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Confused about Graphing Coordinates


winuser2003
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I get

image.png.c1621e857d62b5bc6769267d2a4dfacb.png

NOTE: the 2 values you posted are arrays. The function expects strings of comma-separated values.

If you prefer to pass arrays like those the query can be modified.

 

You should also consider normalizing the data ...

+-------------+
|   user      |
+-------------+
| id          |--------+         +-------------+
| firstname   |        |         | signature   |
| lastname    |        |         +-------------+
+-------------+        +--------<|  user_id    |
                                 |  seq        |
                                 |  x          |
                                 |  y          |
                                 +-------------+

 

Edited by Barand
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33 minutes ago, Barand said:

I get

image.png.c1621e857d62b5bc6769267d2a4dfacb.png

NOTE: the 2 values you posted are arrays. The function expects strings of comma-separated values.

If you prefer to pass arrays like those the query can be modified.

 

You should also consider normalizing the data ...


+-------------+
|   user      |
+-------------+
| id          |--------+         +-------------+
| firstname   |        |         | signature   |
| lastname    |        |         +-------------+
+-------------+        +--------<|  user_id    |
                                 |  seq        |
                                 |  x          |
                                 |  y          |
                                 +-------------+

 

Can you help me do this? if this is a better method? how would the script look?  and your result is exactly what I am looking for.

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28 minutes ago, winuser2003 said:

am I also still passing in sign_x and sign_y as TEXT

They would still be a strings of comma-separated values. Changing to column type TEXT just increases the maximum storage capacity of each column to 65500 (which should be sufficient to hold the longest signature with several thousand points.)

Normalising the  data would allow you store the data as a series of (x,y) points which, to me, seems more logical as that is how the data is used. At the moment you have a huge block of x coordnates and another of y coordinates.

Storing it this way way would be done as part of your transfer from the phone app.

Question: Does the app put the data directly into the mysql db in your current format or is there some sort if interface process between the two?

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The app just directly puts the data directly into the myql db... There is an interface with form fields that get filled in, then what happens is the final step is a signature.  All this is directly sent into the Mysql DB for review on a management UI which is what you and I are working together on at the moment. I know nothing of flutter / DART whatsoever... a collegue of mine is coding that part making his app connect to my DB and sending those entries directly to it. You can see from the actual DB below... this is what we been using for testing

image.thumb.png.4b824ef77b4f63cfb486614ce6192ee3.png

Edited by winuser2003
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so how would i make that an array from this existing code? because your image with the signature showing is exactly what I am looking for.

<?php
mysqli_report(MYSQLI_REPORT_ERROR|MYSQLI_REPORT_STRICT);
$conn = mysqli_connect("localhost", "winuser2003", "homer123", "pmapptest");
$tdata = '';
$res = $conn->query("SELECT userid, fname, lname, sign_x, sign_y FROM winuser_demo");
foreach ($res as $r) {
    $tdata .= "<tr><td>{$r['userid']}</td>
                   <td>{$r['fname']}</td>
                   <td>{$r['lname']}</td>
                   <td>" . drawImage($r['sign_x'], $r['sign_y']) . "</td>\n";
}

function drawImage($xcoords, $ycoords)
{
    $xa = explode(',', $xcoords);
    $ya = explode(',', $ycoords);
    $w = max($xa)+10;
    $h = max($ya)+10;
    $path = "M $xa[0] $ya[0] ";
    unset($xa[0], $ya[0]);
    foreach ($xa as $i => $x) {
        $y = $ya[$i];
        $path .= "L $x $y ";
    }

    $im = "<svg width='$w' height='$h' >
           <path d='$path' stroke='#000' fill='none'/>
           </svg>";
    return $im;  
}     
?>
<!DOCTYPE html>
<html>
<head>
<style type="text/css">
    table {
        border-collapse: collapse;
        width: 60%;
    }
    th {
        background-color: black;
        color: white;
        padding: 8px;
        text-align: left;
    }
    td {
        padding: 4px 8px;;
    }
</style>
</head>
<body>
<table border="1" style="width: 60%;">
    <tr><th>ID</th>
        <th>First name</th>
        <th>Last name</th>
        <th>Image</th>
    <tr>
    <?=$tdata?>
</table>
</body>
</html>

 

