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.*;
import java.util.*;


import java.math.*;
import java.math.BigInteger;


public final class A
{    
	static PrintWriter out = new PrintWriter(System.out); 
	static StringBuilder ans=new StringBuilder();
	static FastReader in=new FastReader();
	static ArrayList<Integer> g[];
	static long mod=(long)1e9+7,INF=Long.MAX_VALUE;
	static boolean set[]; 
	static int par[],partial[];
	static int Days[],P[][];
	static int dp[][],sum=0,size[],D[];
	static int seg[],col[];
	static ArrayList<Long> A;
	//	static HashSet<Integer> visited,imposters;
	//	static HashSet<Integer> set;
	//	static node1 seg[];
	//static pair moves[]= {new pair(-1,0),new pair(1,0), new pair(0,-1), new pair(0,1)};
	public static void main(String args[])throws IOException
	{	
/*
 * cycle for:: 1 x 2
 *             2 x 3 
 *             3 x 1
 */

		int N=i(),M=i();
		char X[][]=new char[N][M];
		for(int i=0; i<N; i++)X[i]=in.next().toCharArray();
		int A[]=new int[M+1];
		TreeSet<Integer> set=new TreeSet<>();
		set.add(-1);
		for(int j=1; j<M; j++)
		{
			for(int i=1; i<N; i++)
			{
				if(X[i][j]=='.' && X[i-1][j]=='X' && X[i][j-1]=='X')
				{
					set.add(j+1);
					break;
				}			
			}
		}
		int Q=i();
		while(Q-->0)
		{
			int l=i(),r=i();
			if(l==r)ans.append("YES\n");
			else
			{
				int a=set.floor(r);
				if(a-1>=l)ans.append("NO\n"); //non determinable is present
				else ans.append("YES\n");
			}
		}
		out.println(ans);
		out.close();
	}
	static int find(int a)
	{
		if(par[a]<0)return a;
		return par[a]=find(par[a]);
	}
	static void union(int a,int b)
	{
		a=find(a);
		b=find(b);
		if(a!=b)
		{
			par[a]+=par[b];
			par[b]=a;
		}
	}
	static int ask(int a,int b)
	{
		System.out.println("? "+a+" "+b);
		return i();
	}
	

	
	static void update(char X[][],int min[][],int i,int j,int N,int M,int d)
	{
		int x=i,y=j;
		int t=d+1;
		while(t-->0 && i>=0 && j>=0 && X[i][j]=='*')
		{
			min[i][j]=Math.max(min[i][j],d);
			i--;
			j--;
		}
		i=x;
		j=y;
		t=d+1;
		while(t-->0 && i>=0 && j<M && X[i][j]=='*')
		{
			min[i][j]=Math.max(min[i][j],d);
			i--;
			j++;
		}	
	}

	static long and(int i,int j)
	{
		System.out.println("and "+i+" "+j);
		return l();
	}
	static long or(int i,int j)
	{
		System.out.println("or "+i+" "+j);
		return l();
	}
	static boolean is_Sorted(int A[])
	{
		int N=A.length;
		for(int i=1; i<=N; i++)if(A[i-1]!=i)return false;
		return true;
	}
	static boolean f(StringBuilder sb,String Y,String order)
	{
		StringBuilder res=new StringBuilder(sb.toString());
		HashSet<Character> set=new HashSet<>();
		for(char ch:order.toCharArray())
		{
			set.add(ch);
			for(int i=0; i<sb.length(); i++)
			{
				char x=sb.charAt(i);
				if(set.contains(x))continue;
				res.append(x);
			}
		}

		String str=res.toString();
		return str.equals(Y);
	}
	static boolean all_Zero(int f[])
	{
		for(int a:f)if(a!=0)return false;
		return true;
	}
	static long form(int a,int l)
	{
		long x=0;
		while(l-->0)
		{
			x*=10;
			x+=a;
		}
		return x;
	}
	static int count(String X)
	{
		HashSet<Integer> set=new HashSet<>();
		for(char x:X.toCharArray())set.add(x-'0');
		return set.size();
	}


