The problem statement looms below, filling you with determination.

Consider a grid in which some cells are empty and some cells are filled. Call a cell in this grid exitable if, starting at that cell, you can exit the grid by moving up and left through only empty cells. This includes the cell itself, so all filled in cells are not exitable. Note that you can exit the grid from any leftmost empty cell (cell in the first column) by going left, and from any topmost empty cell (cell in the first row) by going up.

Let's call a grid determinable if, given only which cells are exitable, we can exactly determine which cells are filled in and which aren't.

You are given a grid a of dimensions n × m , i. e. a grid with n rows and m columns. You need to answer q queries (1 ≤ q ≤ 2 ⋅ 10^5). Each query gives two integers x_1, x_2 (1 ≤ x_1 ≤ x_2 ≤ m) and asks whether the subgrid of a consisting of the columns x_1, x_1 + 1, …, x_2 - 1, x_2 is determinable.

Input

The first line contains two integers n, m (1 ≤ n, m ≤ 10^6, nm ≤ 10^6) — the dimensions of the grid a.

n lines follow. The y-th line contains m characters, the x-th of which is 'X' if the cell on the intersection of the the y-th row and x-th column is filled and "." if it is empty.

The next line contains a single integer q (1 ≤ q ≤ 2 ⋅ 10^5) — the number of queries.

q lines follow. Each line contains two integers x_1 and x_2 (1 ≤ x_1 ≤ x_2 ≤ m), representing a query asking whether the subgrid of a containing the columns x_1, x_1 + 1, …, x_2 - 1, x_2 is determinable.

Output

For each query, output one line containing "YES" if the subgrid specified by the query is determinable and "NO" otherwise. The output is case insensitive (so "yEs" and "No" will also be accepted).

Example

Input


4 5
..XXX
...X.
...X.
...X.
5
1 3
3 3
4 5
5 5
1 5


Output


YES
YES
NO
YES
NO

Note

For each query of the example, the corresponding subgrid is displayed twice below: first in its input format, then with each cell marked as "E" if it is exitable and "N" otherwise.

For the first query: 
    
    
      
    ..X EEN  
    ... EEE  
    ... EEE  
    ... EEE  
    
    
    
      
      
    

For the second query: 
    
    
      
    X N  
    . E  
    . E  
    . E  
    

Note that you can exit the grid by going left from any leftmost cell (or up from any topmost cell); you do not need to reach the top left corner cell to exit the grid.
    
    
      
      
    

For the third query: 
    
    
      
    XX NN  
    X. NN  
    X. NN  
    X. NN  
    

This subgrid cannot be determined only from whether each cell is exitable, because the below grid produces the above "exitability grid" as well: 
    
    
      
    XX  
    XX  
    XX  
    XX  
    
    
    
      
      
    

For the fourth query: 
    
    
      
    X N  
    . E  
    . E  
    . E  
    
    
    
      
      
    

For the fifth query: 
    
    
      
    ..XXX EENNN  
    ...X. EEENN  
    ...X. EEENN  
    ...X. EEENN  
    

This query is simply the entire grid. It cannot be determined only from whether each cell is exitable because the below grid produces the above "exitability grid" as well: 
    
    
      
    ..XXX  
    ...XX  
    ...XX  
    ...XX  
    
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintStream;
import java.util.Arrays;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;

/*
@author : sanskarXrawat
@date   : 10/19/2021
@time   : 6:30 PM
 */
@SuppressWarnings("ALL")
public class OmkarDetermination {


    public static void main(String[] args) throws Throwable {
        Thread thread = new Thread (null, new TaskAdapter (), "", 1 << 29);
        thread.start ();
        thread.join ();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput (inputStream);
            FastOutput out = new FastOutput (outputStream);
            Solution solver = new Solution ();
            solver.solve (1, in, out);
            in.close ();
            out.close ();
        }
    }

