Alexander is learning how to convert numbers from the decimal system to any other, however, he doesn't know English letters, so he writes any number only as a decimal number, it means that instead of the letter A he will write the number 10. Thus, by converting the number 475 from decimal to hexadecimal system, he gets 11311 (475 = 1·162 + 13·161 + 11·160). Alexander lived calmly until he tried to convert the number back to the decimal number system.

Alexander remembers that he worked with little numbers so he asks to find the minimum decimal number so that by converting it to the system with the base n he will get the number k.

Input

The first line contains the integer n (2 ≤ n ≤ 109). The second line contains the integer k (0 ≤ k < 1060), it is guaranteed that the number k contains no more than 60 symbols. All digits in the second line are strictly less than n.

Alexander guarantees that the answer exists and does not exceed 1018.

The number k doesn't contain leading zeros.

Output

Print the number x (0 ≤ x ≤ 1018) — the answer to the problem.

Examples

Input

13
12


Output

12

Input

16
11311


Output

475

Input

20
999


Output

3789

Input

17
2016


Output

594

Note

In the first example 12 could be obtained by converting two numbers to the system with base 13: 12 = 12·130 or 15 = 1·131 + 2·130.
/*
		     * Author- Kishan_25
		     * BTech 2nd Year DAIICT
		     */
		     
		            
		    import java.io.*;
		    import java.math.*;
		    import java.util.*;
		    import javax.print.attribute.SetOfIntegerSyntax;
		     
		    public class TR {
		    	private static InputStream stream;
		    	private static byte[] buf = new byte[1024];
		    	private static int curChar;
		    	private static int numChars;
		    	private static SpaceCharFilter filter;
		    	private static PrintWriter pw;
		    	private static long count = 0,mod=1000000007;
		    	private static TreeSet<Integer>ts[]=new TreeSet[200000];
		    	private static HashSet hs=new HashSet();
		     
		    	public static void main(String args[]) throws Exception {
		    		InputReader(System.in);
		    		pw = new PrintWriter(System.out);
		    		//ans();
		    		soln();
		    		//temp();
		    		pw.close();
		    	}
		    	
		    	public static void temp(){
		    		Scanner in = new Scanner(System.in);
		    		
		    		String s = in.nextLine();
		    		int ind = 0;
		    		char a = s.charAt(0);
		    		for(int i = 1;i<s.length();i++){
		    			if(s.charAt(i) > a){
		    				a = s.charAt(i);
		    				ind = i;
		    			}
		    		}
		    		
		    		String t = s.substring(ind);
		    		String te = s.substring(0,ind);
		    		
		    		s = t+te;
		    		System.out.println(s);
		    	}
		     
		    	public static long gcd(long x, long y) {
		    		if (x == 0)
		    			return y;
		    		else
		    			return gcd( y % x,x);
		    	}
		    	
		    	private static int BinarySearch(int a[], int low, int high, int target) {
		    		if (low > high)
		    			return -1;
		    		int mid = low + (high - low) / 2;
		    		if (a[mid] == target)
		    			return mid;
		    		if (a[mid] > target)
		    			high = mid - 1;
		    		if (a[mid] < target)
		    			low = mid + 1;
		    		return BinarySearch(a, low, high, target);
		    	}
		    	
		    	public static String reverseString(String s) {
		    		StringBuilder sb = new StringBuilder(s);
		    		sb.reverse();
		    		return (sb.toString());
		    	}
		    	
		    	public static long pow(long n, long p) {
		    		if(p==0)
		    			return 1;
		    		if(p==1)
		    			return n%mod;
		    		if(p%2==0){
		    			long temp=pow(n, p/2);
		    		return (temp*temp)%mod;
		    		}else{
		    			 	long temp=pow(n,p/2);
		    			 	temp=(temp*temp)%mod;
		    			 	return(temp*n)%mod;
		    			 	
