Problem: You are given an array of n elements, you must make it a co-prime array in as few moves as possible.

In each move you can insert any positive integral number you want not greater than 109 in any place in the array.

An array is co-prime if any two adjacent numbers of it are co-prime.

In the number theory, two integers a and b are said to be co-prime if the only positive integer that divides both of them is 1.

Input

The first line contains integer n (1 ≤ n ≤ 1000) — the number of elements in the given array.

The second line contains n integers ai (1 ≤ ai ≤ 109) — the elements of the array a.

Output

Print integer k on the first line — the least number of elements needed to add to the array a to make it co-prime.

The second line should contain n + k integers aj — the elements of the array a after adding k elements to it. Note that the new array should be co-prime, so any two adjacent values should be co-prime. Also the new array should be got from the original array a by adding k elements to it.

If there are multiple answers you can print any one of them.

Example

Input

3
2 7 28


Output

1
2 7 9 28

Solution (in JAVA):

Solution:


/*
		     * 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 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();
					
					int arr[] = new int[n];
					
					for(int i = 0;i<n;i++){
						arr[i] = in.nextInt();
					}
					
					ArrayList<Integer> list = new ArrayList<Integer>();
					
					for(int i = 0;i<n-1;i++){
						list.add(arr[i]);
						if(gcd(arr[i],arr[i+1]) >1){
							list.add(1);
						}
					}
					list.add(arr[n-1]);
					
					pw.println(list.size()-n);
					
					for(int i = 0;i<list.size();i++){
						pw.print(list.get(i) + " ");
					}
					
		    	}//-----------------------------------------The End--------------------------------------------------------------------------//

				
				
				
		    	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 point{
		    	int x;
		    	int y;
		    }
		    
		    
		    class Trie{
		    	
		    	int val;
		    	Trie[] arr = new Trie[2];
		    	
		    	public Trie(){
		    		arr[0] = null;
		    		arr[1] = null;
		    	}
		    	public static void insert(Trie t, int pre){
		    		
		    		Trie temp = t;
		    		
		    		for(int i = Integer.SIZE - 1;i>=0;i--){
		    			int b = pre & (1<<i);
		    			
		    			//System.out.println(t.arr[b]);
		    			if(temp.arr[b] == null){
		    				Trie y = new Trie();
		    				y.val = 0;
		    				y.arr[0] = null;
		    				y.arr[1] = null;
		    				
		    				temp = y;
		    			}
		    			
		    			temp = temp.arr[b];
		    		}
		    		
		    		temp.val = pre;
		    	}
		    	
		    	public static int query(Trie root, int pre){
		    		Trie temp = root;
		    	    for (int i=Integer.SIZE-1; i>=0; i--)
		    	    {
		    	        // Find current bit in given prefix
		    	        int val = pre & (1<<i);
		    	 
		    	        // Traverse Trie, first look for a
		    	        // prefix that has opposite bit
		    	        if (temp.arr[1-val]!=null)
		    	            temp = temp.arr[1-val];
		    	 
		    	        // If there is no prefix with opposite
		    	        // bit, then look for same bit.
		    	        else if (temp.arr[val] != null)
		    	            temp = temp.arr[val];
		    	    }
		    	    return pre^(temp.val);
		    	}
		    	
		    	public static int maxSubarrayXOR(int arr[], int n)
		    	{
		    	    // Create a Trie and insert 0 into it
		    	    Trie root;
		    	    root = new Trie();
    				root.val = 0;
    				
		    	    insert(root, 0);
		    	 
		    	    // Initialize answer and xor of current prefix
		    	    int result = Integer.MIN_VALUE, pre_xor =0;
		    	 
		    	    // Traverse all input array element
		    	    for (int i=0; i<n; i++)
		    	    {
		    	        // update current prefix xor and insert it into Trie
		    	        pre_xor = pre_xor^arr[i];
		    	        insert(root, pre_xor);
		    	 
		    	        // Query for current prefix xor in Trie and update
		    	        // result if required
		    	        result = Math.max(result, query(root, pre_xor));
		    	    }
		    	    return result;
		    	}
		    	
		    }
		    
			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 Node{
		    	int d;
		    	int b;
		    	int i;
		    }
		    class MyComp implements Comparator<Node>{
		        
				@Override
				public int compare(Node o1, Node o2) {
					if(o1.d>o2.d){
						return 1;
					}else if(o1.d<o2.d){
						return -1;
					}else{
						return 0;
						
					}
					
					
				}
		    }
	
		    
		    class MyComp2 implements Comparator<Node>{
		        
				@Override
				public int compare(Node o1, Node o2) {
					if(o1.b>o2.b){
						return 1;
					}else if(o1.b<o2.b){
						return -1;
					}else{
						return 0;
						
						
					}
					
					
				}
		    }