Timing Formulas

In my last post, I looked at how much faster the Double VLOOKUP trick was on sorted data compared with the usual linear VLOOKUP on unsorted data.

Below is the code for the timing routine I use. I stole the guts of it from joeu2004 who made some incredibly insightful comments at this great thread at MrExcel

If you’re going to time formulas, then that thread is required reading, because it makes this important point: we cannot always accurately measure the performance of a formula simply by measuring one instance of it. (But that does depend on the nature of the formula and the situation that we are trying to measure. Sometimes we need to measure one instance of a formula, but increase the size of ranges that it references in order to overcome the effects of overhead.)

I’ve assigned my code to a custom button in the ribbon. You just select the cells you want the formula to time, and click the button. (By the way, my upcoming book not only shows you how to do this, but also gives you routines for every one of the icons shown above and a lot more besides.)
 
TimeFormulas 1
 
 
In the above case, I’ve selected a 1 row by 3 column range. If your selection is only one row deep – and there’s more rows with data below – then the app assumes you want to time everything below too, up to the first blank cell it encounters. I may want to rethink that, but it works good for now.

And after I click the magic button, here’s the result:
 
Timing message
 
 
As you can see from the output screenshot above, it puts a new table in a new sheet, populates it with your timings and relevant parameters, and then displays a message with joeu2004’s warning in it. Plus – and I think this is the genius part – it lets you push OK to return back to the sheet where the original formulas are, or push Cancel if you want to stay in the output sheet.

Note the ‘Formula’ column in the output table. For now, it just lists the formula that was in the top-left cell in the user’s selection. I think listing multiple formulas would be overkill. If there’s no formula in the top left cell, it sees if there’s a formula in the cell below. That way you can select headers in a Table, and you’ll still get the formula in the output.

It also can time multiple areas in one pass. So if I select that same range as a non-contiguous selection by holding Ctrl down and clicking each cell as I’ve done here (not that it’s easy to tell the difference visually from the previous screenshot):
 
noncontiguous
 
 
…then here’s what I get:
 
Output 2
 
 
Man, that is sooo much better than having to do each formula separately and then having to manually copy the results from a messagebox into a Table, like I used to do.

As you can see, I put a a databar on the important column, so you can visually eyeball results instead of conceptually juggling scientific notation in your head. But I’m damned if I can get this to display exactly as I want via VBA. For instance, here’s the databars I want if I add them manually:
Nice Databars

Notice that those have nice borders, and sensible setting for the minimum values, meaning that first result also gets a databar. The code that VBA spits out when you add this default databar is pretty ugly:

Selection.FormatConditions.AddDatabar
Selection.FormatConditions(Selection.FormatConditions.Count).ShowValue = True
Selection.FormatConditions(Selection.FormatConditions.Count).SetFirstPriority
With Selection.FormatConditions(1)
.MinPoint.Modify newtype:=xlConditionValueAutomaticMin
.MaxPoint.Modify newtype:=xlConditionValueAutomaticMax
End With
With Selection.FormatConditions(1).BarColor
.Color = 13012579
.TintAndShade = 0
End With
Selection.FormatConditions(1).BarFillType = xlDataBarFillGradient
Selection.FormatConditions(1).Direction = xlContext
Selection.FormatConditions(1).NegativeBarFormat.ColorType = xlDataBarColor
Selection.FormatConditions(1).BarBorder.Type = xlDataBarBorderSolid
Selection.FormatConditions(1).NegativeBarFormat.BorderColorType = _
xlDataBarColor
With Selection.FormatConditions(1).BarBorder.Color
.Color = 13012579
.TintAndShade = 0
End With
Selection.FormatConditions(1).AxisPosition = xlDataBarAxisAutomatic
With Selection.FormatConditions(1).AxisColor
.Color = 0
.TintAndShade = 0
End With
With Selection.FormatConditions(1).NegativeBarFormat.Color
.Color = 255
.TintAndShade = 0
End With
With Selection.FormatConditions(1).NegativeBarFormat.BorderColor
.Color = 255
.TintAndShade = 0
End With

My code is just doing the first line:

'Add DataBars to the Each Cell column for easier comparison
lo.ListColumns("Each Cell (sec)").Range.FormatConditions.AddDatabar

…because no matter what I try, doing anything beyond merely adding the bars causes the code to error out. For instance, even if I just try and set the minpoint and maxpoint I get an error:
 
error 1
 
 
…and this successfully adds the min setting I want, but errors out when I try to add a listrow:
 
error 2
 
 
Even worse, when I end the routine, the screen no longer updates no matter what I do. So I have to close out of Excel entirely.