    @SuppressWarnings("unused")
    static class Solution {
        static final Debug debug = new Debug (true);

        public void solve(int testNumber, FastInput in, FastOutput out) {

            int n=in.ri (),m=in.ri ();
            boolean[][] grid=new boolean[n][m];

            for (int i = 0; i <n; i++) {
                for (int j = 0; j <m; j++) {
                    char c=in.rc ();
                    if(c=='X'){
                        grid[i][j]=true;
                    }
                }
            }
            int[] prefix=new int[m+1];
            prefix[0]=prefix[1]=0;

            for (int j = 1; j <m ; j++) {
                    prefix[j+1]=prefix[j];
                for (int i = 1; i <n; i++) {
                    if(grid[i][j-1] && grid[i-1][j]){
                        prefix[j+1]++;
                    }
                }
            }
            int q=in.ri ();

            for (int i = 0; i <q; i++) {
                int l=in.ri (),r=in.ri ();
                if(prefix[l]==prefix[r]) out.prtl ("YES");
                else
                out.prtl ("No");
            }



        }

    }


    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private final StringBuilder cache = new StringBuilder (THRESHOLD * 2);
        private static final int THRESHOLD = 32 << 10;
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append (csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append (csq, start, end);
            return this;
        }

        private void afterWrite() {
            if (cache.length () < THRESHOLD) {
                return;
            }
            flush ();
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this (new OutputStreamWriter (os));
        }

        public FastOutput append(char c) {
            cache.append (c);
            afterWrite ();
            return this;
        }

        public FastOutput append(String c) {
            cache.append (c);
            afterWrite ();
            return this;
        }

        public FastOutput println(String c) {
            return append (c).println ();
        }

        public FastOutput println() {
            return append ('\n');
        }

        final <T> void prt(T a) {
            append (a + " ");
        }

        final <T> void prtl(T a) {
            append (a + "\n");
        }

        public FastOutput flush() {
            try {
                os.append (cache);
                os.flush ();
                cache.setLength (0);
            } catch (IOException e) {
                throw new UncheckedIOException (e);
            }
            return this;
        }

        public void close() {
            flush ();
            try {
                os.close ();
            } catch (IOException e) {
                throw new UncheckedIOException (e);
            }
        }

        public String toString() {
            return cache.toString ();
        }

        public FastOutput printf(String format, Object... args) {
            return append (String.format (format, args));
        }

        private static int countDigits(long l) {
            if (l >= 1000000000000000000L) return 19;
            if (l >= 100000000000000000L) return 18;
            if (l >= 10000000000000000L) return 17;
            if (l >= 1000000000000000L) return 16;
            if (l >= 100000000000000L) return 15;
            if (l >= 10000000000000L) return 14;
            if (l >= 1000000000000L) return 13;
            if (l >= 100000000000L) return 12;
            if (l >= 10000000000L) return 11;
            if (l >= 1000000000L) return 10;
            if (l >= 100000000L) return 9;
            if (l >= 10000000L) return 8;
            if (l >= 1000000L) return 7;
            if (l >= 100000L) return 6;
            if (l >= 10000L) return 5;
            if (l >= 1000L) return 4;
            if (l >= 100L) return 3;
            if (l >= 10L) return 2;
            return 1;
        }

        private static int countDigits(int l) {
            if (l >= 1000000000) return 10;
            if (l >= 100000000) return 9;
            if (l >= 10000000) return 8;
            if (l >= 1000000) return 7;
            if (l >= 100000) return 6;
            if (l >= 10000) return 5;
            if (l >= 1000) return 4;
            if (l >= 100) return 3;
            if (l >= 10) return 2;
            return 1;
        }