		    		}
		    	}
		     
		    		
		     
		    	public static int[] radixSort(int[] f) {
		    		int[] to = new int[f.length];
		    		{
		    			int[] b = new int[65537];
		    			for (int i = 0; i < f.length; i++)
		    				b[1 + (f[i] & 0xffff)]++;
		    			for (int i = 1; i <= 65536; i++)
		    				b[i] += b[i - 1];
		    			for (int i = 0; i < f.length; i++)
		    				to[b[f[i] & 0xffff]++] = f[i];
		    			int[] d = f;
		    			f = to;
		    			to = d;
		    		}
		    		{
		    			int[] b = new int[65537];
		    			for (int i = 0; i < f.length; i++)
		    				b[1 + (f[i] >>> 16)]++;
		    			for (int i = 1; i <= 65536; i++)
		    				b[i] += b[i - 1];
		    			for (int i = 0; i < f.length; i++)
		    				to[b[f[i] >>> 16]++] = f[i];
		    			int[] d = f;
		    			f = to;
		    			to = d;
		    		}
		    		return f;
		    	}
		     
		    	public static int nextPowerOf2(final int a) {
		    		int b = 1;
		    		while (b < a) {
		    			b = b << 1;
		    		}
		    		return b;
		    	}
		     
		    	public static boolean PointInTriangle(int p1, int p2, int p3, int p4, int p5, int p6, int p7, int p8) {
		    		int s = p2 * p5 - p1 * p6 + (p6 - p2) * p7 + (p1 - p5) * p8;
		    		int t = p1 * p4 - p2 * p3 + (p2 - p4) * p7 + (p3 - p1) * p8;
		     
		    		if ((s < 0) != (t < 0))
		    			return false;
		     
		    		int A = -p4 * p5 + p2 * (p5 - p3) + p1 * (p4 - p6) + p3 * p6;
		    		if (A < 0.0) {
		    			s = -s;
		    			t = -t;
		    			A = -A;
		    		}
		    		return s > 0 && t > 0 && (s + t) <= A;
		    	}
		     
		    	public static float area(int x1, int y1, int x2, int y2, int x3, int y3) {
		    		return (float) Math.abs((x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)) / 2.0);
		    	}
		     
		    	public static boolean isPrime(int n) {
		    		// Corner cases
		    		if (n <= 1)
		    			return false;
		    		if (n <= 3)
		    			return true;
		     
		    		// This is checked so that we can skip 
		    		// middle five numbers in below loop
		    		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;
		    	}
		     
		    	//merge Sort
		     
		    	static long sort1(int a[])
		    	{  int n=a.length;
		    		int b[]=new int[n];	
		    		return mergeSort(a,b,0,n-1);}
		    	static long mergeSort(int a[],int b[],long left,long right)
		    	{ long c=0;if(left<right)
		    	 {   long mid=left+(right-left)/2;
		    		 c= mergeSort(a,b,left,mid);
		    		 c+=mergeSort(a,b,mid+1,right);
		    		 c+=merge(a,b,left,mid+1,right); }	
		    		return c;	 }
		    	static long merge(int a[],int  b[],long left,long mid,long right)
		    	{long c=0;int i=(int)left;int j=(int)mid; int k=(int)left;
		    	while(i<=(int)mid-1&&j<=(int)right)
		    	{ if(a[i]>a[j]) {b[k++]=a[i++]; }
		    	else	{ b[k++]=a[j++];c+=mid-i;}}
		    	while (i <= (int)mid - 1)   b[k++] = a[i++]; 
		    	while (j <= (int)right) b[k++] = a[j++];
		    	for (i=(int)left; i <= (int)right; i++) 
		    		a[i] = b[i];  return c;  }
		    	public static boolean isSubSequence(String large, String small, int largeLen, int smallLen) {
		    		//base cases
		    		if (largeLen == 0)
		    			return false;
		    		if (smallLen == 0)
		    			return true;
		    		// If last characters of two strings are matching
		    		if (large.charAt(largeLen - 1) == small.charAt(smallLen - 1))
		    			isSubSequence(large, small, largeLen - 1, smallLen - 1);
		    		// If last characters are not matching
		    		return isSubSequence(large, small, largeLen - 1, smallLen);
		    	}
		     
