2066: [USACO 2025 US Open Contest, Bronze] Problem 3. It's Mooin' Time III

Elsie is trying to describe her favorite USACO contest to Bessie, but Bessie is having trouble understanding why Elsie likes it so much. Elsie says "And It's mooin' time! Who wants a mooin'? Please, I just want to do USACO". 

Bessie still doesn't understand, so she transcribes Elsie's description in a string of length N (3 ≤ N ≤ 10⁵) containing lowercase alphabetic characters s₁ s₂ … s_N. Elsie considers a string t containing three characters a moo if t₂ = t₃ and t₂ ≠ t₁.

A triplet (i, j, k) is valid if i < j < k and string s_i s_j s_k forms a moo. For the triplet, FJ performs the following to calculate its value:

• FJ bends string s 90-degrees at index j
• The value of the triplet is twice the area of Δijk. 

In other words, the value of the triplet is (j−i)(k−j).

Bessie asks you Q (1 ≤ Q ≤ 3⋅10⁴) queries. In each query, she gives you two integers l and r (1 ≤ l ≤ r ≤ N, r − l + 1 ≥ 3) and ask you for the maximum value among valid triplets (i,j,k) such that l ≤ i and k ≤ r. If no valid triplet exists, output −1. 

Note that the large size of integers involved in this problem may require the use of 64-bit integer data types (e.g., a "long long" in C/C++).

The following line contains s₁ s₂, … s_N.

The following Q lines contain two integers l and r, denoting each query.

12 5
abcabbacabac
1 12
2 7
4 8
2 5
3 10

28
6
1
-1
12