Farmer John believes he has made a major breakthrough in algorithm design: he claims to have found a nearly linear time algorithm for the 3SUM problem, an algorithmic problem famous for the fact that no known solution exists running in substantially better than quadratic time. One formulation of the 3SUM problem is the following: given an array s_1,\dots,s_m of integers, count the number of unordered triples of distinct indices i,j,k such that s_i + s_j + s_k = 0.

To test Farmer John's claim, Bessie has provided an array A of N integers (1 \leq N \leq 5000). Bessie also asks Q queries (1 \leq Q \leq 10^5), each of which consists of two indices 1 \leq a_i \leq b_i \leq N. For each query, Farmer John must solve the 3SUM problem on the subarray A[a_i \dots b_i].

Unfortunately, Farmer John has just discovered a flaw in his algorithm. He is confident that he can fix the algorithm, but in the meantime, he asks that you help him pass Bessie's test!

SCORING:

Test cases 2-4 satisfy N\le 500.
Test cases 5-7 satisfy N\le 2000.
Test cases 8-15 satisfy no additional constraints.

Problem credits: Dhruv Rohatgi

#4145 upload 2 done 1 how_to_reg 1

Farmer John Solves 3SUM timer 2s memory 512MB

#4145

Farmer John Solves 3SUM 2s 512MB