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4 minutes ago, winuser2003 said:

so how would i make that an array from this existing code

The same way that  the function does in the first two lines

function drawImage($xcoords, $ycoords)
{
    $xa = explode(',', $xcoords);        // create array from $xcoord string
    $ya = explode(',', $ycoords);        // create array from $ycoord string
    $w = max($xa)+10;
    $h = max($ya)+10;
    $path = "M $xa[0] $ya[0] ";
    unset($xa[0], $ya[0]);
    foreach ($xa as $i => $x) {
        $y = $ya[$i];
        $path .= "L $x $y ";
    }

    $im = "<svg width='$w' height='$h' >
           <path d='$path' stroke='#000' fill='none'/>
           </svg>";
    return $im;  
}     

example

$x = "1, 2, 3, 4, 5";                                 // comma separated string
$arr = explode (', ', $x);                            // explode into array elements splitting on ", "
echo '<pre>', print_r($arr, 1), '</pre>';             // view the array

/* result :

 Array
(
    [0] => 1
    [1] => 2
    [2] => 3
    [3] => 4
    [4] => 5
)
*/

 

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I got it to output, looks right... correct me if I am wrong anywhere, but am I going to have to count that thing up to a 1000?   HAHA You did this in like a few seconds LOL --- in the earlier post with your signature screenshot. Did you on your end just redo it like this on your side to get that signature to show up?

<?php
mysqli_report(MYSQLI_REPORT_ERROR|MYSQLI_REPORT_STRICT);
$conn = mysqli_connect("localhost", "winuser2003", "homer123", "pmapptest");
$tdata = '';
$res = $conn->query("SELECT userid, fname, lname, sign_x, sign_y FROM winuser_demo");
foreach ($res as $r) {
    $tdata .= "<tr><td>{$r['userid']}</td>
                   <td>{$r['fname']}</td>
                   <td>{$r['lname']}</td>
                   <td>" . drawImage($r['sign_x'], $r['sign_y']) . "</td>\n";
}

function drawImage($xcoords, $ycoords)
{
    $x = "1, 2, 3, 4, 5"; // comma separated string - Would I have to go to 1000 on this then?
    $arr = explode (', ', $x);
    $y = "1, 2, 3, 4, 5"; // comma separated string - Would I have to go to 1000 on this then?
    $arr = explode (', ', $y);
    echo '<pre>', print_r($arr, 1), '</pre>'; 
    
    $w = max($xa)+10;
    $h = max($ya)+10;
    $path = "M $xa[0] $ya[0] ";
    unset($xa[0], $ya[0]);
    foreach ($xa as $i => $x) {
        $y = $ya[$i];
        $path .= "L $x $y ";
    }

 

Edited by winuser2003
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you posted

[44, 44, 44, 45, 45, 45, 45, 45, 45, 43, 42, 41, 40, 39, 39, 39, 37, 37, 37, 37, 37, 37, 37, 39, 40, 43, 47, 47, 49, 51, 52, 52, 53, 54, 55, 57, 58, 59, 64, 68, 73, 80, 85, 89, 93, 94, 94, 95, 95, 95, 93, 91, 89, 87, 85, 83, 81, 79, 75, 75, 72, 69, 66, 63, 60, 57, 55, 52, 50, 47, 45, 43, 41, 41, 41, 123, 124, 124, 123, 122, 119, 117, 111, 105, 100, 94, 89, 85, 82, 78, 76, 75, 73, 73, 72, 72, 72, 72, 75, 77, 79, 81, 83, 83, 87, 91, 95, 101, 109, 118, 127, 137, 144, 150, 153, 155, 155, 155, 155, 155, 155, 154, 154, 153, 150, 147, 147, 145, 144, 144, 144, 144, 144, 149, 152, 155, 158, 163, 167, 170, 176, 184, 191, 197, 201, 203, 204, 205, 206, 206, 206, 205, 203, 203, 202, 202, 202, 202, 202, 202, 202, 204, 207, 210, 213, 219, 220, 222, 223, 224, 226, 228, 230, 234, 237, 242, 246, 252, 259, 269, 278, 287, 293, 301, 309, 316, 325, 333, 340, 345, 345, 343, 341, 341, 339, 335, 332, 329, 327, 327, 327, 327, 328, 328, 329, 329, 332, 332, 335, 336, 338, 339, 343, 343, 346, 346]

