In the interest of trying to align a little better, the generators get more picky about the numbers they actually give to the judge.

They still generate values in the same way, but now they only hand a value to the judge when it meets their criteria:

Generator A looks for values that are multiples of 4. Generator B looks for values that are multiples of 8. Each generator functions completely independently: they both go through values entirely on their own, only occasionally handing an acceptable value to the judge, and otherwise working through the same sequence of values as before until they find one.

The judge still waits for each generator to provide it with a value before comparing them (using the same comparison method as before). It keeps track of the order it receives values; the first values from each generator are compared, then the second values from each generator, then the third values, and so on.

Using the example starting values given above, the generators now produce the following first five values each:

--Gen. A-- --Gen. B-- 1352636452 1233683848 1992081072 862516352 530830436 1159784568 1980017072 1616057672 740335192 412269392 These values have the following corresponding binary values:

01010000100111111001100000100100 01001001100010001000010110001000

01110110101111001011111010110000 00110011011010001111010010000000

00011111101000111101010001100100 01000101001000001110100001111000

01110110000001001010100110110000 01100000010100110001010101001000

00101100001000001001111001011000 00011000100100101011101101010000 Unfortunately, even though this change makes more bits similar on average, none of these values' lowest 16 bits match. Now, it's not until the 1056th pair that the judge finds the first match:

--Gen. A-- --Gen. B-- 1023762912 896885216

00111101000001010110000111100000 00110101011101010110000111100000 This change makes the generators much slower, and the judge is getting impatient; it is now only willing to consider 5 million pairs. (Using the values from the example above, after five million pairs, the judge would eventually find a total of 309 pairs that match in their lowest 16 bits.)

After 5 million pairs, but using this new generator logic, what is the judge's final count?