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<h1>1141. PAT Ranking of Institutions (25)</h1>
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<p>After each PAT, the PAT Center will announce the ranking of institutions based on their students' performances. Now you are asked to generate the ranklist.
</p>
<p><b>
Input Specification:
</b></p>
<p>Each input file contains one test case. For each case, the first line gives a positive integer N (&lt;=10<sup>5</sup>), which is the number of testees. Then N lines follow, each gives the information of a testee in the following format:</p>
<p>
ID Score School
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<p>
where "ID" is a string of 6 characters with the first one representing the test level: "B" stands for the basic level, "A" the advanced level and "T" the top level; "Score" is an integer in [0, 100]; and "School" is the institution code which is a string of no more than 6 English letters (case insensitive). Note: it is guaranteed that "ID" is unique for each testee.
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<p><b>
Output Specification:
</b></p>
<p>For each case, first print in a line the total number of institutions. Then output the ranklist of institutions in nondecreasing order of their ranks in the following format:</p>
<p>
Rank School TWS Ns
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<p>
where "Rank" is the rank (start from 1) of the institution; "School" is the institution code (all in lower case); "TWS" is the <b>total weighted score</b> which is defined to be the integer part of "Score<sub>B</sub>/1.5 + Score<sub>A</sub> + Score<sub>T</sub>*1.5", where "Score<sub>X</sub>" is the total score of the testees belong to this institution on level X; and "Ns" is the total number of testees who belong to this institution.
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<p>
The institutions are ranked according to their TWS. If there is a tie, the institutions are supposed to have the same rank, and they shall be printed in ascending order of Ns. If there is still a tie, they shall be printed in alphabetical order of their codes.
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<b>Sample Input:</b><pre>
10
A57908 85 Au
B57908 54 LanX
A37487 60 au
T28374 67 CMU
T32486 24 hypu
A66734 92 cmu
B76378 71 AU
A47780 45 lanx
A72809 100 pku
A03274 45 hypu
</pre>
<b>Sample Output:</b><pre>
5
1 cmu 192 2
1 au 192 3
3 pku 100 1
4 hypu 81 2
4 lanx 81 2
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