So many remainders

For any natural number \(n\),let's define a sequence\(<R_{i}>\) such that \(R_{100}\) is the remainder obtained when \(n\) is divided by 100. \(R_{99}\) is the remainder when \(R_{100}\) is divided by 99. \(R_{98}\) is remainder when \(R_{99}\) is divided by 98 and so on.

Find the least value of \(n\) for which,

\(\displaystyle H= \sum_{1<i<=100} R_{i}+\sum_{1<i<j<=100} R_{i} R_{j}+(\sum_{1<i<j<k<=100}( R_{i} R_{j} R_{k}))+...+R_{2}R_{3}R_{4}.....R_{100}\) attains its maximum possible value


If you are looking for more such simple but twisted questions, Twisted problems for JEE aspirants is for you!
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