8 10 0 8 12 7 11 10 12 15 3 10 2 0 10 6 5 13

15 7 5 13 15 11 12 7 15 9 6 5 9 12 7 7 11 8 6 11 0 0 6 13 11 12 9 12 11 8 10 14 11 10 8 6 3 12 7 11 2 14 5 11 4 13 3 8 12 15

15 5 1 6 3 6 15 5 3 2 0 4 11 14 9 0 14 11 0 6 5 13 5 11 6 11 10 14 11 10 14 15 15 3 6 13 13 11 4 7 1 6 1 2 0 2 12 15 11 14

15 1 12 5 5 13 7 1 0 4 5 5 7 11 6 5 11 10 8 12 5 3 12 7 5 15 15 15 15 11 14 15 15 13 5 7 11 6 5 13 13 1 0 0 8 8 2 2 14 7

11 12 7 1 8 6 1 12 9 4 1 12 5 11 8 4 3 2 10 14 9 0 6 13 5 15 15 15 3 2 6 3 2 2 8 4 7 9 0 6 15 5 1 4 11 6 9 0 2 12

7 11 8 0 10 8 4 7 3 0 4 15 9 10 10 0 0 4 3 10 6 13 13 11 8 10 14 11 12 5 9 4 1 8 6 13 9 6 13 1 2 12 9 12 3 4 3 0 0 6

1 10 14 9 10 6 1 12 9 12 5 15 7 3 10 12 5 13 5 15 5 11 2 14 7 3 10 14 7 5 7 1 12 15 13 3 14 9 10 4 1 14 7 3 12 9 12 1 12 5

5 11 6 11 14 1 4 7 7 15 1 6 5 9 2 14 9 14 9 10 0 2 8 14 9 8 2 14 13 9 4 5 11 2 10 8 6 3 14 9 4 3 12 9 6 3 6 13 15 13

13 15 5 11 2 12 1 12 5 15 9 8 8 10 8 14 11 14 7 11 0 12 11 10 6 11 12 7 7 7 13 9 10 4 15 7 5 13 3 14 13 1 14 11 8 0 8 6 15 7

3 2 8 14 5 3 0 6 13 15 11 2 2 6 7 3 14 7 13 3 4 11 14 11 0 10 6 13 1 4 7 15 11 4 11 8 8 6 1 6 15 9 10 6 3 12 15 1 6 5

1 8 10 14 9 4 1 4 3 2 6 1 8 8 4 5 15 5 15 9 0 2 6 11 12 3 4 7 1 4 9 10 2 0 6 11 14 1 12 9 6 3 2 8 8 2 2 0 4 5

9 6 7 3 6 1 8 8 12 9 8 4 3 10 8 0 14 13 3 2 12 5 9 6 15 5 9 0 0 0 10 2 12 5 9 6 3 0 6 3 8 8 0 6 15 5 13 1 4 13

7 9 8 4 13 9 2 2 14 3 6 1 8 2 14 13 15 15 1 8 10 0 10 12 3 12 3 0 0 12 15 9 6 1 10 0 12 13 1 4 3 2 8 0 10 0 10 0 8 14

13 11 10 4 11 6 13 1 6 5 5 1 6 1 6 7 11 14 5 15 7 5 7 11 0 14 9 4 13 11 2 14 9 12 3 0 14 3 4 9 4 1 2 4 11 8 14 5 15 15

11 2 6 1 2 12 3 8 4 5 1 0 8 4 13 1 2 2 0 6 1 8 12 3 4 11 6 9 6 3 8 10 2 14 1 4 15 9 4 3 4 5 5 1 10 6 7 13 15 15

3 12 9 4 9 2 4 7 5 5 13 5 3 4 11 8 8 8 12 1 4 11 10 0 4 3 8 2 8 12 7 11 0 10 8 4 11 10 8 12 13 13 1 12 15 1 4 11 2 14

5 3 2 4 15 5 13 13 1 8 6 13 1 0 2 14 3 2 14 5 9 6 7 5 5 5 11 0 6 7 13 3 12 11 10 4 7 11 6 11 10 10 4 15 11 0 4 15 1 14

1 4 9 12 3 4 7 3 0 10 8 10 12 1 0 6 13 5 15 9 6 13 9 12 1 0 10 4 9 0 14 13 7 15 11 12 1 14 1 6 3 6 9 14 11 4 13 7 13 7

13 5 15 11 0 8 12 1 0 2 2 6 11 4 9 0 6 9 10 14 13 3 6 7 5 1 6 5 11 4 11 2 8 14 3 6 13 15 1 12 1 4 11 14 7 13 7 9 10 4

11 12 7 11 12 15 3 12 5 13 1 12 7 9 14 1 0 10 10 2 2 0 8 8 12 5 5 13 7 5 15 9 6 11 4 1 14 3 4 3 8 8 6 7 1 14 13 11 2 12

3 10 12 3 2 2 0 10 0 2 12 3 0 10 6 9 8 10 10 0 8 12 7 11 14 1 12 3 12 5 3 2 8 14 1 8 2 8 12 1 14 11 8 12 9 6 15 11 8 6

