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;

const int Maxn = 200;

int n;
int res[Maxn];
int L, R;

int Ask(int l, int r)
{
    printf("?");
    for (int i = l; i <= r; i++)
        printf(" %d", i);
    printf("\n"); fflush(stdout);
    string res; cin >> res;
    return res == "Red"? -1: 1;
}

int Ask(int x)
{
    printf("? %d", x);
    for (int i = 1; i <= 2 * n; i++)
        if (i != L && i != R && (L < i && i < R) != (L < x && x < R))
            printf(" %d", i);
    printf("\n"); fflush(stdout);
    string res; cin >> res;
    return res == "Red"? -1: 1;
}

int main()
{
    scanf("%d", &n);
    int prv = Ask(1, n);
    int lef = 2, rig = n;
    while (lef <= rig) {
        int mid = lef + rig >> 1;
        if (Ask(mid, mid + n - 1) == prv) lef = mid + 1;
        else rig = mid - 1;
    }
    lef--;
    L = lef; R = lef + n;
    res[L] = prv; res[R] = -prv;
    for (int i = 1; i <= 2 * n; i++)
        if (i != L && i != R) res[i] = Ask(i);
    printf("! ");
    for (int i = 1; i <= 2 * n; i++)
        printf("%c", res[i] == -1? 'R': 'B');
    printf("\n"); fflush(stdout);
    return 0;
}