Problem:
Score : 100 points

Problem Statement

There is a grid with H horizontal rows and W vertical columns.
Let (i, j) denote the square at the i-th row from the top and the j-th column from the left.

For each i and j (1 \leq i \leq H, 1 \leq j \leq W), Square (i, j) is described by a character a_{i, j}.
If a_{i, j} is ., Square (i, j) is an empty square; if a_{i, j} is #, Square (i, j) is a wall square.
It is guaranteed that Squares (1, 1) and (H, W) are empty squares.

Taro will start from Square (1, 1) and reach (H, W) by repeatedly moving right or down to an adjacent empty square.

Find the number of Taro's paths from Square (1, 1) to (H, W).
As the answer can be extremely large, find the count modulo 10^9 + 7.

Constraints

H and W are integers.

2 \leq H, W \leq 1000

a_{i, j} is . or #.

Squares (1, 1) and (H, W) are empty squares.

Input

Input is given from Standard Input in the following format:

H W
a_{1, 1}\ldotsa_{1, W}
:
a_{H, 1}\ldotsa_{H, W}

Output

Print the number of Taro's paths from Square (1, 1) to (H, W), modulo 10^9 + 7.

Sample Input 1

3 4
...#
.#..
....

Sample Output 1

3

There are three paths as follows:

Sample Input 2

5 2
..
#.
..
.#
..

Sample Output 2

0

There may be no paths.

Sample Input 3

5 5
..#..
.....
#...#
.....
..#..

Sample Output 3

24

Sample Input 4

20 20
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................

Sample Output 4

345263555

Be sure to print the count modulo 10^9 + 7.

Solution in Java (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

import org.ietf.jgss.GSSManager;

import java.awt.GridBagConstraints;
import java.io.*;

   public class Main {
	   static int n;
       static int m;
       static char[][]grid;
       static long[][]memo;
       public static boolean valid(int x,int y) {
		return x<n&&y<m&&grid[x][y]=='.';
	}
       public static long dp(int x,int y) {
    	   if(!valid(x, y)) {
    		   return 0;
    	   }
    	   if(memo[x][y]!=-1) {
    		   return memo[x][y];
    	   }
    	   if(x==n-1&&y==m-1) {
    		   return memo[x][y]=1;
    	   }
    	   return memo[x][y]=(dp(x+1, y)+dp(x, y+1))%mod;
       }
    public static void main(String[] args) throws Exception {
    	n=sc.nextInt();
    	m=sc.nextInt();
    	mod=1000000007;
    	grid=new char[n][];
    	memo=new long[n][m];
    	for(long[]i:memo)Arrays.fill(i, -1);
    	for(int i=0;i<n;i++) {
    		grid[i]=sc.next().toCharArray();
    	}
    	pw.println(dp(0, 0));
       pw.close();
    }
    

