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 b[2000];
int n;
char p[2000];
int query(int* a) {
    printf("? ");
    for(int i=1;i<=n;i++) {
        if(i<n) printf("%d ",a[i]);
        else printf("%d\n",a[i]);
    }
    fflush(stdout);
    int o;
    scanf("%s",p);
    if(p[0]=='R') return 1;
    else return 2;
}
int main() {
    scanf("%d",&n);
    int c[2000];
    for(int i=1;i<=n;i++) c[i]=i;
    int t=query(c);
    int l=2,r=n+1;
    while(l<r) {
        int m=(l+r)>>1;
        for(int i=1;i<=n;i++) c[i]=m+i-1;
        if(t!=query(c)) r=m;
        else l=m+1;
    }
    b[l-1]=t;
    b[l+n-1]=3-t;
    for(int i=1;i<=n-1;i++) c[i]=l+i-1;
    for(int i=1;i<l-1;i++) {
        c[n]=i;
        b[i]=query(c);
    }
    for(int i=l+n;i<=2*n;i++) {
        c[n]=i;
        b[i]=query(c);
    }
    int k=n/2;
    for(int i=1;i<=2*n && k>0;i++) {
        if(b[i]==t) {
            c[k]=i;
            k--;
        }
    }
    k=n/2;
    for(int i=1;i<=2*n && k>0;i++) {
        if(b[i]==3-t) {
            c[(n/2)+k]=i;
            k--;
        }
    }
    for(int i=l;i<l+n-1;i++) {
        c[n]=i;
        b[i]=query(c);
    }
    printf("! ");
    for(int i=1;i<=2*n;i++) {
        if(b[i]==1) printf("R");
        if(b[i]==2) printf("B");
    }
    printf("\n");
    fflush(stdout);
    return 0;
}