		    	// To Get Input
		    	// Some Buffer Methods
		     
		    	public static void InputReader(InputStream stream1) {
		    		stream = stream1;
		    	}
		     
		    	private static boolean isWhitespace(int c) {
		    		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		    	}
		     
		    	private static boolean isEndOfLine(int c) {
		    		return c == '\n' || c == '\r' || c == -1;
		    	}
		     
		    	private static int read() {
		    		if (numChars == -1)
		    			throw new InputMismatchException();
		    		if (curChar >= numChars) {
		    			curChar = 0;
		    			try {
		    				numChars = stream.read(buf);
		    			} catch (IOException e) {
		    				throw new InputMismatchException();
		    			}
		    			if (numChars <= 0)
		    				return -1;
		    		}
		    		return buf[curChar++];
		    	}
		     
		    	private static int nextInt() {
		    		int c = read();
		    		while (isSpaceChar(c))
		    			c = read();
		    		int sgn = 1;
		    		if (c == '-') {
		    			sgn = -1;
		    			c = read();
		    		}
		    		int res = 0;
		    		do {
		    			if (c < '0' || c > '9')
		    				throw new InputMismatchException();
		    			res *= 10;
		    			res += c - '0';
		    			c = read();
		    		} while (!isSpaceChar(c));
		    		return res * sgn;
		    	}
		     
		    	private static long nextLong() {
		    		int c = read();
		    		while (isSpaceChar(c))
		    			c = read();
		    		int sgn = 1;
		    		if (c == '-') {
		    			sgn = -1;
		    			c = read();
		    		}
		    		long res = 0;
		    		do {
		    			if (c < '0' || c > '9')
		    				throw new InputMismatchException();
		    			res *= 10;
		    			res += c - '0';
		    			c = read();
		    		} while (!isSpaceChar(c));
		    		return res * sgn;
		    	}
		     
		    	private static String nextToken() {
		    		int c = read();
		    		while (isSpaceChar(c))
		    			c = read();
		    		StringBuilder res = new StringBuilder();
		    		do {
		    			res.appendCodePoint(c);
		    			c = read();
		    		} while (!isSpaceChar(c));
		    		return res.toString();
		    	}
		     
		    	private static String nextLine() {
		    		int c = read();
		    		while (isSpaceChar(c))
		    			c = read();
		    		StringBuilder res = new StringBuilder();
		    		do {
		    			res.appendCodePoint(c);
		    			c = read();
		    		} while (!isEndOfLine(c));
		    		return res.toString();
		    	}
		     
		    	private static int[] nextIntArray(int n) {
		    		int[] arr = new int[n];
		    		for (int i = 0; i < n; i++) {
		    			arr[i] = nextInt();
		    		}
		    		return arr;
		    	}
		     
		    	private static int[][] next2dArray(int n, int m) {
		    		int[][] arr = new int[n][m];
		    		for (int i = 0; i < n; i++) {
		    			for (int j = 0; j < m; j++) {
		    				arr[i][j] = nextInt();
		    			}
		    		}
		    		return arr;
		    	}
		    	private static char[][] nextCharArray(int n,int m){
		    		char [][]c=new char[n][m];
		    		for(int i=0;i<n;i++){
		    			String s=nextLine();
		    			for(int j=0;j<s.length();j++){
		    				c[i][j]=s.charAt(j);
		    			}
		    		}
		    		return c;
		    	}
		     
		    	private static long[] nextLongArray(int n) {
		    		long[] arr = new long[n];
		    		for (int i = 0; i < n; i++) {
		    			arr[i] = nextLong();
		    		}
		    		return arr;
		    	}
		     
		    	private static void pArray(int[] arr) {
		    		for (int i = 0; i < arr.length; i++) {
		    			pw.print(arr[i] + " ");
		    		}
		    		pw.println();
		    		return;
		    	}
		     
		    	private static void pArray(long[] arr) {
		    		for (int i = 0; i < arr.length; i++) {
		    			pw.print(arr[i] + " ");
		    		}
		    		pw.println();
		    		return;
		    	}
		     