9 14 15 13 5 13 13 15 5 13 3 4 5 15 5 11 10 14 7 1 6 15 9 2 2 8 6 13 11 4 13 9 10 14 9 6 9 10 10 4 3 10 10 10 10 8 2 14 3 12

15 3 14 11 0 6 15 15 13 15 9 8 0 10 4 7 11 2 8 4 13 3 10 0 12 11 0 10 2 0 2 6 3 14 11 4 3 2 14 13 13 11 14 3 6 3 8 10 4 7

7 9 6 11 12 13 3 2 10 6 15 7 13 11 8 4 7 13 3 4 15 5 15 5 7 3 8 6 1 4 5 9 0 10 10 4 9 8 10 14 3 6 7 13 1 8 10 6 1 4

9 14 13 3 6 7 1 4 11 8 14 1 6 11 6 9 4 3 4 5 15 9 14 1 8 4 15 9 0 0 12 7 13 7 3 12 7 15 3 6 5 13 9 14 13 11 14 9 4 5

15 15 15 13 13 9 4 13 15 11 14 9 0 14 9 6 5 5 9 12 11 2 6 9 6 5 15 11 0 8 2 4 11 12 1 10 12 15 13 1 8 6 3 2 2 2 10 10 12 5

3 6 15 3 10 10 12 7 3 10 2 6 1 14 15 13 5 13 15 11 2 8 8 6 13 5 15 3 8 6 13 13 11 14 9 14 7 15 11 4 7 9 4 13 9 12 3 14 15 5

5 9 6 9 14 3 14 1 0 6 9 4 9 6 15 15 13 7 15 11 12 11 14 5 3 12 3 8 2 8 10 10 10 10 14 3 8 6 15 9 0 10 12 11 6 7 9 2 10 4

9 2 12 15 11 8 14 1 0 4 7 13 3 0 6 11 6 9 2 10 14 15 11 4 9 2 8 14 9 6 11 6 11 2 2 0 6 13 15 15 1 2 6 3 4 9 14 13 11 4

3 4 11 14 3 10 2 4 9 4 5 15 9 12 1 6 13 7 9 2 14 7 15 9 10 12 11 14 15 9 14 9 14 9 12 1 4 15 3 10 4 5 5 1 4 3 2 10 14 5

9 4 11 10 4 11 12 13 15 5 1 2 10 2 12 1 10 4 11 4 15 13 11 2 10 10 2 6 7 3 14 11 2 2 6 13 5 11 12 7 9 12 9 12 13 13 9 10 10 12

15 9 14 15 9 2 6 7 15 13 5 9 14 13 3 12 7 13 3 4 15 7 3 12 11 6 9 4 13 1 10 14 5 1 12 3 0 14 15 9 10 6 11 2 6 15 15 7 11 6

7 7 7 15 3 0 8 4 3 14 9 2 10 14 1 14 9 2 8 0 6 5 1 2 6 9 10 4 3 8 2 2 4 13 11 0 4 11 6 15 3 0 2 4 9 6 11 8 2 4

13 1 0 6 5 13 11 8 4 3 10 4 7 15 1 14 3 8 6 9 0 8 8 12 1 6 15 9 0 10 0 0 0 14 11 12 5 15 9 2 12 9 8 4 11 12 15 7 5 13

7 1 4 1 12 11 10 14 9 12 3 8 12 11 4 15 1 14 5 7 9 6 15 15 9 8 14 3 0 10 4 5 1 6 15 15 13 11 2 4 7 7 15 13 15 15 3 0 4 15

1 4 1 4 15 7 3 14 7 7 9 6 15 11 8 2 8 2 4 9 2 8 6 15 15 7 15 13 5 3 12 13 1 4 3 6 7 11 12 5 13 5 11 2 6 15 1 0 8 14

13 9 8 12 7 1 0 14 13 9 14 1 10 2 6 1 14 13 1 6 1 2 8 10 6 1 10 10 0 12 11 14 1 0 12 1 12 11 2 12 15 1 10 4 1 10 12 5 15 15

3 2 6 7 13 5 13 11 6 11 14 9 6 1 8 0 6 11 12 1 4 5 11 14 9 8 10 14 13 3 14 7 13 5 3 4 7 3 12 15 7 9 2 0 12 7 7 13 11 6

5 9 12 1 6 1 6 3 12 15 11 10 0 12 7 13 13 3 2 8 12 5 3 14 15 7 3 14 7 13 11 4 7 5 5 13 9 4 11 6 5 3 12 1 2 0 12 7 15 13

1 14 15 13 5 13 1 12 3 10 14 11 8 2 8 2 6 1 12 11 6 5 9 2 10 4 5 7 9 14 3 0 0 8 12 7 7 13 15 13 5 9 10 4 9 0 10 8 6 15

13 11 14 15 9 10 8 14 13 15 11 10 14 9 14 9 8 12 15 11 8 8 10 12 15 13 13 13 15 11 12 9 12 11 14 13 9 14 11 10 8 14 15 9 10 12 15 15 9 14

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