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;
using ll = long long;

ll solve() {
    ll N;
    cin >> N;
    
    auto get_res = []() {
        string s;
        cin >> s;
        if ( s == "Red" ) return 0;
        else if ( s == "Blue" ) return 1;
        else return -1;
    };

    auto check = [&](int k) {
        cout << "?";
        for ( int i = 0; i < N; i++ ) {
            cout << " " << k + i + 1;
        }
        cout << std::endl;
        return get_res();
    };

    int f = check(0);
    int l = 0, r = N+1;
    while ( r - l > 1 ) {
        int m = (l + r) / 2;
        int c = check(m);
        if ( c == -1 ) {
            cout << "! " << std::endl;
            return 0;
        }
        if ( c == f ) l = m;
        else r = m;
    }

    vector<int> cl(2*N);
    for ( int j = 0; j < 2*N; j++ ) {
        if ( j < r  || j >= r+N ) {
            cout << "?";
            for ( int i = r; i < r+N-1; i++ ) {
                cout << " " << i + 1;
            }
            cout << " " << j + 1 << std::endl;
            cl[j] = get_res();
        } else {
            cout << "?";
            for ( int i = 0; i < r-1; i++ ) {
                cout << " " << i + 1;
            }
            for ( int i = r+N; i < 2*N; i++ ) {
                cout << " " << i + 1;
            }
            cout << " " << j + 1 << std::endl;
            cl[j] = get_res();
        }
    }

    cout << "! ";
    for ( int i = 0; i < 2*N; i++ ) {
        char x = cl[i] == 0 ? 'R' : 'B';
        cout << x;
    }
    cout << std::endl;
    return 0;
}

int main() {
    solve();
    return 0;
}