[39, 45, 50, 58, 72, 86, 91, 97, 102, 106, 108, 111, 112, 114, 114, 112, 108, 102, 98, 92, 86, 81, 75, 69, 65, 60, 56, 55, 53, 50, 50, 48, 48, 48, 48, 48, 46, 46, 47, 48, 51, 53, 55, 58, 60, 61, 62, 66, 70, 76, 80, 84, 86, 89, 93, 94, 97, 99, 101, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 72, 72, 71, 69, 68, 65, 64, 62, 61, 61, 61, 61, 61, 61, 62, 64, 64, 66, 68, 71, 76, 81, 86, 92, 94, 96, 100, 102, 102, 104, 104, 104, 104, 104, 101, 98, 94, 91, 86, 84, 80, 78, 76, 74, 73, 72, 71, 70, 69, 71, 75, 76, 82, 86, 92, 95, 98, 102, 105, 108, 108, 110, 111, 111, 111, 110, 106, 102, 98, 94, 91, 88, 84, 82, 79, 77, 74, 71, 70, 68, 68, 66, 66, 65, 64, 63, 62, 62, 59, 58, 57, 57, 56, 56, 56, 56, 58, 58, 60, 61, 63, 64, 66, 68, 68, 68, 68, 68, 65, 63, 59, 55, 51, 50, 47, 47, 48, 50, 51, 52, 55, 57, 58, 60, 59, 58, 57, 56, 55, 55, 54, 53, 52, 51, 50, 50, 48, 47, 47, 46, 46]

I just copy/pasted and changed it to

$xx = "44, 44, 44, 45, 45, 45, 45, 45, 45, 43, 42, 41, 40, 39, 39, 39, 37, 37, 37, 37, 37, 37, 37, 39, 40, 43, 47, 47, 49, 51, 52, 52, 53, 54, 55, 57, 58, 59, 64, 68, 73, 80, 85, 89, 93, 94, 94, 95, 95, 95, 93, 91, 89, 87, 85, 83, 81, 79, 75, 75, 72, 69, 66, 63, 60, 57, 55, 52, 50, 47, 45, 43, 41, 41, 41, 123, 124, 124, 123, 122, 119, 117, 111, 105, 100, 94, 89, 85, 82, 78, 76, 75, 73, 73, 72, 72, 72, 72, 75, 77, 79, 81, 83, 83, 87, 91, 95, 101, 109, 118, 127, 137, 144, 150, 153, 155, 155, 155, 155, 155, 155, 154, 154, 153, 150, 147, 147, 145, 144, 144, 144, 144, 144, 149, 152, 155, 158, 163, 167, 170, 176, 184, 191, 197, 201, 203, 204, 205, 206, 206, 206, 205, 203, 203, 202, 202, 202, 202, 202, 202, 202, 204, 207, 210, 213, 219, 220, 222, 223, 224, 226, 228, 230, 234, 237, 242, 246, 252, 259, 269, 278, 287, 293, 301, 309, 316, 325, 333, 340, 345, 345, 343, 341, 341, 339, 335, 332, 329, 327, 327, 327, 327, 328, 328, 329, 329, 332, 332, 335, 336, 338, 339, 343, 343, 346, 346";
$yy = "39, 45, 50, 58, 72, 86, 91, 97, 102, 106, 108, 111, 112, 114, 114, 112, 108, 102, 98, 92, 86, 81, 75, 69, 65, 60, 56, 55, 53, 50, 50, 48, 48, 48, 48, 48, 46, 46, 47, 48, 51, 53, 55, 58, 60, 61, 62, 66, 70, 76, 80, 84, 86, 89, 93, 94, 97, 99, 101, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 72, 72, 71, 69, 68, 65, 64, 62, 61, 61, 61, 61, 61, 61, 62, 64, 64, 66, 68, 71, 76, 81, 86, 92, 94, 96, 100, 102, 102, 104, 104, 104, 104, 104, 101, 98, 94, 91, 86, 84, 80, 78, 76, 74, 73, 72, 71, 70, 69, 71, 75, 76, 82, 86, 92, 95, 98, 102, 105, 108, 108, 110, 111, 111, 111, 110, 106, 102, 98, 94, 91, 88, 84, 82, 79, 77, 74, 71, 70, 68, 68, 66, 66, 65, 64, 63, 62, 62, 59, 58, 57, 57, 56, 56, 56, 56, 58, 58, 60, 61, 63, 64, 66, 68, 68, 68, 68, 68, 65, 63, 59, 55, 51, 50, 47, 47, 48, 50, 51, 52, 55, 57, 58, 60, 59, 58, 57, 56, 55, 55, 54, 53, 52, 51, 50, 50, 48, 47, 47, 46, 46";

to give me two string variables (as you get from the db table), then

echo drawImage($xx, $yy);

to get the signature displayed.