//    public static class SegmentTree {		// 1-based DS, OOP
//    	
//    	int N; 			//the number of elements in the array as a power of 2 (i.e. after padding)
//    	long[] array ;
//    	long[] sTree;
//    	long[] lazy;
//    	
//    	SegmentTree(long[] a)		
//    	{
//    		
//    		int nn = a.length;
//    		int NN = 1; while(NN < nn) NN <<= 1; //padding
//    		
//    		long[] in = new long[NN + 1];
//    		for(int i = 1; i <= nn; i++)
//    			in[i] = a[i-1];
//    		
//    		array = in;
//    		N = in.length - 1;
//    		sTree = new long[N<<1];		//no. of nodes = 2*N - 1, we add one to cross out index zero
//    		lazy = new long[N<<1];
//    		build(1,1,N);
//    	}
//    	SegmentTree(int[] a)		
//    	{
//    		
//    		int nn = a.length;
//    		int NN = 1; while(NN < nn) NN <<= 1; //padding
//    		
//    		long[] in = new long[NN + 1];
//    		
//    		for(int i = 1; i <= nn; i++)
//    			in[i] = a[i-1];
//    		
//    		array = in;
//    		N = in.length - 1;
//    		sTree = new long[N<<1];		//no. of nodes = 2*N - 1, we add one to cross out index zero
//    		
//    		lazy = new long[N<<1];
//    		
//    		build(1,1,N);
//    	}
//    	
//    	void build(int node, int b, int e)	// O(n)
//    	{
//    		if(b == e)		{			
//    			sTree[node] = array[b];
//    		 
//    		}
//    		else						
//    		{
//    			int mid = b + e >> 1;
//    			build(node<<1,b,mid);
//    			build(node<<1|1,mid+1,e);
//    			sTree[node] = sTree[node<<1]+sTree[node<<1|1];
//    			
//    		
//    		}
//    	}
//    	
//    	
//    	void update_point(int index, long val)			// O(log n)
//    	{
//    		index += N;				
//    		sTree[index] = val;			
//    		while(index>1)				
//    		{
//    			index >>= 1;
//    			sTree[index] = sTree[index<<1] + sTree[index<<1|1];	
//    				
//    		}
//    	}
//    	
//    	
//    	void update_range(int i, int j, long val)		// O(log n) 
//    	{
//    		update_range(1,1,N,i,j,val);
//    	}
//    	
//    	void update_range(int node, int b, int e, int i, int j, long val)
//    	{
//    		if(i > e || j < b)		
//    			return;
//    		if(b >= i && e <= j)		
//    		{
//    			sTree[node] += (e-b+1)*val;			
//    			lazy[node] += val;				
//    		}							
//    		else		
//    		{
//    			int mid = b + e >> 1;
//    			propagate(node, b, mid, e);
//    			update_range(node<<1,b,mid,i,j,val);
//    			update_range(node<<1|1,mid+1,e,i,j,val);
//    			sTree[node] = sTree[node<<1] + sTree[node<<1|1];		
//    		}
//    		
//    	}
//    	void propagate(int node, int b, int mid, int e)		
//    	{
//    		lazy[node<<1] += lazy[node];
//    		lazy[node<<1|1] += lazy[node];
//    		sTree[node<<1] += (mid-b+1)*lazy[node];		
//    		sTree[node<<1|1] += (e-mid)*lazy[node];		
//    		lazy[node] = 0;
//    	}
//    	
//    	long query(int i, int j)
//    	{
//    		return query(1,1,N,i+1,j+1);
//    	}
//    	
//    	long query(int node, int b, int e, int i, int j)	// O(log n)
//    	{
//    		if(i>e || j <b)
//    			return 0;		
//    		if(b>= i && e <= j)
//    			return sTree[node];
//    		int mid = b + e >> 1;
//    		propagate(node, b, mid, e);
//    		long q1 = query(node<<1,b,mid,i,j);
//    		long q2 = query(node<<1|1,mid+1,e,i,j);
//    		return q1 + q2;	
//    	   
//    				
//    	}
//    	
//    	
//    	
//    	
//    }
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;
 
		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}
 
		public Scanner(FileReader r) {
			br = new BufferedReader(r);
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public double nextDouble() throws IOException {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++)
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}
		public long[] nextlongArray(int n) throws IOException {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
		public Long[] nextLongArray(int n) throws IOException {
            Long[] a = new Long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
		public int[] nextIntArray(int n) throws IOException {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }
		public Integer[] nextIntegerArray(int n) throws IOException {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }
		public boolean ready() throws IOException {
			return br.ready();
		}
 
	}
 
	static class pair implements Comparable<pair> {
		long x;
		long y;
 
		public pair(long x, long y) {
			this.x = x;
			this.y = y;
		}
 
		public String toString() {
			return x + " " + y;
		}
		public boolean equals(Object o) {
            if (o instanceof pair) {
                pair p = (pair)o;
                return p.x == x && p.y == y;
            }
            return false;
        }
        public int hashCode() {
            return new Double(x).hashCode() * 31 + new Double(y).hashCode();
        }
        public int compareTo(pair other) {
        	if(this.x==other.x) {
        		return Long.compare(this.y, other.y);
        	}
			return Long.compare(this.x, other.x);
		}
	}
 
	static class tuble implements Comparable<tuble> {
		int x;
		int y;
		int z;
 
		public tuble(int x, int y, int z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}
 
		public String toString() {
			return x + " " + y + " " + z;
		}
 
		public int compareTo(tuble other) {
			if (this.x == other.x) {
				if(this.y==other.y) {
					return this.z - other.z;
				}
				return this.y - other.y;
			} else {
				return this.x - other.x;
			}
		}
	}
 
