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.IOException;
import java.io.InputStream;
import java.util.*;
//Oficial solution for IO comparison.
public class Q3 {

  /**
   * Template @author William Fiset, william.alexandre.fiset@gmail.com
   *
   */
  static InputReader in = new InputReader(System.in);
  private Scanner sc = new Scanner(System.in);

  static class InputReader {

    private static final int DEFAULT_BUFFER_SIZE = 1 << 16;
    private static final InputStream DEFAULT_STREAM = System.in;
    private static final int MAX_DECIMAL_PRECISION = 21;
    private int c;
    private byte[] buf;
    private int bufferSize, bufIndex, numBytesRead;

    private InputStream stream;

    private static final byte EOF = -1;
    private static final byte NEW_LINE = 10;
    private static final byte SPACE = 32;
    private static final byte DASH = 45;
    private static final byte DOT = 46;

    private char[] charBuffer;

    private static byte[] bytes = new byte[58];
    private static int[] ints = new int[58];
    private static char[] chars = new char[128];

    static {
      char ch = ' ';
      int value = 0;
      byte _byte = 0;
      for (int i = 48; i < 58; i++) {
        bytes[i] = _byte++;
      }
      for (int i = 48; i < 58; i++) {
        ints[i] = value++;
      }
      for (int i = 32; i < 128; i++) {
        chars[i] = ch++;
      }
    }

    private static final double[][] doubles = {
      {0.0d, 0.00d, 0.000d, 0.0000d, 0.00000d, 0.000000d, 0.0000000d, 0.00000000d, 0.000000000d, 0.0000000000d, 0.00000000000d, 0.000000000000d,
        0.0000000000000d, 0.00000000000000d, 0.000000000000000d, 0.0000000000000000d, 0.00000000000000000d, 0.000000000000000000d,
        0.0000000000000000000d, 0.00000000000000000000d, 0.000000000000000000000d},
      {0.1d, 0.01d, 0.001d, 0.0001d, 0.00001d, 0.000001d, 0.0000001d, 0.00000001d, 0.000000001d, 0.0000000001d, 0.00000000001d, 0.000000000001d,
        0.0000000000001d, 0.00000000000001d, 0.000000000000001d, 0.0000000000000001d, 0.00000000000000001d, 0.000000000000000001d,
        0.0000000000000000001d, 0.00000000000000000001d, 0.000000000000000000001d},
      {0.2d, 0.02d, 0.002d, 0.0002d, 0.00002d, 0.000002d, 0.0000002d, 0.00000002d, 0.000000002d, 0.0000000002d, 0.00000000002d, 0.000000000002d,
        0.0000000000002d, 0.00000000000002d, 0.000000000000002d, 0.0000000000000002d, 0.00000000000000002d, 0.000000000000000002d,
        0.0000000000000000002d, 0.00000000000000000002d, 0.000000000000000000002d},
      {0.3d, 0.03d, 0.003d, 0.0003d, 0.00003d, 0.000003d, 0.0000003d, 0.00000003d, 0.000000003d, 0.0000000003d, 0.00000000003d, 0.000000000003d,
        0.0000000000003d, 0.00000000000003d, 0.000000000000003d, 0.0000000000000003d, 0.00000000000000003d, 0.000000000000000003d,
        0.0000000000000000003d, 0.00000000000000000003d, 0.000000000000000000003d},
      {0.4d, 0.04d, 0.004d, 0.0004d, 0.00004d, 0.000004d, 0.0000004d, 0.00000004d, 0.000000004d, 0.0000000004d, 0.00000000004d, 0.000000000004d,
        0.0000000000004d, 0.00000000000004d, 0.000000000000004d, 0.0000000000000004d, 0.00000000000000004d, 0.000000000000000004d,
        0.0000000000000000004d, 0.00000000000000000004d, 0.000000000000000000004d},
      {0.5d, 0.05d, 0.005d, 0.0005d, 0.00005d, 0.000005d, 0.0000005d, 0.00000005d, 0.000000005d, 0.0000000005d, 0.00000000005d, 0.000000000005d,
        0.0000000000005d, 0.00000000000005d, 0.000000000000005d, 0.0000000000000005d, 0.00000000000000005d, 0.000000000000000005d,
        0.0000000000000000005d, 0.00000000000000000005d, 0.000000000000000000005d},
      {0.6d, 0.06d, 0.006d, 0.0006d, 0.00006d, 0.000006d, 0.0000006d, 0.00000006d, 0.000000006d, 0.0000000006d, 0.00000000006d, 0.000000000006d,
        0.0000000000006d, 0.00000000000006d, 0.000000000000006d, 0.0000000000000006d, 0.00000000000000006d, 0.000000000000000006d,
        0.0000000000000000006d, 0.00000000000000000006d, 0.000000000000000000006d},
      {0.7d, 0.07d, 0.007d, 0.0007d, 0.00007d, 0.000007d, 0.0000007d, 0.00000007d, 0.000000007d, 0.0000000007d, 0.00000000007d, 0.000000000007d,
        0.0000000000007d, 0.00000000000007d, 0.000000000000007d, 0.0000000000000007d, 0.00000000000000007d, 0.000000000000000007d,
        0.0000000000000000007d, 0.00000000000000000007d, 0.000000000000000000007d},
      {0.8d, 0.08d, 0.008d, 0.0008d, 0.00008d, 0.000008d, 0.0000008d, 0.00000008d, 0.000000008d, 0.0000000008d, 0.00000000008d, 0.000000000008d,
        0.0000000000008d, 0.00000000000008d, 0.000000000000008d, 0.0000000000000008d, 0.00000000000000008d, 0.000000000000000008d,
        0.0000000000000000008d, 0.00000000000000000008d, 0.000000000000000000008d},
      {0.9d, 0.09d, 0.009d, 0.0009d, 0.00009d, 0.000009d, 0.0000009d, 0.00000009d, 0.000000009d, 0.0000000009d, 0.00000000009d, 0.000000000009d,
        0.0000000000009d, 0.00000000000009d, 0.000000000000009d, 0.0000000000000009d, 0.00000000000000009d, 0.000000000000000009d,
        0.0000000000000000009d, 0.00000000000000000009d, 0.000000000000000000009d}
    };