 

Why are you changing the function like that?

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this is correct so far right?

<?php
mysqli_report(MYSQLI_REPORT_ERROR|MYSQLI_REPORT_STRICT);
$conn = mysqli_connect("localhost", "winuser2003", "homer123", "pmapptest");
$tdata = '';
$res = $conn->query("SELECT userid, fname, lname, sign_x, sign_y FROM winuser_demo");
foreach ($res as $r) {
    $tdata .= "<tr><td>{$r['userid']}</td>
                   <td>{$r['fname']}</td>
                   <td>{$r['lname']}</td>
                   <td>" . drawImage($r['sign_x'], $r['sign_y']) . "</td>\n";
}

function drawImage($xcoords, $ycoords)
{
    $xa = explode(',', $xcoords);        // create array from $xcoord string
    $ya = explode(',', $ycoords);        // create array from $ycoord string
    $w = max($xa)+10;
    $h = max($ya)+10;
    $path = "M $xa[0] $ya[0] ";
    unset($xa[0], $ya[0]);
    foreach ($xa as $i => $x) {
        $y = $ya[$i];
        $path .= "L $x $y ";
    }

    $im = "<svg width='$w' height='$h' >
           <path d='$path' stroke='#000' fill='none'/>
           </svg>";
    return $im;  
}     
?>

 

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I'll try to explain what the function is doing

First, in the test data we are trying to achieve this

image.png.c25c21bd2a76dfcbca1cbb75682a5d25.png

and we are starting with two sets of numbers

  • sign_x  -  "0,0,100,100,0,50,100,0,100"
  • sign_y  -  "100,20,20,100,20,0,20,100,100"

These numbers need to be put into (x, y) pairs. The first x with first y give (0, 100). The second x with the second y gives (0, 20), the third (100, 20) and so on.

By far the easiest way to do this is with indexed arrays so we use explode to put the x and y values into two arrays

$xa = Array             $ya = Array
(                       (
    [0] => 0                [0] => 100
    [1] => 0                [1] => 20
    [2] => 100              [2] => 20
    [3] => 100              [3] => 100
    [4] => 0                [4] => 20
    [5] => 50               [5] => 0
    [6] => 100              [6] => 20
    [7] => 0                [7] => 100
    [8] => 100              [8] => 100
)                       )

As described inthe above figure, we first want to move to the start point (0, 100) then, after that, we want to draw lines to each successive point.

Using SVG (Scalable Vector Graphics) the way to this is to create a path which has a definition of

"M 0 100 L 0 20 L 100 20 L 100 100 L 0 20 L 50 0 L 100 20 L 0 100 L 100 100" 

where M x y means "move to x,y" and L x y means "line to x,y"

The function line by line

function drawImage($xcoords, $ycoords)
{
    $xa = explode(',', $xcoords);                                               // put x coords string into an array
    $ya = explode(',', $ycoords);                                               // put x coords string into an array
    $w = max($xa)+1;                                                            // get the max coord values so we know the size
    $h = max($ya)+1;
    
                                                                                // define the path
    $path = "M $xa[0] $ya[0] ";                                                    // move to the first x,y position
    unset($xa[0], $ya[0]);                                                         // remove the the first items from the array
    foreach ($xa as $i => $x) {                                                    // loop through arrays
        $y = $ya[$i];                                                              // pairing the i'th x with the i'th y
        $path .= "L $x $y ";                                                       // define line to x y
    }
                                                                                // create svg object $w x $h to display image
    $im = "<svg width='$w' height='$h'>                                         
           <path d='$path' stroke='#000' stroke-width='1' fill='none'/>
           </svg>";
    return $im;  
}

 