If anyone can tell me where I’m going wrong, I’d be much obliged. Might be another peculiarity of Excel Tables. Meanwhile, I’ll just run with those simple bars.

Here’s my draft code:

Option Explicit

Public Declare Function QueryPerformanceFrequency Lib "kernel32" _
(ByRef freq As Currency) As Long
Public Declare Function QueryPerformanceCounter Lib "kernel32" _
(ByRef cnt As Currency) As Long

'Code adapted from http://www.mrexcel.com/forum/excel-questions/762910-speed-performance-measure-visual-basic-applications-function.html
' Description: Determines formusa execution time
' Programmer: Jeff Weir
' Contact: excelforsuperheroes@gmail.com

' Name/Version: Date: Ini: Modification:
' TimeFormula 20150426 JSW Added in ability to record times to ListObject

Sub TimeFormula()
Dim sc As Currency
Dim ec As Currency
Dim dt As Double
Dim sMsg As String
Dim sResults As String
Dim i As Long
Dim N As Long
Dim oldCalc As Variant
Dim myRng As Range
Dim lo As ListObject
Dim lr As ListRow
Dim bUnique As Boolean
Dim strFormula As String
Dim myArea As Range
Dim lngArea As Long
Dim ws As Worksheet
Dim wsOriginal As Worksheet
Dim bNewListObject As Boolean
Dim lngAreas As Long
Dim varResults As Variant
Dim varMsg As Variant
Dim fc As FormatCondition

Const passes As Long = 10

With Application
.ScreenUpdating = False
.EnableEvents = False
oldCalc = .Calculation
.Calculation = xlCalculationManual
End With

Set myArea = Selection
lngAreas = myArea.Areas.Count
Set wsOriginal = myArea.Worksheet
ReDim varResults(1 To lngAreas, 1 To 6)
For Each myArea In Selection.Areas
lngArea = lngArea + 1
dt = 0
Set myRng = myArea
If myRng.Rows.Count = 1 Then
If Not IsEmpty(myRng.Cells(1).Offset(1)) Then Set myRng = Range(myRng, myRng.End(xlDown))
End If
N = myRng.Count
If myRng.Cells.Count > 1 Then
'Get formula from 2nd row in case we're dealing with multiple cells and happen to be on a header
If myRng.Cells(2).HasFormula Then strFormula = myRng.Cells(1).Formula
If myRng.Cells(2).HasArray Then strFormula = myRng.Cells(1).HasArray
End If

If myRng.Cells(1).HasFormula Then strFormula = myRng.Cells(1).Formula
If myRng.Cells(1).HasArray Then strFormula = myRng.Cells(1).HasArray

With myRng
For i = 1 To passes
sc = myTimer
.Calculate
ec = myTimer
dt = dt + myElapsedTime(ec - sc)
Next

'Record results for this pass
varResults(lngArea, 1) = myRng.Address
If strFormula <> "" Then varResults(lngArea, 2) = "'" & strFormula
varResults(lngArea, 3) = N
varResults(lngArea, 4) = dt / passes
varResults(lngArea, 5) = dt / N / passes
varResults(lngArea, 6) = Now
End With

Next

bNewListObject = True
For Each ws In ActiveWorkbook.Worksheets
For Each lo In ws.ListObjects
If lo.Name = "appTimeFormulas" Then
bNewListObject = False
ws.Activate
Exit For
End If
Next
Next

If bNewListObject Then
Set ws = ActiveWorkbook.Worksheets.Add
On Error Resume Next
ws.Name = "TimeFormula"
On Error GoTo 0
Range("A1").Value = "Range"
Range("B1").Value = "Formula"
Range("C1").Value = "Count"
Range("D1").Value = "Entire Range (sec)"
Range("E1").Value = "Each Cell (sec)"
Range("F1").Value = "TimeStamp"
Set lo = ws.ListObjects.Add(xlSrcRange, Range("A1").CurrentRegion, , xlYes)
lo.Name = "appTimeFormulas"

