Problem 4. For a sequence a₁ < a₂ < · · · < a_n of integers, a pair ( a_i, a_j ) with 1 ≤ i < j ≤ n is called interesting if there exists a pair ( a_k, a_ℓ ) of integers with 1 ≤ k < ℓ ≤ n such that

$\frac{{\mathrm{<span\; style="font-size:12px;">a</span>}}_{\mathrm{<span\; style="font-size:12px;">l</span>}}<span\; style="font-size:12px;">\; </span><span\; style="font-size:12px;">-</span><span\; style="font-size:12px;"> </span>{\mathrm{<span\; style="font-size:12px;">a</span>}}_{\mathrm{<span\; style="font-size:12px;">k</span>}}}{{\mathrm{<span\; style="font-size:12px;">a</span>}}_{\mathrm{<span\; style="font-size:12px;">j</span>}}<span\; style="font-size:12px;"> </span><span\; style="font-size:12px;">-</span><span\; style="font-size:12px;"> </span>{\mathrm{<span\; style="font-size:12px;">a</span>}}_{\mathrm{<span\; style="font-size:12px;">i</span>}}}<span\; style="font-size:12px;">=</span>\mathrm{<span\; style="font-size:12px;">2</span>}<span\; style="font-size:12px;">.</span>$

For each n ≥ 3, find the largest possible number of interesting pairs in a sequence of length n .