A special calculator contains a red key. When the red key is pressed, the number on the screen will be added by its unit digit. For instance, if the screen shows 27 and the red key is pressed, the number on screen becomes 27 + 7 = 34, if the red key is pressed again the number on screen becomes 34 + 4 = 38, and so on. A positive integer is now input to the calculator. The red button is then pressed some number of times, and the integer on the screen becomes 1234. What is the smallest possible value of the integer input?