	public static long GCD(long a, long b) {
		if (b == 0)
			return a;
		if (a == 0)
			return b;
		return (a > b) ? GCD(a % b, b) : GCD(a, b % a);
	}
 
	public static long LCM(long a, long b) {
		return a * b / GCD(a, b);
	}
 
	static long Pow(long a, long e, long mod) // O(log e)
	{
		a %= mod;
		long res = 1l;
		while (e > 0) {
			if ((e & 1) == 1)
				res = (res * a) % mod;
			a = (a * a) % mod;
			e >>= 1l;
		}
		return res;
	}
   public static long modinverse(long a,long mod) {
	   return Pow(a, mod-2, mod);
   }
	static long nc(int n, int r) {
		if (n < r)
			return 0;
		long v = fac[n];
		v *= Pow(fac[r], mod - 2, mod);
		v %= mod;
		v *= Pow(fac[n - r], mod - 2, mod);
		v %= mod;
		return v;
	}
	static long np(int n,int r) {
		return (nc(n, r)*fac[r])%mod;
	}
	public static boolean isprime(long a) {
		if (a == 0 || a == 1) {
			return false;
		}
		if (a == 2) {
			return true;
		}
		for (int i = 2; i < Math.sqrt(a) + 1; i++) {
			if (a % i == 0) {
				return false;
			}
		}
		return true;
	}
 
	public static boolean isPal(String s) {
		boolean t = true;
		for (int i = 0; i < s.length(); i++) {
			if (s.charAt(i) != s.charAt(s.length() - 1 - i)) {
				t = false;
				break;
			}
		}
		return t;
	}
 
	public static long RandomPick(long[] a) {
		int n = a.length;
		int r = rn.nextInt(n);
		return a[r];
	}
 
	public static int RandomPick(int[] a) {
		int n = a.length;
		int r = rn.nextInt(n);
		return a[r];
	}
 static class hash {
	 int[]HashsArray;
	 boolean reverse;
	 int prelen;
	public  hash(String s, boolean r) {
		prelen = s.length();
		reverse=r;
		HashsArray = new int[prelen + 1];
		if (HashsArrayInd == 0) {
			int[] mods = { 1173017693, 1173038827, 1173069731, 1173086977, 1173089783, 1173092147, 1173107093,
					1173114391, 1173132347, 1173144367, 1173150103, 1173152611, 1173163993, 1173174127, 1173204679,
					1173237343, 1173252107, 1173253331, 1173255653, 1173260183, 1173262943, 1173265439, 1173279091,
					1173285331, 1173286771, 1173288593, 1173298123, 1173302129, 1173308827, 1173310451, 1173312383,
					1173313571, 1173324371, 1173361529, 1173385729, 1173387217, 1173387361, 1173420799, 1173421499,
					1173423077, 1173428083, 1173442159, 1173445549, 1173451681, 1173453299, 1173454729, 1173458401,
					1173459491, 1173464177, 1173468943, 1173470041, 1173477947, 1173500677, 1173507869, 1173522919,
					1173537359, 1173605003, 1173610253, 1173632671, 1173653623, 1173665447, 1173675577, 1173675787,
					1173684683, 1173691109, 1173696907, 1173705257, 1173705523, 1173725389, 1173727601, 1173741953,
					1173747577, 1173751499, 1173759449, 1173760943, 1173761429, 1173762509, 1173769939, 1173771233,
					1173778937, 1173784637, 1173793289, 1173799607, 1173802823, 1173808003, 1173810919, 1173818311,
					1173819293, 1173828167, 1173846677, 1173848941, 1173853249, 1173858341, 1173891613, 1173894053,
					1173908039, 1173909203, 1173961541, 1173968989, 1173999193};
			mod = RandomPick(mods);
			int[] primes = { 59, 61, 67, 71, 73, 79, 83, 89, 97, 101 };
			prime = RandomPick(primes);
			prepow = new int[1000010];
			prepow[0] = 1;
			for (int i = 1; i < 1000010; i++) {
				prepow[i] = (int) ((1l * prepow[i - 1] * prime) % mod);
				
