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A DNA sequence can be represented as a string consisting of the letters `A`, `C`, `G` and `T`, which correspond to the types of successive nucleotides in the sequence. Each nucleotide has an *impact factor*, which is an integer. Nucleotides of types `A`, `C`, `G` and `T` have impact factors of 1, 2, 3 and 4, respectively. You are going to answer several queries of the form: What is the minimal impact factor of nucleotides contained in a particular part of the given DNA sequence?

The DNA sequence is given as a non-empty string S = `S[0]S[1]...S[N-1]` consisting of N characters. There are M queries, which are given in non-empty arrays P and Q, each consisting of M integers. The K-th query (0 ≤ K < M) requires you to find the minimal impact factor of nucleotides contained in the DNA sequence between positions P[K] and Q[K] (inclusive).

For example, consider string S = `CAGCCTA` and arrays P, Q such that:

`P[0] = 2 Q[0] = 4 P[1] = 5 Q[1] = 5 P[2] = 0 Q[2] = 6`

The answers to these M = 3 queries are as follows:

- The part of the DNA between positions 2 and 4 contains nucleotides
GandC(twice), whose impact factors are 3 and 2 respectively, so the answer is 2.- The part between positions 5 and 5 contains a single nucleotide
T, whose impact factor is 4, so the answer is 4.- The part between positions 0 and 6 (the whole string) contains all nucleotides, in particular nucleotide
Awhose impact factor is 1, so the answer is 1.

Write a function:

function solution(S, P, Q);

that, given a non-empty string S consisting of N characters and two non-empty arrays P and Q consisting of M integers, returns an array consisting of M integers specifying the consecutive answers to all queries.

Result array should be returned as an array of integers.

For example, given the string S = `CAGCCTA` and arrays P, Q such that:

`P[0] = 2 Q[0] = 4 P[1] = 5 Q[1] = 5 P[2] = 0 Q[2] = 6`

the function should return the values [2, 4, 1], as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..100,000];
- M is an integer within the range [1..50,000];
- each element of arrays P and Q is an integer within the range [0..
N - 1];- P[K] ≤ Q[K], where 0 ≤ K < M;
- string S consists only of upper-case English letters
A, C, G, T.

*not defined yet*