		    	private static void pArray(boolean[] arr) {
		    		for (int i = 0; i < arr.length; i++) {
		    			pw.print(arr[i] + " ");
		    		}
		    		pw.println();
		    		return;
		    	}
		     
		    	private static boolean isSpaceChar(int c) {
		    		if (filter != null)
		    			return filter.isSpaceChar(c);
		    		return isWhitespace(c);
		    	}
		     
		    	private interface SpaceCharFilter {
		    		public boolean isSpaceChar(int ch);
		    	}
		     
		    	   
			    public static int find(int parent[], int i)
			    {
			        if (parent[i] == -1)
			            return i;
			        return find(parent, parent[i]);
			    }
			     
			    // A utility function to do union of two subsets 
			    public static void Union(int parent[], int x, int y)
			    {
			        int xset = find(parent, x);
			        int yset = find(parent, y);
			        parent[xset] = yset;
			    }
		    	//----------------------------------------My Code------------------------------------------------//
		
	 
		    	private static void soln() {
		    	
		    	  	Scanner in = new Scanner(System.in);
			    	
		    		int n = in.nextInt();
		    		in.nextLine();
		    		char[] cc = in.nextLine().toCharArray();
		    		int k = cc.length;
		    		long inf = (long) 1e18;
		    		long[][] dp = new long[k + 1][k + 1];
		    		for (int i = 0; i <= k; i++)
		    			for (int j = 0; j <= k; j++)
		    				dp[i][j] = inf;
		    		dp[0][0] = 0;
		    		for (int i = 0; i < k; i++)
		    			for (int j = 0; j < k; j++)
		    				if (dp[i][j] < inf) {
		    					long x = dp[i][j];
		    					if (cc[i] == '0') {
		    						if ((double) x * n <= inf)
		    							dp[i + 1][j + 1] = Math.min(dp[i + 1][j + 1], x * n);
		    					} else {
		    						long y = 0;
		    						for (int l = i; l < k; l++) {
		    							y = y * 10 + (cc[l] - '0');
		    							if (y >= n)
		    								break;
		    							if ((double) x * n + y <= inf)
		    								dp[l + 1][j + 1] = Math.min(dp[l + 1][j + 1], x * n + y);
		    						}
		    					}
		    				}
		    		
		    		long min = inf;
		    		
//		    		for(int i = 0;i<=k;i++){
//		    			for(int j = 0;j<=k;j++){
//		    				System.out.print(dp[i][j] + " ");
//		    			}
//		    			System.out.println();
//		    		}
		    		for (int j = 0; j <= k; j++)
		    			min = Math.min(min, dp[k][j]);
		    		System.out.println(min);
		    	}//-----------------------------------------The End--------------------------------------------------------------------------//
		    public static int call(int n,int m){
		    	
		    	if(n == 2 && m == 1){
		    		return 1;
		    	}else if(n == 1 && m == 2){
		    		return 1;
		    	}else if(n <=1 || m <=1){
		    		return 0;
		    	}
		    	
		    	
		    	if(n >= m){
		    		return 1 + call(n-2,m-1);
		    	}else{
		    		return 1+ call(n-1,m-2);
		    	}
		    }
		    	
		    	public static boolean compq(Queue<Integer> q1,Queue<Integer> q2){
		    		
		    		
		    		
		    		if(q1.size() != q2.size())
		    			return false;
		    		
