Problem:
Score : 400 points

Problem Statement

We have a string S of length N consisting of R, G, and B.

Find the number of triples (i,~j,~k)~(1 \leq i < j < k \leq N) that satisfy both of the following conditions:

S_i \neq S_j, S_i \neq S_k, and S_j \neq S_k.

j - i \neq k - j.

Constraints

1 \leq N \leq 4000

S is a string of length N consisting of R, G, and B.

Input

Input is given from Standard Input in the following format:

N
S

Output

Print the number of triplets in question.

Sample Input 1

4
RRGB

Sample Output 1

1

Only the triplet (1,~3,~4) satisfies both conditions. The triplet (2,~3,~4) satisfies the first condition but not the second, so it does not count.

Sample Input 2

39
RBRBGRBGGBBRRGBBRRRBGGBRBGBRBGBRBBBGBBB

Sample Output 2

1800

Solution in Pascal (FPC 3.0.4) (judge verdict: Accepted)

const max=5000;
var
  r,b,g:array[0..max] of longint;
  n,i,j:longint;
  ans:int64;
  s:ansistring;
begin
  readln(n);
  readln(s);
  for i:=n downto 1 do
  begin
    r[i]:=r[i+1];
    g[i]:=g[i+1];
    b[i]:=b[i+1];
    if (s[i]='R') then inc(r[i]);
    if (s[i]='G') then inc(g[i]);
    if (s[i]='B') then inc(b[i]);
  end;
  for i:=2 to n-1 do
   begin
     for j:=i-1 downto 1 do
     if (s[i]<>s[j]) then
     begin
       if (s[i]='R') and (s[j]='G') or (s[i]='G') and (s[j]='R') then
       begin
         ans:=ans+b[i+1];
         if (i-j+i<=n) then if (s[i-j+i]='B') then dec(ans);
       end;
       if (s[i]='R') and (s[j]='B') or (s[i]='B') and (s[j]='R') then
       begin
         ans:=ans+g[i+1];
         if (i-j+i<=n) then if (s[i-j+i]='G') then dec(ans);
       end;
       if (s[i]='G') and (s[j]='B') or (s[i]='B') and (s[j]='G') then
       begin
         ans:=ans+r[i+1];
         if (i-j+i<=n) then if (s[i-j+i]='R') then dec(ans);
       end;
     end;
   end;
   writeln(ans);
end.