			}
		}
		if (!reverse) {
 
			for (int i = 0; i < prelen; i++) {
				if (s.charAt(i) >= 'a' && s.charAt(i) <= 'z')
					HashsArray[i + 1] = (int) ((1l * HashsArray[i]
							+ ((1l * s.charAt(i) - 'a' + 1) *prepow[i]) % mod) % mod);
				else
					HashsArray[i + 1] = (int) ((1l * HashsArray[i]
							+ ((1l * s.charAt(i) - 'A' + 27) * prepow[i]) % mod) % mod);
			}
 
		} else {
			
			for (int i = 0; i < prelen; i++) {
				if (s.charAt(i) >= 'a' && s.charAt(i) <= 'z')
					HashsArray[i + 1] = (int) ((1l * HashsArray[i]
							+ ((1l * s.charAt(i) - 'a' + 1) * prepow[1000010 - 1 - i]) % mod) % mod);
				else
					HashsArray[i + 1] = (int) ((1l * HashsArray[i]
							+ ((1l * s.charAt(i) - 'A' + 27) * prepow[1000010 - 1 - i]) % mod) % mod);
			}
 
		}
 
		HashsArrayInd++;
 
	}
 
	public int PHV(int l, int r) {
		if (l > r) {
			return 0;
		}
		int val = (int) ((1l * HashsArray[r] + mod - HashsArray[l - 1]) % mod);
		if (!reverse) {
 
//			val = (int) ((1l * val *  modinverse(prepow[l-1], mod)) % mod);
			val = (int) ((1l * val * prepow[1000010 - l]) % mod);
		} else {
//			val = (int) ((1l * val * modinverse(prepow[prelen-r], mod)) % mod);
			
			val = (int) ((1l * val * prepow[r - 1]) % mod);
		}
		return val;
	}
 }
    public static void genprime(int n) {
    	 boolean prime[] = new boolean[n+1]; 
         for(int i=0;i<n;i++) 
             prime[i] = true; 
           
         for(int p = 2; p*p <=n; p++) 
         { 
             if(prime[p] == true) 
             { 
                 for(int i = p*p; i <= n; i += p) 
                     prime[i] = false; 
             } 
         } 
         for(int i = 2; i <= n; i++) 
         { 
             if(prime[i] == true) {
                primes.put(i,primes.size());
                primes2.put(primes2.size(),i);
             }
             
         }
    }
   
   
    public static long LSB(long x) {
		return x&-x;
	}
	static class fenwick {
		long[] arr;
		public fenwick(PriorityQueue<Integer> a) {
			PriorityQueue<Integer>q=new PriorityQueue<Integer>(a);
			arr=new long[a.size()+1];
			int i=1;
			while(!q.isEmpty()) {
				int z=q.poll();
				arr[i]+=z;
				if(i+LSB(i)<=a.size()) {
					arr[(int) (i+LSB(i))]+=arr[i];
				}
				i++;
			}
		}
		public fenwick(TreeSet<Integer> a) {
			arr=new long[a.size()+1];
			int i=1;
			for(int h:a) {
				arr[i]+=h;
				if(i+LSB(i)<=a.size()) {
					arr[(int) (i+LSB(i))]+=arr[i];
				}
				i++;
			}
		}
		public fenwick(Integer a) {
			arr=new long[a];
			
		}
		public fenwick(Integer[] a) {
			arr=new long[a.length+1];
			for(int i=1;i<=a.length;i++) {
				arr[i]+=a[i-1];
				if(i+LSB(i)<=a.length) {
					arr[(int) (i+LSB(i))]+=arr[i];
				}
			}
		}
		public fenwick(int[] a) {
			arr=new long[a.length+1];
			for(int i=1;i<=a.length;i++) {
				arr[i]+=a[i-1];
				if(i+LSB(i)<=a.length) {
					arr[(int) (i+LSB(i))]+=arr[i];
				}
			}
		}public fenwick(long[] a) {
			arr=new long[a.length+1];
			for(int i=1;i<=a.length;i++) {
				arr[i]+=a[i];
				if(i+LSB(i)<=a.length) {
					arr[(int) (i+LSB(i))]+=arr[i];
				}
			}
		}
		public void update(int ind,long x) {
			int i=ind;
			while(i<arr.length) {
				arr[i]+=x;
				i+=LSB(i);
			}
		}
		public long PrefixSum(int ind) {
			long sum=0;
			int i=ind;
			while(i>0) {
				sum+=arr[i];
				i=(int) (i-LSB(i));
			}
			return sum;
		}
		public long RangeQuerey(int l,int r) {
			return  this.PrefixSum(r+1)-this.PrefixSum(l);
		}
		public long maxConsecutiveValue(int k) {
			long max=Long.MIN_VALUE;
			for(int i=k-1;i<arr.length-1;i++) {
				
