Problem: Warawreh created a great company called Nanosoft. The only thing that Warawreh still has to do is to place a large picture containing its logo on top of the company's building.

The logo of Nanosoft can be described as four squares of the same size merged together into one large square. The top left square is colored with red, the top right square is colored with green, the bottom left square is colored with yellow and the bottom right square is colored with blue.

An Example of some correct logos:

<image>

An Example of some incorrect logos:

<image>

Warawreh went to Adhami's store in order to buy the needed picture. Although Adhami's store is very large he has only one picture that can be described as a grid of n rows and m columns. The color of every cell in the picture will be green (the symbol 'G'), red (the symbol 'R'), yellow (the symbol 'Y') or blue (the symbol 'B').

Adhami gave Warawreh q options, in every option he gave him a sub-rectangle from that picture and told him that he can cut that sub-rectangle for him. To choose the best option, Warawreh needs to know for every option the maximum area of sub-square inside the given sub-rectangle that can be a Nanosoft logo. If there are no such sub-squares, the answer is 0.

Warawreh couldn't find the best option himself so he asked you for help, can you help him?

Input

The first line of input contains three integers n, m and q (1 ≤ n , m ≤ 500, 1 ≤ q ≤ 3 ⋅ 10^{5}) — the number of row, the number columns and the number of options.

For the next n lines, every line will contain m characters. In the i-th line the j-th character will contain the color of the cell at the i-th row and j-th column of the Adhami's picture. The color of every cell will be one of these: {'G','Y','R','B'}.

For the next q lines, the input will contain four integers r_1, c_1, r_2 and c_2 (1 ≤ r_1 ≤ r_2 ≤ n, 1 ≤ c_1 ≤ c_2 ≤ m). In that option, Adhami gave to Warawreh a sub-rectangle of the picture with the upper-left corner in the cell (r_1, c_1) and with the bottom-right corner in the cell (r_2, c_2).

Output

For every option print the maximum area of sub-square inside the given sub-rectangle, which can be a NanoSoft Logo. If there are no such sub-squares, print 0.

Examples

Input


5 5 5
RRGGB
RRGGY
YYBBG
YYBBR
RBBRG
1 1 5 5
2 2 5 5
2 2 3 3
1 1 3 5
4 4 5 5


Output


16
4
4
4
0


Input


6 10 5
RRRGGGRRGG
RRRGGGRRGG
RRRGGGYYBB
YYYBBBYYBB
YYYBBBRGRG
YYYBBBYBYB
1 1 6 10
1 3 3 10
2 2 6 6
1 7 6 10
2 1 5 10


Output


36
4
16
16
16


Input


8 8 8
RRRRGGGG
RRRRGGGG
RRRRGGGG
RRRRGGGG
YYYYBBBB
YYYYBBBB
YYYYBBBB
YYYYBBBB
1 1 8 8
5 2 5 7
3 1 8 6
2 3 5 8
1 2 6 8
2 1 5 5
2 1 7 7
6 5 7 5


Output


64
0
16
4
16
4
36
0

Note

Picture for the first test:

<image>

The pictures from the left to the right corresponds to the options. The border of the sub-rectangle in the option is marked with black, the border of the sub-square with the maximal possible size, that can be cut is marked with gray.

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;


public class Main {
    static int inf = (int) 1e9 + 7;
    static int n, m, q;
    static char h[][];
    static int sz[][];
    static sparse_table a;
    static void scan() throws IOException {
        n = sc.nextInt();
        m = sc.nextInt();
        q = sc.nextInt();
        h = new char[n][m];
        for(int i = 0;i < n;i++) h[i] = sc.next().toCharArray();
        sz = new int [n][m];
    }

    static boolean check(int x, int y) {
        return x >= 0 && y >= 0 && x < n && y < m;
    }

    static char sgn(int x, int y) {
        if (x >= 0 && y >= 0) return 'B';
        if (x >= 0) return 'Y';
        if (y >= 0) return 'G';
        return 'R';
    }