    }


    static class FastInput {
        private final StringBuilder defaultStringBuf = new StringBuilder (1 << 13);
        private final ByteBuffer tokenBuf = new ByteBuffer ();
        private final byte[] buf = new byte[1 << 13];
        private SpaceCharFilter filter;
        private final InputStream is;
        private int bufOffset;
        private int bufLen;
        private int next;
        private int ptr;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read (buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read ();
            }
        }

        public String next() {
            return readString ();
        }

        public int ri() {
            return readInt ();
        }

        public int readInt() {
            boolean rev = false;

            skipBlank ();
            if (next == '+' || next == '-') {
                rev = next == '-';
                next = read ();
            }

            int val = 0;
            while (next >= '0' && next <= '9') {
                val = val * 10 - next + '0';
                next = read ();
            }

            return rev ? val : -val;
        }

        public long readLong() {
            boolean rev = false;

            skipBlank ();
            if (next == '+' || next == '-') {
                rev = next == '-';
                next = read ();
            }

            long val = 0L;
            while (next >= '0' && next <= '9') {
                val = val * 10 - next + '0';
                next = read ();
            }

            return rev ? val : -val;
        }

        public long rl() {
            return readLong ();
        }

        public String readString(StringBuilder builder) {
            skipBlank ();

            while (next > 32) {
                builder.append ((char) next);
                next = read ();
            }

            return builder.toString ();
        }

        public String readString() {
            defaultStringBuf.setLength (0);
            return readString (defaultStringBuf);
        }

        public int rs(char[] data, int offset) {
            return readString (data, offset);
        }

        public char[] rsc() {
            return readString ().toCharArray ();
        }

        public int rs(char[] data) {
            return rs (data, 0);
        }

        public int readString(char[] data, int offset) {
            skipBlank ();

            int originalOffset = offset;
            while (next > 32) {
                data[offset++] = (char) next;
                next = read ();
            }

            return offset - originalOffset;
        }

        public char rc() {
            return readChar ();
        }

        public char readChar() {
            skipBlank ();
            char c = (char) next;
            next = read ();
            return c;
        }

        public double rd() {
            return nextDouble ();
        }

        public double nextDouble() {
            int c = read ();
            while (isSpaceChar (c))
                c = read ();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read ();
            }
            double res = 0;
            while (!isSpaceChar (c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow (10, readInt ());
                if (c < '0' || c > '9')
                    throw new InputMismatchException ();
                res *= 10;
                res += c - '0';
                c = read ();
            }
            if (c == '.') {
                c = read ();
                double m = 1;
                while (!isSpaceChar (c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow (10, readInt ());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException ();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read ();
                }
            }
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar (c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }

        public final int readByteUnsafe() {
            if (ptr < bufLen) return buf[ptr++];
            ptr = 0;
            try {
                bufLen = is.read (buf);
                if (bufLen > 0) {
                    return buf[ptr++];
                } else {
                    return -1;
                }
            } catch (IOException e) {
                throw new UncheckedIOException (e);
            }
        }

        public final int readByte() {
            if (ptr < bufLen) return buf[ptr++];
            ptr = 0;
            try {
                bufLen = is.read (buf);
                if (bufLen > 0) {
                    return buf[ptr++];
                } else {
                    throw new java.io.EOFException ();
                }
            } catch (IOException e) {
                throw new UncheckedIOException (e);
            }
        }

        public final String nextLine() {
            tokenBuf.clear ();
            for (int b = readByte (); b != '\n'; b = readByteUnsafe ()) {
                if (b == -1) break;
                tokenBuf.append (b);
            }
            return new String (tokenBuf.getRawBuf (), 0, tokenBuf.size ());
        }

        public final String nl() {
            return nextLine ();
        }

        public final boolean hasNext() {
            for (int b = readByteUnsafe (); b <= 32 || b >= 127; b = readByteUnsafe ()) {
                if (b == -1) return false;
            }
            --ptr;
            return true;
        }