	//	static void build(int v,int tl,int tr,long A[])
	//	{
	//		if(tl==tr)
	//		{
	//			seg[v]=A[tl];
	//		}
	//		else
	//		{
	//			int tm=(tl+tr)/2;
	//			build(v*2,tl,tm,A);
	//			build(v*2+1,tm+1,tr,A);
	//			seg[v]=Math.min(seg[v*2], seg[v*2+1]);
	//		}
	//	}
	static long ask(int v,int tl,int tr,int l,int r)
	{
		if(l>r)return (long)(1e10);
		if(tl==l && tr==r)
		{
			return seg[v];
		}
		int tm=(tl+tr)/2;
		return Math.min(ask(v*2,tl,tm,l,Math.min(tm, r)), ask(v*2+1,tm+1,tr,Math.max(l,tm+1),r));
	}
	static int [] sub(int A[],int B[])
	{
		int N=A.length;
		int f[]=new int[N];
		for(int i=N-1; i>=0; i--)
		{
			if(B[i]<A[i])
			{
				B[i]+=26;
				B[i-1]-=1;
			}
			f[i]=B[i]-A[i];
		}
		for(int i=0; i<N; i++)
		{
			if(f[i]%2!=0)f[i+1]+=26;
			f[i]/=2;
		}
		return f;
	}





	static int max(int a ,int b,int c,int d)
	{
		a=Math.max(a, b);
		c=Math.max(c,d);
		return Math.max(a, c);
	}
	static int min(int a ,int b,int c,int d)
	{
		a=Math.min(a, b);
		c=Math.min(c,d);
		return Math.min(a, c);
	}



	static HashMap<Integer,Integer> Hash(int A[])
	{
		HashMap<Integer,Integer> mp=new HashMap<>();
		for(int a:A)
		{
			int f=mp.getOrDefault(a,0)+1;
			mp.put(a, f);
		}
		return mp;
	}
	static long mul(long a, long b)
	{
		return ( a %mod * 1L * b%mod )%mod;
	}
	static void swap(int A[],int a,int b)
	{
		int t=A[a];
		A[a]=A[b];
		A[b]=t;
	}


	
	static boolean isSorted(int A[])
	{
		for(int i=1; i<A.length; i++)
		{
			if(A[i]<A[i-1])return false;
		}
		return true;
	}

	static boolean isDivisible(StringBuilder X,int i,long num)
	{
		long r=0;
		for(; i<X.length(); i++)
		{
			r=r*10+(X.charAt(i)-'0');
			r=r%num;
		}
		return r==0;
	}    



	static int lower_Bound(int A[],int low,int high, int x) 
	{ 
		if (low > high) 
			if (x >= A[high]) 
				return A[high]; 

		int mid = (low + high) / 2; 

		if (A[mid] == x) 
			return A[mid]; 

		if (mid > 0 && A[mid - 1] <= x && x < A[mid]) 
			return A[mid - 1]; 

		if (x < A[mid]) 
			return lower_Bound( A, low, mid - 1, x); 

		return lower_Bound(A, mid + 1, high, x); 
	} 

	static String f(String A)
	{
		String X="";
		for(int i=A.length()-1; i>=0; i--)
		{
			int c=A.charAt(i)-'0';
			X+=(c+1)%2;
		}
		return X;
	}

	static void sort(long[] a) //check for long
	{
		ArrayList<Long> l=new ArrayList<>();
		for (long i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}

	static String swap(String X,int i,int j)
	{
		char ch[]=X.toCharArray();
		char a=ch[i];
		ch[i]=ch[j];
		ch[j]=a;
		return new String(ch);
	}

	static int sD(long n)  
	{  

		if (n % 2 == 0 )  
			return 2;  

		for (int i = 3; i * i <= n; i += 2) {  
			if (n % i == 0 )  
				return i;  
		}  

		return (int)n;  
	}  

	static void setGraph(int N)
	{
		//		tot=new int[N+1];
		partial=new int[N+1];
		Days=new int[N+1];
		P=new int[N+1][(int)(Math.log(N)+10)];
		set=new boolean[N+1];
		g=new ArrayList[N+1];
		D=new int[N+1];
		for(int i=0; i<=N; i++)
		{

