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<iostream>
#include<cstdio>
#include<vector>
const int N=205;
int n;
char s[30],ans[N];
void query(std::vector<int> &g) {
    printf("? ");
    for(int v:g) printf(" %d",v);printf("\n");
    fflush(stdout);
    scanf("%s",s);
}
int main() {
    scanf("%d",&n);
    std::vector<int> w;
    for(int i=1;i<=n;i++) w.push_back(i);
    query(w);
    char u=s[0],v=(s[0]=='R'?'B':'R');
    int l=1,r=n+1,mid;
    while(l+1<r) {
        mid=(l+r)>>1;
        w.clear();
        for(int j=0;j<n;j++) w.push_back(j+mid);
        query(w);
        if(s[0]==u) l=mid;
        else r=mid;
    }
    ans[l]=u;
    ans[l+n]=v;
    //printf("%d\n",l);
    w.clear();
    for(int j=1;j<l;j++) w.push_back(j);
    for(int j=l+n+1;j<=n+n;j++) w.push_back(j);
    for(int j=l+1;j<l+n;j++) {
        w.push_back(j);
        query(w);
        ans[j]=s[0];
        w.pop_back();
    }w.clear();
    for(int j=l+1;j<l+n;j++) w.push_back(j);
    for(int j=1;j<l;j++) {
        w.push_back(j);
        query(w);
        ans[j]=s[0];
        w.pop_back();
    }
    for(int j=l+n+1;j<=n+n;j++) {
        w.push_back(j);
        query(w);
        ans[j]=s[0];
        w.pop_back();
    }
    ans[n+n+1]='\0';
    printf("! %s",ans+1);
    return 0;
}