		    		Queue<Integer> c1 = new LinkedList<Integer>();
		    		Queue<Integer> c2 = new LinkedList<Integer>();
		    		
		    		for(int i = 0;i<q1.size();i++){
		    			int a =q1.remove();
		    			c1.add(a);
		    			q1.add(a);
		    			int b = q2.remove();
		    			c2.add(b);
		    			q2.add(b);
		    		//	System.out.println(a + " " + b + " " );
		    		}
		    		
		    		int n =q1.size();
		    		
		    		for(int i = 0;i<n;i++){
		    			if(q1.peek() != q2.peek()){
		    				q1 =c1;
		    				q2 =c2;
		    				return false;
		    			}else{
		    				q1.remove();
		    				q2.remove();
		    			}
		    		}
		    		
		    		q1 =c1;
		    		q2 =c2;
		    		return true;
		    	} 
		    	
		    	public static BigInteger min(BigInteger a,BigInteger b){
		    		if(a.compareTo(b) == -1){
		    			return a;
		    		}else{
		    			return b;
		    		}
		    	}
		    	
		    	public static BigInteger max(BigInteger a,BigInteger b){
		    		if(a.compareTo(b) == -1){
		    			return b;
		    		}else{
		    			return a;
		    		}
		    	}
		    	 public static int toDecimal(String str) {
		    		    int decimal = 0;
		    		    int base0 = (int)'0';
		    		    char ch;
		    		    for (int i = 0; i < str.length(); i++) {
		    		      ch = str.charAt(i);
		    		      if (charIsNotBinary(ch)) {
		    		        return 0;
		    		      }
		    		      decimal = decimal * 2 + ((int)str.charAt(i) - base0);
		    		    }
		    		    return decimal;
		    		  }
		    	 
		    	 private static boolean charIsNotBinary(char ch) {
		    		    return '1' < ch || ch < '0';
		    		  }
		 }
		    class node{
		    	int s;
		    	int v;
		    }
		   
		    
			class Pair implements Comparable<Pair>{
			    long id; 
				long w;
				long h;
				Pair(long id,long w,long h){
					this.id=id;
					this.w=w;
					this.h=h;
				}
				@Override
				public int compareTo(Pair o) {
					// TODO Auto-generated method stub
				//	Sort in increasing order
	 
					if(w>o.w)
						return 1;
					else if(w<o.w)
						return -1;
					else{
						if(h>o.h){
							return 1;
						}else if(o.h>h)
							return -1;
						else return 0;
					}
					
				}
			
			}
		        class Graph{
		        	private static int V,level[][],count=-1,lev_dfs[],degree=0,no_vert_conn_comp=0;
		        	private Stack <Integer>st=new Stack();
		        	private static LinkedList<Integer > adj[];
		        	private boolean[][] Visite;
		        	private static boolean [] Visited;
		        	private static TreeSet<Integer> ts=new TreeSet();
		    Graph(int V){
		    V++;
		    this.V=(V);
		    adj=new LinkedList[V];
		    Visite=new boolean[100][100];
	 
	 	   Visited=new boolean[V];
		    level=new int[100][100];
		   lev_dfs=new int[V]; 
		   for(int i=0;i<V;i++)
			   adj[i]=new LinkedList<Integer>();
		    }
		     
		    void addEdge(int v,int w){
		    	
		    	if(adj[v]==null){
		    		adj[v]=new LinkedList();
		    	}
		    	if(adj[w] == null){
		    		adj[w] = new LinkedList();
		    	}
		    	adj[v].add(w);
		    
		    	
		    }
		    
		    
		    public static int conCop(int startVert){
		    	Visited=new boolean[V];
		    	int totalcon = 1;
		    	Queue<Integer> q=new LinkedList<Integer>();
		    	q.add(startVert);
		    	Visited[startVert] = true;
		    	
		    	while(!q.isEmpty()){
		    		int top=q.poll();
		    		
		    		Iterator<Integer> i= adj[top].listIterator();
		    		while(i.hasNext()){
		    			int n=i.next();
		    			if(!Visited[n]){
		    				q.add(n);
		    				Visited[n]=true;
		    				totalcon++;	    			
		    			}
		    		}
		    	}
		    	q.clear();
		    	return totalcon;
		    }
		    
		    
		    public static int NoConEdge(int startVert){
		    	Visited=new boolean[V];
		    
		    	Queue<Integer> q=new LinkedList<Integer>();
		    	q.add(startVert);
		    	Visited[startVert] = true;
		    	long ed = adj[startVert].size();
		    	while(!q.isEmpty()){
		    		int top=q.poll();
		    		