'Add DataBars to the Each Cell column for easier comparison
lo.ListColumns("Each Cell (sec)").Range.FormatConditions.AddDatabar

Else: Set lo = ActiveSheet.ListObjects("appTimeFormulas")
End If

Set lr = lo.ListRows.Add
lr.Range.Resize(lngAreas).Value = varResults
lo.Range.EntireColumn.AutoFit
With lo.ListColumns("Formula").Range
If .ColumnWidth > 30 Then
.ColumnWidth = 30
.WrapText = True
End If
End With

With Application
.EnableEvents = True
.Calculation = oldCalc
.ScreenUpdating = True
End With

sMsg = "Here are the average timings for the selected range over " & passes & " passes "
sMsg = sMsg & vbNewLine & vbNewLine
sMsg = sMsg & "Note that timings include some overhead incurred during the actual measurement process itself. "
sMsg = sMsg & "So if the functions you are tring to time are really really fast, then it's possible that "
sMsg = sMsg & "the measurement time included in the above result dwarfs the "
sMsg = sMsg & "actual recalculation time of the formulas themselves."
sMsg = sMsg & vbNewLine & vbNewLine
sMsg = sMsg & "For best results, either time the functions over a really big range (hundreds "
sMsg = sMsg & "of rows or more) or increase the size of the ranges that the formulas "
sMsg = sMsg & "refer to. Furthermore, pay more heed to the average per-formula time than the overall time when "
sMsg = sMsg & "making comparisons with other formulas."
sMsg = sMsg & vbNewLine & vbNewLine
sMsg = sMsg & "Do you want to return to the formulas, or stay in the result sheet?"
sMsg = sMsg & vbNewLine & vbNewLine
sMsg = sMsg & "(Press YES to return to formulas, and NO to stay in this results sheet.)"

varMsg = MsgBox(Prompt:=sMsg, Title:="Recalculation time for selection:", Buttons:=vbYesNo)
If varMsg = vbYes Then wsOriginal.Activate

End Sub

Function myTimer() As Currency
' defer conversion to seconds until myElapsedTime
QueryPerformanceCounter myTimer
End Function

Function myElapsedTime(dc As Currency) As Double ' return seconds
Static df As Double
Dim freq As Currency
If df = 0 Then QueryPerformanceFrequency freq: df = freq
myElapsedTime = dc / df
End Function

How much faster is the double-VLOOKUP trick?

Quick post. I was writing up the Double-VLOOKUP trick I learnt from Charles Williams for the book.

Standard VLOOKUP on unsorted data:
=VLOOKUP([@ID],Table2,2,FALSE)

Double VLOOKUP trick on sorted data:
=IF(VLOOKUP([@ID],Table2,1,TRUE)=[@ID],VLOOKUP([@ID],Table2,2,TRUE),NA())

The point of the double VLOOKUP trick is this:

  • Standard VLOOKUPS on unsorted data are slow, because your VLOOKUP has to look at each item in turn until it finds a match. So on average, it looks at – and discounts – half the things in your lookup list before it finds that match.
  • Binary searches are lightning fast. Because your data is sorted, they can start half way through the lookup list, and check if the item at that point is bigger or smaller than what they’re looking for. Meaning they can ditch half the list immediately, then look halfway through the remainder. And over and over, ditching half the list each time until they either find the item they are looking for, or rule out all items.
  • VLOOKUP and MATCH will quite happily do a binary search for you. But for reasons known only to Microsoft, they offer an exciting plot-twist: if they don’t find what you’re looking for in the list, they return the closest match they can find to it, which happens to be the only thing left in the list when they’d divided it in half enough times. Only they don’t tell you its not an exact match. Phooey.
  • Charles’ brilliant trick is to do two lightning-fast Binary searches – the first one simply looks for the closest match to your input term among the Lookup terms. If it’s an exact match with what you fed it, you know your lookup term is in the list. So now that you KNOW it’s there for sure, you kick off a second approximate match VLOOKUP, which will grab the corresponding value you want from the lookup table. Go read his blog for the specifics.

I’ve known about this for a while, but it’s only as I’m writing this up for the book that I’ve gained an appeciation of just how much faster Binary Searches – and the Double VLOOKUP trick that gets around Microsoft’s crap implementation of them – are, compared to unsorted/linear VLOOKUPs.

