# It's hard but easy

$\large \sum { { ({ s }_{ i }+{ s }_{ k }) }^{ 3 } }$

$$N$$ is natural number such that $${ 2 }^{ n }|N$$ for some whole number $$n$$.Let $${ s }_{ a }$$ be defined as a number formed from last $$a+1$$ digits on $$N$$.Then find value of above expression modulo $${ 2 }^{ n }$$ if $$n-1\le i,k<j$$ and $$n+2<j$$.

Details:

$$1)$$ If $$N=123456$$ then number $${ s }_{ 3 }$$ is $$3456$$.

$$2)$$ $$j$$ is number of digits of $$N$$.

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