    public InputReader() {
      this(DEFAULT_STREAM, DEFAULT_BUFFER_SIZE);
    }

    public InputReader(int bufferSize) {
      this(DEFAULT_STREAM, bufferSize);
    }

    public InputReader(InputStream stream) {
      this(stream, DEFAULT_BUFFER_SIZE);
    }

    public InputReader(InputStream stream, int bufferSize) {
      if (stream == null || bufferSize <= 0) {
        throw new IllegalArgumentException();
      }
      buf = new byte[bufferSize];
      charBuffer = new char[128];
      this.bufferSize = bufferSize;
      this.stream = stream;
    }

    private byte read() throws IOException {

      if (numBytesRead == EOF) {
        throw new IOException();
      }

      if (bufIndex >= numBytesRead) {
        bufIndex = 0;
        numBytesRead = stream.read(buf);
        if (numBytesRead == EOF) {
          return EOF;
        }
      }

      return buf[bufIndex++];
    }

    private void doubleCharBufferSize() {
      char[] newBuffer = new char[charBuffer.length << 1];
      for (int i = 0; i < charBuffer.length; i++) {
        newBuffer[i] = charBuffer[i];
      }
      charBuffer = newBuffer;
    }

    private int readJunk(int token) throws IOException {

      if (numBytesRead == EOF) {
        return EOF;
      }

      do {

        while (bufIndex < numBytesRead) {
          if (buf[bufIndex] > token) {
            return 0;
          }
          bufIndex++;
        }

        numBytesRead = stream.read(buf);
        if (numBytesRead == EOF) {
          return EOF;
        }
        bufIndex = 0;

      } while (true);

    }

    public byte nextByte() throws IOException {
      return (byte) nextInt();
    }

    public int nextInt() throws IOException {

      if (readJunk(DASH - 1) == EOF) {
        throw new IOException();
      }
      int sgn = 1, res = 0;

      c = buf[bufIndex];
      if (c == DASH) {
        sgn = -1;
        bufIndex++;
      }

      do {

        while (bufIndex < numBytesRead) {
          if (buf[bufIndex] > SPACE) {
            res = (res << 3) + (res << 1);
            res += ints[buf[bufIndex++]];
          } else {
            bufIndex++;
            return res * sgn;
          }
        }

        numBytesRead = stream.read(buf);
        if (numBytesRead == EOF) {
          return res * sgn;
        }
        bufIndex = 0;

      } while (true);

    }

    public int[] nextIntArray(int n) throws IOException {
      int[] ar = new int[n];
      for (int i = 0; i < n; i++) {
        ar[i] = nextInt();
      }
      return ar;
    }

    public void close() throws IOException {
      stream.close();
    }

    public long nextLong() throws IOException {
      if (readJunk(DASH - 1) == EOF) {
        throw new IOException();
      }
      int sgn = 1;
      long res = 0L;
      c = buf[bufIndex];
      if (c == DASH) {
        sgn = -1;
        bufIndex++;
      }
      do {
        while (bufIndex < numBytesRead) {
          if (buf[bufIndex] > SPACE) {
            res = (res << 3) + (res << 1);
            res += ints[buf[bufIndex++]];
          } else {
            bufIndex++;
            return res * sgn;
          }
        }
        numBytesRead = stream.read(buf);
        if (numBytesRead == EOF) {
          return res * sgn;
        }
        bufIndex = 0;
      } while (true);
    }

    public String nextString() throws IOException {
      if (numBytesRead == EOF) {
        return null;
      }
      if (readJunk(SPACE) == EOF) {
        return null;
      }

      for (int i = 0;;) {
        while (bufIndex < numBytesRead) {
          if (buf[bufIndex] > SPACE) {
            if (i == charBuffer.length) {
              doubleCharBufferSize();
            }
            charBuffer[i++] = (char) buf[bufIndex++];
          } else {
            bufIndex++;
            return new String(charBuffer, 0, i);
          }
        }

        // Reload buffer
        numBytesRead = stream.read(buf);
        if (numBytesRead == EOF) {
          return new String(charBuffer, 0, i);
        }
        bufIndex = 0;
      }
    }
  }

  public static void main(String args[]) throws Exception {
    StringBuilder sb = new StringBuilder();
    int n = in.nextInt();
    int m = in.nextInt();
    int[][] grid = new int[n][m];
    String s;
    char cc;
    for (int i = 0; i < n; i++) {
      s = in.nextString();
      for (int j = 0; j < m; j++) {
        if (s.charAt(j) == 'X') {
          grid[i][j] = 1;
        } else {
          grid[i][j] = 0;
        }
      }
    }
    int[] numBad = new int[m + 1];
    int total = 0;
    for (int j = 0; j < m - 1; j++) {
      for (int i = 1; i < n; i++) {
        if (grid[i][j] == 1 && grid[i - 1][j + 1] == 1) {
          total++;
        }
      }
      numBad[j + 1] = total;
    }
    numBad[m] = total;
    int q = in.nextInt();
    int a, b;
    for (int i = 0; i < q; i++) {
      a = in.nextInt();
      b = in.nextInt();
      if (numBad[b] - numBad[a] == 0) {
        sb.append("yes\n");
      } else {
        sb.append("no\n");
      }
    }
    System.out.println(sb);
  }
}