        public void readArray(Object T) {
            if (T instanceof int[]) {
                int[] arr = (int[]) T;
                for (int i = 0; i < arr.length; i++) {
                    arr[i] = ri ();
                }
            }
            if (T instanceof long[]) {
                long[] arr = (long[]) T;
                for (int i = 0; i < arr.length; i++) {
                    arr[i] = rl ();
                }
            }
            if (T instanceof double[]) {
                double[] arr = (double[]) T;
                for (int i = 0; i < arr.length; i++) {
                    arr[i] = rd ();
                }
            }
            if (T instanceof char[]) {
                char[] arr = (char[]) T;
                for (int i = 0; i < arr.length; i++) {
                    arr[i] = readChar ();
                }
            }
            if (T instanceof String[]) {
                String[] arr = (String[]) T;
                for (int i = 0; i < arr.length; i++) {
                    arr[i] = next ();
                }
            }
            if (T instanceof int[][]) {
                int[][] arr = (int[][]) T;
                for (int i = 0; i < arr.length; i++) {
                    for (int j = 0; j < arr[0].length; j++) {
                        arr[i][j] = ri ();
                    }
                }
            }
            if (T instanceof char[][]) {
                char[][] arr = (char[][]) T;
                for (int i = 0; i < arr.length; i++) {
                    for (int j = 0; j < arr[0].length; j++) {
                        arr[i][j] = readChar ();
                    }
                }
            }
            if (T instanceof long[][]) {
                long[][] arr = (long[][]) T;
                for (int i = 0; i < arr.length; i++) {
                    for (int j = 0; j < arr[0].length; j++) {
                        arr[i][j] = rl ();
                    }
                }

            }
        }

        public final void close() {
            try {
                is.close ();
            } catch (IOException e) {
                throw new UncheckedIOException (e);
            }
        }


        private static final class ByteBuffer {
            private static final int DEFAULT_BUF_SIZE = 1 << 12;
            private byte[] buf;
            private int ptr = 0;

            private ByteBuffer(int capacity) {
                this.buf = new byte[capacity];
            }

            private ByteBuffer() {
                this (DEFAULT_BUF_SIZE);
            }

            private ByteBuffer append(int b) {
                if (ptr == buf.length) {
                    int newLength = buf.length << 1;
                    byte[] newBuf = new byte[newLength];
                    System.arraycopy (buf, 0, newBuf, 0, buf.length);
                    buf = newBuf;
                }
                buf[ptr++] = (byte) b;
                return this;
            }

            private char[] toCharArray() {
                char[] chs = new char[ptr];
                for (int i = 0; i < ptr; i++) {
                    chs[i] = (char) buf[i];
                }
                return chs;
            }

            private byte[] getRawBuf() {
                return buf;
            }

            private int size() {
                return ptr;
            }

            private void clear() {
                ptr = 0;
            }
        }


    }


    static class Debug {
        private final boolean offline;
        private final PrintStream out = System.err;
        static int[] empty = new int[0];

        public Debug(boolean enable) {
            offline = enable && System.getSecurityManager () == null;
        }

        public Debug debug(String name, Object x) {
            return debug (name, x, empty);
        }

        public Debug debug(String name, long x) {
            if (offline) {
                debug (name, "" + x);
            }
            return this;
        }

        public Debug debug(String name, String x) {
            if (offline) {
                out.printf ("%s=%s", name, x);
                out.println ();
            }
            return this;
        }

        public Debug debug(String name, Object x, int... indexes) {
            if (offline) {
                if (x == null || !x.getClass ().isArray ()) {
                    out.append (name);
                    for (int i : indexes) {
                        out.printf ("[%d]", i);
                    }
                    out.append ("=").append ("" + x);
                    out.println ();
                } else {
                    indexes = Arrays.copyOf (indexes, indexes.length + 1);
                    if (x instanceof byte[]) {
                        byte[] arr = (byte[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof short[]) {
                        short[] arr = (short[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof boolean[]) {
                        boolean[] arr = (boolean[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof char[]) {
                        char[] arr = (char[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof int[]) {
                        int[] arr = (int[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof float[]) {
                        float[] arr = (float[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof double[]) {
                        double[] arr = (double[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else if (x instanceof long[]) {
                        long[] arr = (long[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    } else {
                        Object[] arr = (Object[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug (name, arr[i], indexes);
                        }
                    }
                }
            }
            return this;
        }

    }
}