Score : $500$ points

Problem Statement

Consider a string $t$ consisting only of characters A, B, and C. We can do the following operation with it:

• Choose any substring $t[l:r]$ and any permutation $(X, Y, Z)$ of characters $($A$,$B$,$C$)$. Here, $t[l:r]$ denotes the substring formed by the $l$-th through the $r$-th characters of $t$, where $l$ and $r$ are of your choice. Then, replace each character A, B, and C in $t[l:r]$ by $X$, $Y$, and $Z$, respectively.

For example, for a string $t =$ ACBAAC, we can choose a substring $t[3:6]$ and $(X,Y,Z)=($C$,$B$,$A$)$. After this operation, the string will become ACBCCA.

Alina likes strings in which all characters are the same. She defines the beauty of a string $t$ as the minimum number of operations required to make all its characters equal.

You are given a string $S$ of length $N$ consisting only of characters A, B, and C. Answer $Q$ queries. The $i$-th query is the following:

• Given integers $L_i$ and $R_i$, find the beauty of the substring $t=S[L_i:R_i]$.

Constraints

• $1 \le N \le 10^5$
• $S$ is a string of length $N$ consisting only of characters A, B, and C.
• $1 \le Q \le 10^5$
• $1 \le L_i \le R_i \le N$
• All numbers in the input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $Q$

$S$

$L_1$ $R_1$

$L_2$ $R_2$

$\vdots$

$L_Q$ $R_Q$

Output

Output $Q$ lines. In the $i$-th line, output the answer to the $i$-th query.

6 4
ABCCCA
3 5
2 3
1 3
1 6

0
1
2
2

In the first query, the string is $t =$ CCC, in which all letters are already equal. The answer is $0$.

In the second query, the string is $t =$ BC. We can change it to BB in one operation, by choosing a substring $t[2:2]$ and $(X,Y,Z)=($A$,$C$,$B$)$.

In the third query, the string is $t =$ ABC. We can change it to AAB in one operation, by choosing a substring $t[2:3]$ and $(X,Y,Z)=($C$,$A$,$B$)$, and then to BBB in the next operation, by choosing a substring $t[1:2]$ and $(X,Y,Z)=($B$,$A$,$C$)$.