See for yourself:
 
Double VLOOKUPv2
 
 
That says that:

  • At one extreme, if your lookup table has 10,000 things in it, the double VLOOKUP trick on sorted data is 28 times faster than the standard VLOOKUP on unsorted data
  • At the other, if your lookup table has 1,000,000 things in it, the double VLOOKUP trick on sorted data is 3,600 times faster than the standard VLOOKUP on unsorted data

Kinda puts the ‘hassle’ of sorting your lookup table ascending into perspective, don’t it!

April Fools, Excel-style.

Thought I’d share my two favorite pranks with you.

Number one: Take a screenshot of an MVP from their own website, subtly change it somehow, then email it back to them saying “Did you really say this, or was your site hacked”.

Here’s an example. Spot the original.
Jon Originaljon

Number two: Take a screenshot of someone’s spreadsheet next time they walk away from their desk, then paste it neatly over the real thing – like this one that I’m in the process of doing:

 
screenshot

 
 

Hopefully you’ll catch them before they quit Excel forcibly using End Task. (But don’t worry if you don’t…they’ll be none the wiser.)

My only problem is that I’m forced to play this last prank on myself, which kinda ruins the surprise. But I’ve still got that first one to get me through.

Any new Excel-related April Fools pranks out there from anyone? I still have a chapter to write of my Evil Genius book on arrays or something unimportant like that, but I’m running out of steam. So I’ll just put your nastiest pranks in there instead. That outta help folk out with career progression, one way or the other…

I want a global feed of them there comments

I wish more Excel blogs had a global site-wide comments feed that you could subscribe to, like this one does. (Daily Dose of Excel: http://www.dailydoseofexcel.com/comments/feed/)

Comments are where the party is. Sure, you can subscribe to comments on blogs post by post, but sometimes the article doesn’t seem that relevant to you at the time, so you don’t bother. And then someone posts some gem that you wished you had known about. And you missed it, because it wasn’t in the original piece.

And on a site like this one that predates my interest in Excel by like over a decade, I find comments from the Comment Feed often alert me to helpful stuff I’ve missed. But retrospectively subscribing one post at a time in order to catch them ain’t a serious option. So a global comments feed is one of the handiest ways for people to consume great content – often NOT written by the original author – for years to come.

Here’s the site-wide comments feeds for the main sites I know about that have ’em:
Chandoo: http://feeds2.feedburner.com/CommentsForPointyHairedDilbert-Chandoo
Contextures: http://feeds.feedburner.com/ContexturesBlogComments
ExcelXOR: http://excelxor.com/comments/feed/
Newton Excel Bach: http://newtonexcelbach.wordpress.com/comments/feed/
Bacon Bits: http://feeds.feedburner.com/CommentsForBaconBits
PowerPivotPro: http://www.powerpivotpro.com/comments/feed/
Excel & UDF Performance (Charles Williams): http://fastexcel.wordpress.com/comments/feed/
YourSumBuddy: http://yoursumbuddy.com/comments/feed/
MyOnlineTrainingHub (Mynda Treacy): http://www.myonlinetraininghub.com/comments/feed
Jon Peltier: http://feeds.feedburner.com/CommentsForPtsBlog
RAD Excel (Colin Legg): http://feeds.feedburner.com/CommentsForRadExcel
Andrew’s Excel Tips: http://andrewexcel.blogspot.com/feeds/comments/default

My favorite used to be the Bacon Bits comments feed: most of those comments were as risque as Mike’ articles. But then he had to go spoil things by adding a spam filter.

Ah well…the Captcha almost makes up for it:
 
Bacon Bits Captcha

Anyone else have any great global comments feeds on the main Excel sites out there worth sharing?

Today() ain’t so bad…

Finding non-VBA alternatives for the volatile TODAY and NOW functions is tricky, but here’s an example of some creative workarounds for the Evil Boss’ report generator.
 
Non volatile today 2
 
 
That last one that uses a dropdown I pulled from a at the ExcelHero LinkedIn group . It’s pretty clever: what you do is create a small Table somewhere, and populate it using the naughtily volatile =TODAY() function, as well as the words “Please choose…” .
 
Please Choose
 
(An alternate wording to “Please choose…” would be “Choose wisely…”).

Then you point a dropdown list at that Table. And then you assign the name TodaysDate to the cell that the dropdown lives in, and use that instead of TODAY() throughout the rest of your workbook.

