Problem: This is an interactive task.

We have 2N balls arranged in a row, numbered 1, 2, 3, ..., 2N from left to right, where N is an odd number. Among them, there are N red balls and N blue balls.

While blindfolded, you are challenged to guess the color of every ball correctly, by asking at most 210 questions of the following form:

* You choose any N of the 2N balls and ask whether there are more red balls than blue balls or not among those N balls.



Now, let us begin.

Constraints

* 1 \leq N \leq 99
* N is an odd number.



* * *



Example

Input




Output

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int n,i,j,le,ri;
char c,s[7],r[222];
int main() {
  scanf("%d",&n);
  printf("?");
  for (j=1; j<=n; j++) printf(" %d",j);
  puts("");
  fflush(stdout);
  scanf("%s",s);
  c=s[0];
  le=2; ri=n+1;
  while (le<ri) {
    i=(le+ri)/2;
    printf("?");
    for (j=0; j<n; j++) printf(" %d",i+j);
    puts("");
    fflush(stdout);
    scanf("%s",s);
    if (s[0]==c) le=i+1; else ri=i;
  }
  r[ri-1]=c;
  r[ri+n-1]='R'+'B'-c;
  for (i=1; i<=2*n; i++) if (i<ri-1 || i>=ri+n) {
    printf("? %d",i);
    for (j=0; j<n-1; j++) printf(" %d",ri+j);
    puts("");
    fflush(stdout);
    scanf("%s",s);
    r[i]=s[0];
  } else if (i>=ri && i<ri+n-1) {
    printf("? %d",i);
    for (j=1; j<=2*n; j++) if (j<ri-1 || j>=ri+n) printf(" %d",j);
    puts("");
    fflush(stdout);
    scanf("%s",s);
    r[i]=s[0];
  }
  printf("! %s\n",r+1);
  fflush(stdout);
  return 0;
}