Junior Mathematical Olympiad

Ikram has a large bowl with little balls in it. On each ball a positive integer is written. If he randomly picks three balls from the bowl and takes the difference between the largest and smallest number on these three balls, it turns out that the outcome is always also on one of the balls in the bowl (or on one of the three balls he just picked up). He always puts the balls back in the bowl. Ikram knows for sure that there are balls with $3$, $6$ and $2023$ in the bowl. At least how many balls are in the bowl?