			g[i]=new ArrayList<>();		
			Days[i]=-1;
			D[i]=Integer.MAX_VALUE;
			//D2[i]=INF;
		}
	}



	static  long pow(long a,long b)
	{
		//long mod=1000000007;
		long pow=1;
		long x=a;
		while(b!=0)
		{
			if((b&1)!=0)pow=(pow*x)%mod;
			x=(x*x)%mod;
			b/=2;
		}
		return pow;
	}

	static long toggleBits(long x)//one's complement || Toggle bits
	{
		int n=(int)(Math.floor(Math.log(x)/Math.log(2)))+1;

		return ((1<<n)-1)^x;
	}

	static int countBits(long a)
	{
		return (int)(Math.log(a)/Math.log(2)+1);
	}

	static long fact(long N)
	{ 
		long n=2; 
		if(N<=1)return 1;
		else
		{
			for(int i=3; i<=N; i++)n=(n*i)%mod;
		}
		return n;
	}

	static int kadane(int A[])
	{
		int lsum=A[0],gsum=A[0];
		for(int i=1; i<A.length; i++)
		{
			lsum=Math.max(lsum+A[i],A[i]);
			gsum=Math.max(gsum,lsum);
		}
		return gsum;
	}

	static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}

	static boolean isPrime(long N)
	{
		if (N<=1)  return false; 
		if (N<=3)  return true; 
		if (N%2 == 0 || N%3 == 0) return false; 
		for (int i=5; i*i<=N; i=i+6) 
			if (N%i == 0 || N%(i+2) == 0) 
				return false; 
		return true; 
	}
	static void print(char A[])
	{
		for(char c:A)System.out.print(c+" ");
		System.out.println();
	}
	static void print(boolean A[])
	{
		for(boolean c:A)System.out.print(c+" ");
		System.out.println();
	}
	static void print(int A[])
	{
		for(int a:A)System.out.print(a+" ");
		System.out.println();	
	}
	static void print(long A[])
	{
		for(long i:A)System.out.print(i+ " ");
		System.out.println();

	}
	static void print(boolean A[][])
	{
		for(boolean a[]:A)print(a);
	}
	static void print(long A[][])
	{
		for(long a[]:A)print(a);
	}
	static void print(int A[][])
	{
		for(int a[]:A)print(a);
	}
	static void print(ArrayList<Integer> A)
	{
		for(int a:A)System.out.print(a+" ");
		System.out.println();
	}

	static int i()
	{
		return in.nextInt();
	}

	static long l()
	{
		return in.nextLong();
	}

	static int[] input(int N){
		int A[]=new int[N];
		for(int i=0; i<N; i++)
		{
			A[i]=in.nextInt();
		}
		return A;
	}

	static long[] inputLong(int N)     {
		long A[]=new long[N];
		for(int i=0; i<A.length; i++)A[i]=in.nextLong();
		return A;
	}

	static long GCD(long a,long b) 
	{
		if(b==0)
		{
			return a;
		}
		else return GCD(b,a%b );
	}

}
class Edge
{
	int a,cnt;
	//	boolean said;
	Edge(int a,int cnt)
	{
		this.a=a;
		//		this.said=said;
		this.cnt=cnt;
	}

}


//Code For FastReader
//Code For FastReader
//Code For FastReader
//Code For FastReader
class FastReader
{
	BufferedReader br;
	StringTokenizer st;
	public FastReader()
	{
		br=new BufferedReader(new InputStreamReader(System.in));
	}

	String next()
	{
		while(st==null || !st.hasMoreElements())
		{
			try
			{
				st=new StringTokenizer(br.readLine());
			}
			catch(IOException e)
			{
				e.printStackTrace();
			}
		}
		return st.nextToken();
	}

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

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

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

	String nextLine()
	{
		String str="";
		try
		{
			str=br.readLine();
		}
		catch (IOException e)
		{
			e.printStackTrace();
		}
		return str;
	}

}