Arithmetic Sequence

A sequence b₁,b₂,⋯,b_n are called (d₁,d₂)-arithmetic sequence if and only if there exist i(1≤i≤n) such that for every j(1≤j< i),b_j+1=b_j+d₁ and for every j(i≤j< n),b_j+1=b_j+d₂.

Teacher Mai has a sequence a₁,a₂,⋯,a_n. He wants to know how many intervals [l,r](1≤l≤r≤n) there are that a_l,a_l+1,⋯,a_r are (d₁,d₂)-arithmetic sequence.

There are multiple test cases.

For each test case, the first line contains three numbers n,d₁,d₂(1≤n≤10⁵,|d₁|,|d₂|≤1000), the next line contains n integers a₁,a₂,⋯,a_n(|a_i|≤10⁹).

For each test case, print the answer.