Can anyone please help me with the formula they used to count the number of ordered pairs.
[{(m1 + 1)^2 – m1^2} * {(m2 + 1)^2 – m2^2} * ……* {(mn + 1)^2 – mn^2} ]
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That can be derived with intuition. Please check out this link and watch it from 3:00-13:00, you will get ur doubt clarified.
Hope it’s helpful. 
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Thanks a lot 
.