Cyclic powers of 2! IMO 2015 problem#2

Find all positive unordered multi-sets of integers (a,b,c)(a,b,c) such that abc,bca,cab{ab-c,bc-a,ca-b} are powers of 2.

If these sets can be represented as (a1,b1,c1),(a2,b2,c2),,(an,bn,cn).(a_1,b_1,c_1),(a_2,b_2,c_2),\dots,(a_n,b_n,c_n). Evaluate (i=1nai+bi+ci)+n\displaystyle\large{\left(\sum_{i=1}^{n} a_i + b_i + c_i\right) +n}.

This is from IMO 2015-Problem #2.
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