Returns unexpected value

I wrote this code for an online course I am taking and you cant post code and get specific help there. I hope that someone here will help. Code -

largest = None
smallest = None
numI = 0
while True:
    num = raw_input("Prompt you")
    if num == "done":
        break
    try:
        numI = int(num)
    except:
        print "Invalid input"
        continue
    if numI >= largest or numI < smallest:
        if numI > largest:
            largest = numI
        else:
            smallest = numI 

print "Maximum is",largest
print "Minimum is",smallest

Why does it return "Minimum is None"? I tried with two If loops, an If and and Elif, and now this nested loop. No matter what I dont seem to reach setting of the minimum value.

Any help greatly appreciated.

(Code is turned in and rated, so you cant ruin that part :) )