		    		Iterator<Integer> i= adj[top].listIterator();
		    		while(i.hasNext()){
		    			int n=i.next();
		    			if(!Visited[n]){
		    				q.add(n);
		    				Visited[n]=true;
		    				ed+= adj[n].size();
		    			}
		    		}
		    	}
		    	q.clear();
		    	return (int)ed/2;
		    }
		 
		    public static int BFS2(int startVert){
		    	Visited=new boolean[V];
		    	for(int i=0;i<V;i++){
		    		lev_dfs[i]=-1;
		    	}
		    	Queue<Integer> q=new LinkedList<Integer>();
		    	q.add(startVert);
		    	
		    	lev_dfs[startVert]=0;
		    	while(!q.isEmpty()){
		    		int top=q.poll();
		    		
		    		Iterator<Integer> i= adj[top].listIterator();
		    		while(i.hasNext()){
		    			int n=i.next();
		    			if(!Visited[n]){
		    				q.add(n);
		    				Visited[n]=true;
		    				lev_dfs[n]=lev_dfs[top]+1;
		    				//System.out.println(top + " " + n);
		    			}
		    		}
		    	}
		    	q.clear();
		    	
		    	int mx = 0;
		    	for(int i = 0;i<V;i++){
		    		mx = Math.max(mx, lev_dfs[i]);
		    	}
		    	return mx;
		    }
		    public int getEd(){
		    	return degree/2;
		    }
		    public void get(int from,int to){
		    	int h=lev_dfs[from]-lev_dfs[to];
		    	if(h<=0){
		    		System.out.println(-1);
		    	}else{
		    		System.out.println(h-1);
		    	}
		    }
		    private static boolean check(int x,int y,char c[][]){
			
				if((x>=0 && y>=0) && (x<c.length && y<c[0].length) && c[x][y]!='#'){
					
					return true;
				}
				return false;
			}
		    public int BFS(int x,int y,int k,char[][] c)
		    {
		    	 LinkedList<Pair> queue = new LinkedList<Pair>();
		        //Visited[s]=true;
		   //     queue.add(new Pair(x,y));
		       int count=0;
		   level[x][y]=-1;
		   c[x][y]='M';
		        while (!queue.isEmpty())
		        {
		            Pair temp = queue.poll();
		            //x=temp.idx;
		            //y=temp.val;
		            
		            c[x][y]='M';
		      // System.out.println(x+" "+y+" ---"+count);
		         count++;
		     	if(count==k)
		         {
		         	for(int i=0;i<c.length;i++){
		         		for(int j=0;j<c[0].length;j++){
		         			if(c[i][j]=='M'){
		         				System.out.print(".");
		         			}
		         			else if(c[i][j]=='.')
		         				System.out.print("X");
		         			else
		         				System.out.print(c[i][j]);
		         		}
		         		System.out.println();
		         	}
		         System.exit(0);
		         }
		     	
		         // System.out.println(x+" "+y);
		           // V--;
		           
		        }
		        return V;
		    }
		    
		    private void getAns(int startVertex){
		    	for(int i=0;i<adj[startVertex].size();i++){
		    		int ch=adj[startVertex].get(i);
		    		for(int j=0;j<adj[ch].size();j++){
		    			int ch2=adj[ch].get(j);
		    			if(adj[ch2].contains(startVertex)){
		    				System.out.println(startVertex+" "+ch+" "+ch2);
		    				System.exit(0);
		    			}
		    		}
		    	}
		    }
		    
		     public long dfs(int startVertex){
		    //	 getAns(startVertex);
		    	 
		    	 if(!Visited[startVertex])  {
		    
		   return dfsUtil(startVertex,Visited);
		    	//return getAns();
		    	}
		    	 
		    
		     
		    return 0;
		    	}
		 private long dfsUtil(int startVertex, boolean[] Visited) {//0-Blue 1-Pink
		 
			 int c=1;
			 long cout=0;
		      degree=0;
		    	Visited[startVertex]=true;
		    	lev_dfs[startVertex]=1;
		      st.push(startVertex);
		    while(!st.isEmpty()){
		    	
