github.com/captn3m0/codechef.git

---
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---
<span class="solution-visible-txt">All submissions for this problem are available.</span><h3> Read problems statements in <a target="_blank" href="http://www.codechef.com/download/translated/LTIME37/mandarin/LCOLLIS.pdf">Mandarin Chinese</a>, <a target="_blank" href="http://www.codechef.com/download/translated/LTIME37/russian/LCOLLIS.pdf">Russian</a> and <a target="_blank" href="http://www.codechef.com/download/translated/LTIME37/vietnamese/LCOLLIS.pdf">Vietnamese</a> as well.</h3>


<p>Once <b>N</b> boys and <b>M</b> girls attended a party. You are given a matrix <b>A</b> of <b>N</b> rows and <b>M</b> columns where <b>A<sub>ij</sub></b> is <b>1</b> if the <b>i-th</b> boy likes the <b>j-th</b> girl, otherwise it will be 0. Note that it is not necessary that if a boy <b>x</b> likes girl <b>y</b>, then girl <b>y</b> should like boy <b>x</b>.</p>

<p>You know that if there are two different boys <b>x</b> and <b>y</b>, who both like girl <b>z</b>, then there will be a collision.
Can you calculate the number of different collisions at this party? Note that order of boys in the collision doesn't matter.</p>

<h3>Input</h3>
<p>The first line contains a single integer <b>T</b> denoting the number of test cases. Then <b>T</b> test cases follow.</p>
<p>The first line of each test case contains two space separated integers <b>N</b>, <b>M</b> denoting the number of boys and girls, respectively.</p>
<p>Each of the following <b>N</b> lines contain <b>M</b> characters, each of them is either <b>'0'</b> or <b>'1'</b>.</p>

<h3>Output</h3>
<p>For each test case output a single line containing an integer corresponding to the number of collisions at the party.</p>

<h3>Constraints</h3>
<ul>
<li><b>1</b> ≤ <b>T</b> ≤ <b>100</b></li>
<li><b>1</b> ≤ <b>N, M</b> ≤ <b>10</b></li>
</ul>

<h3>Example</h3>
<pre><b>Input:</b>
2
4 3
111
100
110
000
2 2
10
01

<b>Output:</b>
4
0
</pre>

<h3>Explanation</h3>
<p><b>Example Case 1.</b> All three boys like the first girl, so there are <b>(1, 2, 1), (1, 3, 1), (2, 3, 1)</b> collisions with her. Boys <b>1</b> and <b>3</b> both like the second girl so this is one more collision. Only one boy likes the third girl, so there are no collisions with her and thus we have <b>4</b> collisions total.</p>

<p><b>Example Case 2.</b> For each girl there is only one boy who likes her, so there are no collisions at all.</p>