				max= Math.max(max,  this.RangeQuerey(i-k+1, i));
				
			}
			return max;
		}
		public long minConsecutiveValue(int k) {
			long min=Long.MAX_VALUE;
			
			for(int i=k-1;i<arr.length-1;i++) {
				
				min= Math.min(min,  this.RangeQuerey(i-k+1, i));
				
			}
			return min;
		}
		public long value(int ind) {
			return arr[ind];
		}
	}
	static void sieveLinear(int N)
	{
		ArrayList<Integer> primes = new ArrayList<Integer>();
		lp = new int[N + 1];								//lp[i] = least prime divisor of i
		for(int i = 2; i <= N; ++i)
		{
			if(lp[i] == 0)
			{
				primes.add(i);
				lp[i] = i;
			}
			int curLP = lp[i];
			for(int p: primes)//all primes smaller than or equal my lowest prime divisor
				if(p > curLP || p * 1l * i > N)
					break;
				else
					lp[p * i] = p;
		}
	}
	public static void primefactorization(int n) {
		int x=n;
	while(x>1) {
		int lowestDivisor=lp[x];
		while(x%lowestDivisor==0) {
			primefactors.add(lowestDivisor);
			x/=lowestDivisor;
		}
	}
	}
	public static class SuffixArray {

		int[] SA;
		int[] AS;
		String SS;
		public SuffixArray(String S)					//has a terminating character (e.g. '$')
		{
			SS=S;
			char[] s=new char[S.length()+1];
			for(int i=0;i<S.length();i++) {
				s[i]=S.charAt(i);
			}
			s[S.length()]='$';
			int n = s.length, RA[] = new int[n];
			SA = new int[n];
			
			for(int i = 0; i < n; ++i) { RA[i] = s[i]; SA[i] = i; }
			
			for(int k = 1; k < n; k <<= 1)
			{
				sort(SA, RA, n, k);
				sort(SA, RA, n, 0);
				int[] tmp = new int[n];

				for(int i = 1, r = 0, s1 = SA[0], s2; i < n; ++i)
				{
					s2 = SA[i];
					tmp[s2] = RA[s1] == RA[s2] && RA[s1 + k] == RA[s2 + k] ? r : ++r;
					s1 = s2;
				}
				for(int i = 0; i < n; ++i)
					RA[i] = tmp[i];
				
				if(RA[SA[n-1]] == n - 1)
					break;
			}
			AS=new int[SA.length];
			for(int i=0;i<SA.length;i++) {
				AS[SA[i]]=i;
			}
		}
		public String toString() {
			
			return Arrays.toString(SA);
		}
		public int get(int n) {
			return SA[n];
		}
		public int Substring(String s) {  // log(n)*|s|
			int low=0;
			int high=SA.length;
			int mid=(low+high)/2;
			int ind=-1;
			
			while(low<high-1) {
				
				if(SS.length()-SA[mid]<s.length()) {
				
					boolean less=false;
					for(int i=SA[mid];i<SS.length();i++) {
						if(SS.charAt(i)>s.charAt(i-SA[mid])) {
							less=true;
							break;
						}
						if(SS.charAt(i)<s.charAt(i-SA[mid])) {
							less=false;
							break;
						}
					}
					if(!less) {
						low=mid;
					}else {
						high=mid;
					}
				}else {
					boolean less=true;
					boolean equal=true;
					for(int i=SA[mid];i<SA[mid]+s.length();i++) {
						if(SS.charAt(i)<s.charAt(i-SA[mid])&&equal) {
							less=false;
							equal=false;
							break;
						}
						if(SS.charAt(i)!=s.charAt(i-SA[mid])){
							equal=false;
						}
					}
					if(equal) {
						ind=SA[mid];
					}
					if(!less) {
						low=mid;
					}else {
						high=mid;
					}
				}
				