The beauty of dropdowns is that while they may reference that volatile function, as soon as the Evil Boss makes a choice, the choice gets written to the cell as a string, and not as a reference to that volatile function. So it IS today’s date, but it is NOT volatile. Of course, you need a big obnoxious message pointing at it so that:

  1. The Evil Boss remembers to fill it out today; and
  2. The Evil Boss also remembers to update it tomorrow

But obnoxious is my middle name.

What help forum would you recommend, and why?

One of the key premises of my book is that Excel has many passionate online user communities. And on that subject, I say:

If you don’t utilize them, you are missing out. If you tap into them, your work isn’t just based on what you know, but on what the collective we know. Which is pretty much everything, between collective us.

One of the things I cover in the book is how to get great results out of a help forum. Ah, but which one?

In the past, I’ve spent some time hanging out at Ken Puls’ ExcelGuru forum – although not too much for the last couple of years. More recently, I’ve been hanging out on the Chandoo forum, although not for the last 6 months due to spending more and more time on the book.

I guess why I started hanging out on the Chandoo forum more and more was that the volumes of questions were good but not overwhelming, meaning you could not only keep an eye on all the questions, but all the answers. Which really fostered a great little community among the regular respondants, I thought.

Of course, I always end up on the Mr Excel forum when Googling – and when I still had my VLOOKUP training wheels on, I learnt some incredible things there from the likes of Fazza and Aladin Akyurek (who has taken part in 68k posts, would you believe). But I’ve never spent much time monitoring content there, largely because of the overwhelming volume of it.

Increasingly I find Google directing me to Stack Overflow. For some reason I don’t really ‘get’ SO. I find it kind of scary looking, from a newbie’s perspective. Anyone feel the same? (Obviously not Dick – he’s been hanging out there for 6 years 6 months, and was last seen there 10 hours ago. Not that I’m stalking.)

Anyways, what forum would you recommend, Hive Mind, and why? I haven’t finished this part of the book yet, and would appreciate your inspiration and wisdom, if you have some to contribute.

6. Doug

VLOOKUP: V is for Volatile.

Well THAT sure got your attention.

I was doing a bit of research for the book (the only bit, mind), and I came across this great old thread on VLOOKUP vs INDEX/MATCH.

There’s a few false starts in terms of test methodology until Jon von der Hayden puts things back on the right track about halfway through the thread.

Conclusion is that INDEX/MATCH is probably way to go, but there’s not a great deal in it.

But I think there’s another important point in the INDEX/MATCH combo’s favor that has been overlooked in this thread: and that’s this bit in bold:

=VLOOKUP(lookup_value,table_array,col_index_num,range_lookup)

The fact that a VLOOKUP functions points at an entire table of data – even though it only ever actually makes use of two columns of it (the key column on the far left, and the nth column given by the col_index_num argument) – means that any time you change any cell in that table, your VLOOKUP is going to recalculate. And then so are ALL formulas downstream of those VLOOKUPS. It’s exactly as if VLOOKUP is a volatile function, where changes to that that Table is concerned.

Whereas with INDEX/MATCH, your functions will ONLY recalculate if you change something in the specific columns that the INDEX and MATCH combo references.

Given that, I’ll take INDEX/MATCH any time.

One thing still puzzles me hugely about VLOOKUP though: the recalculation time incurred from updating the lookup table seems much much longer than the recalculation time incurred from changing an input parameter for the VLOOKUP itself. And the same goes with INDEX/MATCH.

Take the situation where you’ve got a VLOOKUP and Table that looks like this:
 
vlookup issue
 
 

The KEY column is just the numbers 2 through 1,048,576 sorted in random order. And the Value column is just the row number. I won’t post a sample file because it runs to about 20MB, but it’s easy to set up yourself in about 20 seconds.

Changing the orange input cell triggers the VLOOKUP, which gets the right answer pretty quick. I haven’t timed it, but we’re talking ‘blink of an eye’… even when I tell it to look for a number that I happen to know is right at the bottom. Really fast.

But if I type anything in that middle column in the Table – which also causes our VLOOKUP to recalc – Excel acts really really sluggish. Maybe a second of delay in some cases, plus it makes my screen flash.

Which is weird, because it’s the same one VLOOKUP that gets triggered in both cases.

Why would that be?