		    	int top=st.pop();
		    int child=adj[top].size();
		    if(top!=startVertex)
		    	child--;
		    
		    	ts.add(top);
		    	Iterator<Integer> i=adj[top].listIterator();
		     degree+=adj[top].size();
		     
		    while(i.hasNext()){
		    
		    	int n=i.next();
		     if( !Visited[n]){
		    				Visited[n]=true;
		    					st.push(n);
		    					if(adj[n].size()-1>child)
		    					cout++;	
		    				c++;
		    					lev_dfs[n]=lev_dfs[top]+1;
		    			
		    		 }
		         }
		 }
		    return cout;
		    	
		    		
		    
		  //  System.out.println("NO");
		   // return c;
		    	
		    
		    
		    
		    }
		        
		        }     
		        	
		        
		    class Dsu{
		    	private int rank[], parent[] ,n;
		    	
		    	Dsu(int size){
		    		this.n=size+1;
		    		rank=new int[n];
		    		parent=new int[n];
		    	makeSet();
		    	}
		    	
		    	void makeSet(){
		    		for(int i=0;i<n;i++){
		    			parent[i]=i;
		    		}
		    	}
		    	
		    	int find(int x){
		    		if(parent[x]!=x){
		    			
		    			parent[x]=find(parent[x]);
		    		}
		    		return parent[x];
		    	}	
		    	
		    	void union(int x,int y){
		    		int xRoot=find(x);
		    		int yRoot=find(y);
		    		
		    		if(xRoot==yRoot)
		    			return;
		    		if(rank[xRoot]<rank[yRoot]){
		    		parent[xRoot]=yRoot;	
		    		}else if(rank[yRoot]<rank[xRoot]){
		    			parent[yRoot]=xRoot;
		    		}else{
		    			parent[yRoot]=xRoot;
		    			rank[xRoot]++;
		    		}
		    		
		    	}
		     
		    }
		    
		 
		    class Heap{
		    	
		    	public static void build_max_heap(long []a,int size){
		    		
		    		for(int i=size/2;i>0;i--){
		    			max_heapify(a, i,size);
		    		}
		    		
		    			}
		    	private static void max_heapify(long[] a,int i,int size){
		    		int left_child=2*i;
		    		int right_child=(2*i+1);
		    		int largest=0;
		    		
		    		if(left_child<size && a[left_child]>a[i]){
		    			largest=left_child;
		    		}else{
		    			largest=i;
		    		}
		    		
		    		if(right_child<size && a[right_child]>a[largest]){
		    			largest=right_child;
		    		}
		    		if(largest!=i){
		    			long temp=a[largest];
		    			a[largest]=a[i];
		    			a[i]=temp;
		    			max_heapify(a, largest,size);
		    		}
		    	}
		    	private static void min_heapify(int[] a,int i){
		    		int left_child=2*i;
		    		int right_child=(2*i+1);
		    		int largest=0;
		    		
		    		if(left_child<a.length && a[left_child]<a[i]){
		    			largest=left_child;
		    		}else{
		    			largest=i;
		    		}
		    		
		    		if(right_child<a.length && a[right_child]<a[largest]){
		    			largest=right_child;
		    		}
		    		if(largest!=i){
		    			int temp=a[largest];
		    			a[largest]=a[i];
		    			a[i]=temp;
		    			min_heapify(a, largest);
		    		}
		    	}
		    	public static void extract_max(int size,long a[]){
		    		if(a.length>1){
		    			long max=a[1];
		    			a[1]=a[a.length-1];
		    			size--;
		    			max_heapify(a, 1,a.length-1);
		    		}
		    	}
		    }
		    class no{
		    	String s;
		    	int i;
		    }
		    class MyComp implements Comparator<node>{
		        
				@Override
				public int compare(node o1, node o2) {
					if(o1.v>o2.v){
						return 1;
					}else if(o1.v<o2.v){
						return -1;
					}
					return 0;
					
				}
		    }
  
