Up-and-down Number

In an up-and-down counting number, the digits increase to a maximum digit and then decrease. This maximum is not the first or last digit. (A few examples: 1247321 is an up-and-down counting number; 12477321 is not an up-and-down counting number; 13557321 is not an up-and-down counting number.) How many different 4-digit up-and-down numbers are there in which the maximum digit is 6 and at least one of the digits is a 3?