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15 hours ago, Barand said:

$xa = Array $ya = Array ( ( [0] => 0 [0] => 100 [1] => 0 [1] => 20 [2] => 100 [2] => 20 [3] => 100 [3] => 100 [4] => 0 [4] => 20 [5] => 50 [5] => 0 [6] => 100 [6] => 20 [7] => 0 [7] => 100 [8] => 100 [8] => 100 ) )

if I am defining these, would that cause a problem though?  I mean we may have quite a bit of signatures, and if I am defining a set of X and Y points won't they be all the same? example, I gave you the X and Y coordinates of a signatre and you were able to see the output which is what I expected.  Lets say I give you another set of XY coordinates based on be defining the array, are they still going to be the same?  or is the array going to say from this X point and to this Y point I will plot this image based on these newly submitted coordinates.  Hope that makes sense.

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Upon closer analysis it seems there is a bracket in the XY coordinates which is why it was not working originally on my end...

[44, 44, 44, 45, 45, 45, 45, 45, 45, 43, 42, 41, 40, 39, 39, 39, 37, 37, 37, 37, 37, 37, 37, 39, 40, 43, 47, 47, 49, 51, 52, 52, 53, 54, 55, 57, 58, 59, 64, 68, 73, 80, 85, 89, 93, 94, 94, 95, 95, 95, 93, 91, 89, 87, 85, 83, 81, 79, 75, 75, 72, 69, 66, 63, 60, 57, 55, 52, 50, 47, 45, 43, 41, 41, 41, 123, 124, 124, 123, 122, 119, 117, 111, 105, 100, 94, 89, 85, 82, 78, 76, 75, 73, 73, 72, 72, 72, 72, 75, 77, 79, 81, 83, 83, 87, 91, 95, 101, 109, 118, 127, 137, 144, 150, 153, 155, 155, 155, 155, 155, 155, 154, 154, 153, 150, 147, 147, 145, 144, 144, 144, 144, 144, 149, 152, 155, 158, 163, 167, 170, 176, 184, 191, 197, 201, 203, 204, 205, 206, 206, 206, 205, 203, 203, 202, 202, 202, 202, 202, 202, 202, 204, 207, 210, 213, 219, 220, 222, 223, 224, 226, 228, 230, 234, 237, 242, 246, 252, 259, 269, 278, 287, 293, 301, 309, 316, 325, 333, 340, 345, 345, 343, 341, 341, 339, 335, 332, 329, 327, 327, 327, 327, 328, 328, 329, 329, 332, 332, 335, 336, 338, 339, 343, 343, 346, 346]

Once i removed these brackets from the beginning and end the image showed up fine.  I am not sure if we can do anything about that though... Does this just mean its being sent as an array rather than a string?

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1 hour ago, winuser2003 said:

Does this just mean its being sent as an array rather than a string?

It's a json array.

Try this version of the "drawImage" function with your db table

function drawImage($xcoords, $ycoords)
{
    $xa = $xcoords[0]=='[' ? json_decode($xcoords, 1) : explode(',', $xcoords);               // put x coords into an array
    $ya = $ycoords[0]=='[' ? json_decode($ycoords, 1) : explode(',', $ycoords);               // put x coords into an array
    $w = max($xa)+1;                                                            // get the max coord values so we know the size
    $h = max($ya)+1;
    
                                                                                // define the path
    $path = "M $xa[0] $ya[0] ";                                                    // move to the first x,y position
    unset($xa[0], $ya[0]);                                                         // remove the the first items from the array
    foreach ($xa as $i => $x) {                                                    // loop through arrays
        $y = $ya[$i];                                                              // pairing the ith x with the ith y
        $path .= "L $x $y ";                                                       // define line to x y
    }
                                                                                // create svg object $w x $h to display image
    $im = "<svg width='$w' height='$h'>                                         
           <path d='$path' stroke='#000' stroke-width='2' fill='none'/>
           </svg>";
    return $im;  
}

 

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Result :

image.thumb.png.c2af2d15bc9593e9f7be89c4f31a24f6.png

 

Coordinates Used :

X Coordinate:

