For how many integral values of x will |(x-1!)| + |(x-2!)| + |(x-3!)| + |(x-4!)| asuume a minimum value?

Since there is a modulus function, all the values except 1,2,3,4 will not give minimum values. So, for x = 1, 4 . Value = 9. for x = 2,3 . Value = 4. There for for values, x = 2,3. We have minimum value for the expression. Please correct me if I'm wrong.