—UPDATE—
If you haven’t already, go and read Charles Williams’ awesome article Developing Faster Lookups – Part 1 – Using Excel’s functions efficiently – updated

Look for the bit “Large dependency ranges trigger unnecessary Lookups”.

Read it, and don’t weep.

The great “Your Name Here” competition.

I’m getting close to finishing off the first draft of my book, and I’m putting some goofy images at the start of every major section, to lighten it up. I want this to be a laugh-out-loud Excel book: my goal with these images is to make some schmuck reading an Excel book snort out loud on the train during their commute, so that fellow commuters figure this is one sad individual.

In fact, I’m hoping more people will buy it “just for the pictures”, like my mother has promised to. Which is why I put an attractive picture of my wife and I on the cover:
BookCover

So anyways, while I was putting some sample images and text together – all the while snorting out loud to myself at the endless possibilities for entertainment that random animal pictures combined with Excel witticisms provide – I thought why not get you lot in on some of the fun as well. And so I’ve cooked up a grand scheme: the great “Your Name Here” competition.

So here’s the deal: below are some of the sample images I’ve put together so far, using comp images I’ve downloaded from iStock. (I’m sure that my publisher Bill Jelen is going to choke on his morning podcast when he sees I’m serious about some of these).

Your mission – should you choose not to simply laugh it off – is to improve on these in some way if you dare. (I was going to say if you can, but I can tell by your face that you have innate comic ability).

By ‘improve on these in some way’, you’ve got two options:

  1. Come up with a better caption with your name in it; or
  2. Come up with a better image a better caption with your name in it.

Prize? Oh yeah…hmmm…okay, let me think. How about you get to win a copy of my as yet unfinished book. With that winning picture in it. And caption. With your name in the caption. Just your first name, mind, given that tens, possibly twenties of people will see your name next to some random monkey picture or whatever, and wonder what it means in terms of your Excel prowess. Can’t drag your good name down with mine, can we….

Couple of rules:

     

  1. Entries close at the end of this Month (March 2015), and I’ll endeavor to review submissions and get back with some winners and honorable mentions within a fortnight after that.
  2.  

  3. If you just want to just submit a caption, don’t email it to me, but instead simply put it below in the comments along with the heading number and name its’ associated with, so we can all share your mirth right away. (You don’t have to put your email address in the comment, because this blog keeps track of your email when you post a comment, so I’ll be able to contact you if you have a winning entry).
  4.  

  5. If you want to provide a different image than the ones below as well as a caption, feel free. But please ether use a free image from WikiMedia and include the link in your submission, or a free comp image from iStockPhoto, again with the link. And I need an aspect ratio along the lines of these ones i.e. wider than they are tall like the samples below, so they will fit where I plan to put them in the book, and so that I can purchase the image if it’s going to be used.

    Also, if providing an image, make sure it’s of an animal – the wilder the better – so that it fits with the general theme of the other pictures I’ll be using in the book.

 

Images 6 and 11 below come from Wikimedia. Simply Google WikiMedia and some animal name to see what’s available there. Here’s an example, that shows a Monkey taking a selfie. (I kid you not):

Wikimedia Monkey

The rest came from iStock. What’s iStock, and what’s a comp image? Just head to www.iStockPhoto.com, type something like ‘Animals’ or what-not in the big search box on the home page, and when you get to the search page, refine it further by unchecking illustrations, video, and audio options:
iStock seach options

Then when you see something you want to use, click on it, which will bring it up bigger:
Comp

Then you can either click that ‘Get a comp’ option and copy the image that comes up, or simply right click the image shown above and select ‘Copy as Image’ and then paste it into this template and add a caption:
Competition Template

Then simply email it to me at excelforsuperheroes@gmail.com

Have fun, people.

Here’s my sample images, with placeholder text/names. But first, a disclaimer

Disclaimer

All physical characteristics appearing in this work are fictitious. Any resemblance to real MVPs, past or future, is purely coincidental.

1. Chris

1. Chris

2. Rob

2. Rob

3. Ken

3. Ken

4. Jeff

4. Jeff

5. Jon

5. Jon v3

6. Doug

6. Doug

7. Ian

7. Ian v2

8. Deb

8. Deb

9. Dick

9. Dick

10. Mike

10. Mike

11. Charles

11. Charles

12.Oz

12. Oz

13. Mynda

13. Mynda

14. Dave

14. Dave