				
				mid=(low+high)/2;
			}
			return ind;
		}
		public int LastSubstring(String s) {  // log(n)*|s|
			int low=0;
			int high=SA.length;
			int mid=(low+high)/2;
			int ind=-1;
			
			while(low<high-1) {
				
				if(SS.length()-SA[mid]<s.length()) {
				
					boolean less=true;
					for(int i=SA[mid];i<SS.length();i++) {
						if(SS.charAt(i)<s.charAt(i-SA[mid])) {
							break;
						}
						if(SS.charAt(i)>s.charAt(i-SA[mid])) {
							less=false;
							break;
						}
					}
					if(less) {
						low=mid;
					}else {
						high=mid;
					}
				}else {
					boolean less=true;
					boolean equal=true;
					for(int i=SA[mid];i<SA[mid]+s.length();i++) {
						if(SS.charAt(i)>s.charAt(i-SA[mid])&&equal) {
							less=false;
							equal=false;
							break;
						}
						if(SS.charAt(i)!=s.charAt(i-SA[mid])){
							equal=false;
						}
					}
					if(equal) {
						ind=SA[mid];
					}
					if(less) {
						low=mid;
					}else {
						high=mid;
					}
				}
				
				
				mid=(low+high)/2;
			}
			return ind;
		}
		public int CountSubstring(String s) {
			int z=LastSubstring(s);
			if(z==-1)
				return 0;
			return AS[z]-AS[Substring(s)]+1;
		}
		public void sort(int[] SA, int[] RA, int n, int k)
		{
			int maxi = Math.max(256, n), c[] = new int[maxi];  
			for(int i = 0; i < n; ++i)
				c[i + k < n ? RA[i + k] : 0]++;
			for(int i = 0, sum = 0; i < maxi; ++i)
			{
				int t = c[i];
				c[i] = sum;
				sum += t;
			}
			int[] tmp = new int[n];
			for(int i = 0; i < n; ++i)
			{
				int j = SA[i] + k;
				tmp[c[j < n ? RA[j] : 0]++] = SA[i];
			}
			
			for(int i = 0; i < n; ++i)
				SA[i] = tmp[i];
		}
	}
	  public static class UnionFind {                                              
	    	int[] p, rank, setSize;
	    	int numSets;

	    	public UnionFind(int N) 
	    	{
	    		p = new int[numSets = N];
	    		rank = new int[N];
	    		setSize = new int[N];
	    		for (int i = 0; i < N; i++) {  p[i] = i; setSize[i] = 1; }
	    	}

	    	public int findSet(int i) { return p[i] == i ? i : (p[i] = findSet(p[i])); }

	    	public boolean isSameSet(int i, int j) { return findSet(i) == findSet(j); }

	    	public void unionSet(int i, int j) 
	    	{ 
	    		if (isSameSet(i, j)) 
	    			return;
	    		numSets--; 
	    		int x = findSet(i), y = findSet(j);
	    		if(rank[x] > rank[y]) { p[y] = x; setSize[x] += setSize[y]; }
	    		else
	    		{	p[x] = y; setSize[y] += setSize[x];
	    			if(rank[x] == rank[y]) rank[y]++; 
	    		} 
	    	}

	    	public int numDisjointSets() { return numSets; }

	    	public int sizeOfSet(int i) { return setSize[findSet(i)]; }
	    }
	static LinkedList<Integer>primefactors=new LinkedList<>();
	static TreeMap<Integer,Integer>primes=new TreeMap<Integer, Integer>();
	static TreeMap<Integer,Integer>primes2=new TreeMap<Integer, Integer>();
	static int[]lp;
    
	
	static int HashsArrayInd = 0;
	static int[] prepow;
	static int prime = 61;
	static long fac[];
	static int mod = 1000000007;
	static Random rn = new Random();
	static Scanner sc = new Scanner(System.in);
	static PrintWriter pw = new PrintWriter(System.out);
}