61, 62, 64, 66, 73, 79, 84, 92, 100, 107, 112, 118, 121, 122, 123, 123, 123, 123, 123, 123, 121, 118, 114, 110, 108, 105, 103, 102, 99, 96, 92, 88, 86, 83, 80, 75, 69, 64, 58, 52, 47, 44, 40, 36, 34, 32, 30, 29, 29, 29, 29, 29, 31, 32, 36, 40, 45, 49, 56, 62, 70, 79, 85, 90, 96, 101, 104, 105, 108, 108, 109, 109, 109, 109, 109, 108, 105, 100, 95, 91, 88, 85, 82, 80, 77, 76, 72, 70, 67, 64, 61, 58, 57, 56, 56, 56, 56, 56, 56, 58, 61, 62, 64, 65, 68, 71, 76, 82, 89, 94, 100, 109, 117, 123, 127, 129, 130, 130, 130, 130, 128, 127, 125, 125, 125, 124, 124, 125, 127, 129, 132, 134, 135, 137, 137, 137, 137, 136, 134, 129, 126, 121, 116, 110, 106, 103, 102, 101, 98, 97, 97, 97, 102, 107, 115, 125, 135, 144, 152, 159, 168, 174, 182, 192, 202, 212, 223, 231, 239, 242, 243, 240, 231, 218, 206, 199, 190, 184, 181, 180, 180, 181, 187, 194, 206, 215, 222, 226, 227, 227, 224, 220, 215, 209, 203, 195, 190, 189, 192, 195, 199, 200, 204, 205, 207, 208, 203, 200, 198, 197, 196, 196, 197, 200, 201, 203, 207, 208, 210, 211, 214, 215, 214, 213, 211, 210, 209, 207, 204, 200, 196, 193, 189, 188, 187, 187, 187, 188, 189, 192, 194, 196, 200, 207, 217, 228, 239, 249, 260, 272, 276, 280, 282, 282, 339, 339, 338, 337, 334, 330, 325, 315, 306, 297, 289, 284, 279, 276, 275, 273, 273, 273, 275, 279, 282, 288, 294, 302, 310, 319, 328, 337, 348, 355, 359, 362, 363, 365, 366, 368, 369, 369

 

Y Coordinate:

56, 57, 57, 58, 58, 58, 58, 58, 58, 57, 55, 52, 51, 49, 47, 46, 43, 40, 37, 33, 28, 24, 20, 17, 15, 13, 13, 13, 13, 13, 14, 17, 19, 22, 26, 31, 36, 41, 46, 50, 54, 56, 59, 63, 64, 67, 71, 73, 76, 79, 81, 84, 86, 87, 89, 90, 90, 90, 90, 90, 90, 90, 90, 90, 89, 87, 87, 87, 85, 84, 83, 80, 77, 76, 74, 71, 67, 64, 62, 62, 62, 62, 62, 62, 64, 64, 68, 70, 74, 78, 83, 89, 95, 101, 108, 114, 119, 123, 126, 128, 132, 133, 134, 135, 135, 135, 135, 133, 129, 125, 118, 112, 106, 99, 93, 86, 79, 74, 68, 65, 60, 58, 55, 54, 53, 52, 51, 52, 57, 60, 65, 71, 79, 88, 96, 104, 111, 117, 122, 127, 131, 136, 140, 143, 144, 144, 144, 144, 141, 138, 130, 121, 110, 97, 85, 74, 63, 55, 49, 42, 38, 37, 36, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 35, 37, 39, 43, 44, 45, 45, 46, 46, 46, 46, 46, 44, 44, 43, 43, 44, 48, 52, 57, 64, 69, 75, 79, 80, 80, 78, 74, 72, 69, 67, 66, 66, 71, 74, 78, 81, 82, 83, 83, 83, 83, 81, 79, 78, 76, 76, 74, 73, 76, 77, 80, 81, 84, 88, 92, 97, 102, 109, 116, 123, 128, 133, 135, 138, 139, 139, 139, 139, 139, 135, 129, 124, 117, 110, 103, 94, 90, 86, 84, 84, 51, 50, 50, 50, 50, 53, 57, 63, 70, 77, 85, 91, 98, 105, 111, 118, 124, 130, 135, 139, 142, 145, 146, 146, 146, 144, 139, 133, 123, 116, 107, 100, 93, 87, 81, 78, 76, 76

 

Why are the brackets making a difference though?  I appreciate you teaching me along this project... learning quite a bit.

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