PowerShell Add_Click in foreach loop

Question

What I am trying to accomplish is to create buttons that launch exe files in a certain directory when clicked, but when I try using a foreach loop to create a few buttons, all of the buttons just launch the file the last button is supposed to launch.

Add-Type -AssemblyName System.Windows.Forms
Add-Type -AssemblyName System.Drawing

$form = New-Object System.Windows.Forms.Form
$form.Text = 'Main Window'
$form.Size = New-Object System.Drawing.Size(600,400)

$flp = New-Object System.Windows.Forms.FlowLayoutPanel
$flp.Location = New-Object System.Drawing.Point(0,0)
$flp.Height = $form.Height
$flp.Width = $form.Width
$form.Controls.Add($flp)

$files = Get-ChildItem "$home\Downloads" -Include *.exe -Name

foreach ($file in $files){
    $button = New-Object System.Windows.Forms.Button
    $flp.Controls.Add($button)
    $button.Width = 100
    $button.Height = 50
    $button.Text = $file
    $button.Add_Click{
        Start-Process -FilePath "$home\Downloads\$file"
    }
}

$form.Topmost = $true
$form.ShowDialog()

Whatever I'm doing is probably pretty stupid, so I was just looking for any alternatives or solutions to this other than to just hard code everything.