prithivMLmods/Coder-Stat

1 2 3<H1>4Nets of Dice5</H1>6 7 8<P>9In mathematics, some plain words have special meanings.10The word "<I>net</I>" is one of such technical terms.11In mathematics, the word "<I>net</I>" is sometimes used to12mean a plane shape 13which can be folded into some solid shape.14</P>15 16<P>17The following are a solid shape (Figure 1) and one of its <I>net</I> (Figure 2).18</P>19 20 21<TABLE>22<TR><TD ALIGN=center><img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_prism"></TD><TD ALIGN=center><img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_netprism"></TD></TR>23<TR><TD ALIGN=center>Figure 1: a prism</TD><TD ALIGN=center>Figure 2: a net of a prism</TD></TR>24</TABLE>25 26<P>27Nets corresponding to a solid shape are not unique.28For example, Figure 3 shows three of the nets of a cube.29</P>30 31<TABLE>32<TR><TD ALIGN=center><img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_netcube"></TD></TR>33<TR><TD ALIGN=center>Figure 3: examples of nets of a cube</TD></TR>34</TABLE>35 36<P>37In this problem, we consider nets of dice.38The definition of a die is as follows.39<OL>40<LI> A die is a cube, each face marked with a number between one and six.41<LI> Numbers on faces of a die are different from each other.42<LI> The sum of two numbers on the opposite faces is always 7.43</OL>44<p>45Usually, a die is used in pair with another die.46The plural form of the word "die" is "dice".47</P>48 49<P>50Some examples of proper nets of dice are shown in Figure 4,51and those of improper ones are shown in Figure 5.52</P>53 54<TABLE>55 56<TR><TD ALIGN=center><img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_netdice2"></TD></TR>57<TR><TD ALIGN=center>Figure 4: examples of proper nets of dice</TD></TR>58</TABLE>59 60<TABLE>61<TR><TD ALIGN=center><img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_netdice3"></TD></TR>62<TR><TD ALIGN=center>Figure 5: examples of improper nets</TD></TR>63</TABLE>64 65<P>66The reasons why each example in Figure 5 is improper are as follows.67<DL>68<DD>(a) The sum of two numbers on the opposite faces is not always 7.69<DD>(b) Some faces are marked with the same number.70<DD>(c) This is not a net of a cube. Some faces overlap each other.71<DD>(d) This is not a net of a cube.72Some faces overlap each other and one face of a cube is not covered.73<DD>(e) This is not a net of a cube. 74The plane shape is cut off into two parts.75The face marked with '2' is isolated.76<DD>(f) This is not a net of a cube.77The plane shape is cut off into two parts.78<DD>(g) There is an extra face marked with '5'.79</DL>80</P>81 82<P>83Notice that there are two kinds of dice.84For example, the solid shapes formed from 85the first two examples in Figure 4 86are mirror images of each other.87</P>88 89 90<P>91Any net of a die can be expressed on a sheet of 5x5 mesh like the one in Figure 6.92In the figure, gray squares are the parts to be cut off.93When we represent the sheet of mesh by numbers as in Figure 7,94squares cut off are marked with zeros.95</P>96 97<TABLE>98<TR><TD ALIGN=center><img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_mesh"></TD><TD ALIGN=center><img src="https://judgeapi.u-aizu.ac.jp/resources/images/IMAGE1_matrix"></TD></TR>99<TR><TD ALIGN=center>Figure 6: 5x5 mesh</TD><TD ALIGN=center>Figure 7: representation by numbers</TD></TR>100</TABLE>101 102<P>103Your job is to write a program which tells104the proper nets of a die from the improper ones automatically.105</P>106 107 108<H2>Input</H2>109 110<P>111The input consists of multiple sheets of 5x5 mesh.112</P>113 114<TABLE>115<TR><TD><I>N</I></TD></TR>116<TR><TD><I>Mesh</I><SUB>0</SUB></TD></TR>117<TR><TD><I>Mesh</I><SUB>1</SUB></TD></TR>118<TR><TD>...</TD></TR>119<TR><TD><I>Mesh</I><SUB><I>N</I>-1</SUB></TD></TR>120</TABLE>121 122<P>123<I>N</I> is the number of sheets of mesh.124Each <I>Mesh<SUB>i</SUB></I> gives a sheet of mesh125on which a net of a die is expressed.126<I>Mesh<SUB>i</SUB></I> is in the following format.127</P>128 129<TABLE>130<TR>131        <TD><I>F</I><SUB>00</SUB></TD>132	<TD><I>F</I><SUB>01</SUB></TD>133	<TD><I>F</I><SUB>02</SUB></TD>134	<TD><I>F</I><SUB>03</SUB></TD>135	<TD><I>F</I><SUB>04</SUB></TD>136</TR>137<TR>  138	<TD><I>F</I><SUB>10</SUB></TD>139	<TD><I>F</I><SUB>11</SUB></TD>140	<TD><I>F</I><SUB>12</SUB></TD>141	<TD><I>F</I><SUB>13</SUB></TD>142	<TD><I>F</I><SUB>14</SUB></TD>143</TR>144<TR>  145	<TD><I>F</I><SUB>20</SUB></TD>146	<TD><I>F</I><SUB>21</SUB></TD>147	<TD><I>F</I><SUB>22</SUB></TD>148	<TD><I>F</I><SUB>23</SUB></TD>149	<TD><I>F</I><SUB>24</SUB></TD>150</TR>151<TR>  152	<TD><I>F</I><SUB>30</SUB></TD>153	<TD><I>F</I><SUB>31</SUB></TD>154	<TD><I>F</I><SUB>32</SUB></TD>155	<TD><I>F</I><SUB>33</SUB></TD>156	<TD><I>F</I><SUB>34</SUB></TD>157</TR>158<TR>  159	<TD><I>F</I><SUB>40</SUB></TD>160	<TD><I>F</I><SUB>41</SUB></TD>161	<TD><I>F</I><SUB>42</SUB></TD>162	<TD><I>F</I><SUB>43</SUB></TD>163	<TD><I>F</I><SUB>44</SUB></TD>164</TR>165</TABLE>166 167<P>168Each <I>F<SUB>ij</SUB></I> is an integer between 0 and 6.169They are separated by a space character.170</P>171 172<H2>Output</H2>173<p>174For each <I>Mesh<SUB>i</SUB></I>, 175the truth value, <I>true</I> or <I>false</I>, 176should be output, each in a separate line.177When the net of a die expressed on the <I>Mesh<SUB>i</SUB></I> is proper, 178output "true".179Otherwise, output "false".180</p>181<H2>Sample Input</H2>182<PRE>18361840 0 0 0 01850 0 0 0 61860 2 4 5 31870 0 1 0 01880 0 0 0 01890 0 3 0 01900 0 2 0 01910 0 4 1 01920 0 0 5 01930 0 0 6 01940 0 0 3 01950 0 2 5 01960 4 1 0 01970 0 6 0 01980 0 0 0 01990 6 2 0 02000 0 4 0 02010 1 5 0 02020 0 3 0 02030 0 0 0 02040 0 0 0 62050 2 4 5 32060 0 1 0 02070 0 0 0 02080 0 0 1 02090 0 0 0 62100 2 4 5 32110 0 0 0 02120 0 0 0 02130 0 0 1 0214</PRE>215 216<H2>Output for the Sample Input</H2>217<PRE>218true219true220false221false222false223false224</PRE>225