Continuously display variables value within EventHandler

Consider this code:

DynamicModule[{cnt = 0}, Dynamic@ EventHandler[Dynamic[cnt], "MouseDown" :> (While[CurrentValue["MouseButtons"] == {1}, cnt++])]]

I want this code to continuously displays the value of “cnt”, as it changes, on mousedown. Currently it displays only the final value when the mousebutton is released. Could somebody please tell me.

Also posted at https://mathematica.stackexchange.com/questions/305439/mousedown-event.

Neat. I was carried away by the elegant implementation of the “While” loop approach.
Your solution is a simple fix. Thanks.

I wish it were my solution. It was the user Domen who always gives great answers.