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;

typedef long long ll;
typedef long double ld;
typedef pair<int, int> ii;
typedef pair<int, ii> iii;
typedef pair<ii, int> ri3;
#define mp make_pair
#define pb push_back
#define fi first
#define sc second
#define SZ(x) (int)(x).size()
#define ALL(x) begin(x), end(x) 
#define REP(i, n) for (int i = 0; i < n; ++i) 
#define FOR(i, a, b) for (int i = a; i <= b; ++i)
#define RFOR(i, a, b) for (int i = a; i >= b; --i)

int main() {
    //freopen("in.txt", "r", stdin);
    ios::sync_with_stdio(false);
    cin.tie(0);

    int N; cin >> N;

    int lo = 1, hi = N+1;
    string s, u;
    cout << '?'; FOR(i,0,N-1) cout << ' ' << lo+i; cout << endl; cin >> s;
    while (hi-lo > 1) {
        int mid = (lo+hi)/2;
        cout << '?'; FOR(i,0,N-1) cout << ' ' << mid+i; cout << endl; cin >> u;
        if (u == s) lo = mid;
        else hi = mid;
    }

    char ans[2*N+1];
    int x = lo, y = lo+N;
    if (s == "Red") ans[x] = 'R', ans[y] = 'B';
    else ans[x] = 'B', ans[y] = 'R';

    FOR(i,1,2*N){
        if (i == x || i == y) continue;
        else if (i < x || i > y) { cout << '?'; FOR(j,x+1,y-1) cout << ' ' << j; }
        else { cout << '?'; FOR(j,1,x-1) cout << ' ' << j; FOR(j,y+1,2*N) cout << ' ' << j; }
        cout << ' ' << i << endl; cin >> u;
        ans[i] = (u == "Red" ? 'R' : 'B');
    }

    cout << "! ";
    FOR(i,1,2*N) cout << ans[i];
    cout << endl;
}