    static boolean check(int xc, int yc, int x, int y) {
        return check(x, y) && sgn(x - xc, y - yc) == h[x][y];
    }


    static boolean check(int xc, int yc, int s) {
        int x1 = xc - s;
        int y1 = yc - s;
        boolean q = true;
        for(int i = 0;i < 2 * s;i++) {
            q &= check(xc, yc, i + x1, y1);
            q &= check(xc, yc, i + x1, y1 + 2 * s - 1);
            q &= check(xc, yc, x1, i + y1);
            q &= check(xc, yc, x1 + 2 * s - 1, i + y1);
        }
        return q;
    }

    static void build_sz() {
        for(int xc = 0;xc < n;xc++) {
            for(int yc = 0;yc < m;yc++) {
                int s = 1;
                while (true) {
                    if (!check(xc, yc, s)) break;
                    s++;
                }
                sz[xc][yc] = s - 1;
            }
        }
    }

    static int get(int x1, int y1, int x2, int y2) {
        int l = 0;
        int r = 500;
        while(r - l > 1) {
            int mid = ((l + r) >> 1);
            if (a.get(x1 + mid, y1 + mid, x2 - mid + 1, y2 - mid + 1) >= mid) l = mid;
            else r = mid;
        }
        return l * l * 4;
    }

    static void solve() throws IOException {
        scan();
        build_sz();
        a = new sparse_table(sz);
        for(int i = 0;i < q;i++) {
            int ans = get(sc.nextInt() - 1, sc.nextInt() - 1, sc.nextInt() - 1, sc.nextInt() - 1);
            pw.println(ans);
        }
    }


    public static void main(String[] args) throws IOException {
        sc = new Scanner(System.in);
        pw = new PrintWriter(System.out);
        solve();
        pw.close();
    }

    static Scanner sc;
    static PrintWriter pw;

    static class Scanner {
        BufferedReader br;
        StringTokenizer st = new StringTokenizer("");

        Scanner(InputStream in) throws FileNotFoundException {
            br = new BufferedReader(new InputStreamReader(in));
        }

        Scanner(String in) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(in));
        }

        String next() throws IOException {
            while (!st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
    }
}

class sparse_table {
    int log[] = new int [501];
    int n, m, log_n = 10, log_m = 10;
    int max[][][][];

    sparse_table(int sz[][]) {
        log[1] = 0;
        for(int i = 2;i <= 500;i++) log[i] = log[i / 2] + 1;
        n = sz.length;
        m = sz[0].length;
        max = new int [log_n][log_m][n][m];
        for(int i = 0;i < n;i++) {
            for(int j = 0;j < m;j++) {
                max[0][0][i][j] = sz[i][j];
            }
        }

        for(int q = 0;q < log_n;q++) {
            for(int w = 0;w < log_m;w++) {
                if (q == 0 && w == 0) continue;
                for(int i = 0;i < n;i++) {
                    for(int j = 0;j < m;j++) {
                        int ans;
                        if (q == 0) {
                            ans = Math.max(max[q][w - 1][i][j],
                                    max[q][w - 1][i][Math.min(m - 1, j + (1 << (w - 1)))]);
                        }else{
                            ans = Math.max(max[q - 1][w][i][j],
                                    max[q - 1][w][Math.min(n - 1, i + (1 << (q - 1)))][j]);
                        }
                        max[q][w][i][j] = ans;
                    }
                }
            }
        }
    }

    int get(int x1, int y1, int x2, int y2) {
        if (y1 > y2 || x1 > x2) return 0;
        int log1 = log[x2 - x1 + 1];
        int log2 = log[y2 - y1 + 1];
        int ans1 = max[log1][log2][x1][y1];
        int ans2 = max[log1][log2][x2 - (1 << log1) + 1][y1];
        int ans3 = max[log1][log2][x1][y2 - (1 << log2) + 1];
        int ans4 = max[log1][log2][x2 - (1 << log1) + 1][y2 - (1 << log2) + 1];
        return Math.max(ans1, Math.max(ans2, Math.max(ans3, ans4)));
    }
}